When 2 is better than 3

            When my father developed the first strategies for video poker, a few surprises definitely showed up.  Playing 4-Card Flushes over Low Pairs was not such a surprise, but playing the Low Pair over 4-Card Straights was.   One of the other significant surprises was how to play the numerous hands that contain High Cards.   If you had 3 High Cards of the same suit, it wasn't much of a surprise to hold all three.  Even if one of those 'High' cards was only a 10.  A 3-Card Royal is a pretty strong hand, even if it takes a bit of a long shot to actually hit the Royal.

            Without the mathematical analysis of video poker to guide the Player, most found themselves holding on to all cards Jack or Higher.  This would probably be the right play if you were sitting at a Poker table.  When playing Poker, there is little benefit to drawing a Royal over a Straight or a Flush.  All are very likely to leave you as a winner and the amount you win will not change based on your final hand value.  In the meantime, you'll increase your chance (or will you?) of grabbing a High Pair which will may be enough to win the hand.

            But video poker is not table poker and a Royal has a good deal more value than a Straight or a Flush - 200 to 130+ times as much.  This makes taking the risk of getting the Royal far more worthwhile in video poker than table Poker.  As a result, the decision of what to do when you're dealt a J♥, Q♦, A♥ not as clear as one might think.  Let's take a look at the detailed analysis.

            If the Player holds the 3 High Cards, there are 1081 possible resulting draws.  32.2% of the time the Player will wind up with a High Pair.  If the Player holds only the 2 suited High Cards, he will wind up with a High Pair 30.3% of the time.  So, the probability is a little less, but we're not talking a huge difference.  The Player may only have 2 High Cards instead of 3, but he will draw 3 cards instead of 2 helping to even things out a bit.

            Moving on, with the 3 High Cards, the Player will draw a Two Pair about 2.5% of the time.  With the 2 High Cards he will pull a Two Pair about 4.4% of the time.  The score has been quickly settled with the High Pair frequencies.  For as often as the Player will wind up with fewer Pairs he will wind up with more Two Pairs.  Given Two Pairs pay twice as much, this puts the 2 suited High Cards in the lead.            The pattern continues with Trips, with the Player drawing about twice as many by holding onto only the 2 suited High Cards.  

            Things turn around when we look at Straights.  It should be no surprise that the probability of drawing a Straight goes way up when you hold 3 High Cards as compared to 2 High Cards.   The exact probabilities will be impacted by the specific cards, but in this particular case the probability with 3 High Cards is about 1.5% vs 0.3% for 2 High Cards. 

            For the 3 High Card hands, the hands stop there.  There is ZERO chance of drawing a Flush, Full House, Quads, a Straight Flush or the Royal.  For the 2 High Card hand, we still have a 1% chance of drawing a Flush and slim, yet possible chances to get a Full House, Quads or the elusive Royal.  In this particular case, there is no chance for a Straight Flush, but if I had chosen a suited J-K for my example, this would exist as well.

            If we were to ignore all the hands Flush and above, the two hands would have nearly identical expected values, with the 3 High Card hand slightly higher, However, there is no reason to ignore these hands.  In fact, we specifically play the 2 High Card hand for the specific reason that we have the opportunity to draw all these relatively high paying hands simply by discarding the 1 off-suit card, all while barely impacting the overall expected value of the lower hands. 

            As a result, the decision is not really a hard one to make, even if it was an originally surprising part of the strategy.  Our 2-Card Royal with an Ace has an expected value of about 0.58.  Our 3 High Card expected value is a mere 0.46%. 

            This type of hand is a fairly common one and repeatedly playing it the wrong way will take a bite out of your bankroll.  This is why the 'seat of your pants' approach or using table Poker strategy can be quite ruinous to your results.  Sometimes, 2 can be better than 3.

VP Machines Playing Themselves

            This past week, I received an e-mail from a reader who told me about some video poker machines at the Soboba Indian Casino in Banning, California that sort of played themselves.  After being dealt the initial five cards, the machine would mark the cards that should be held (presumably according to some form of 'perfect' strategy).   If you wanted to hold a different set of cards, you had to 'uncheck' the hold buttons on those cards and hold the ones you wanted.  My reader wanted to know if this is the direction that video poker is heading.

            A little over a year ago, I received an e-mail from a company called Incredible Technologies that asked my opinion on a video poker game that they were offering at Red Rock Station.  It allowed the player to 'earn' strategy tips through winning hands.  This is not quite the same as the first situation as this only provides the Player with tips that he still has to listen to as opposed to going out of his way to ignore the strategy.   Is this the direction that video poker is heading?

            I tend to doubt it, and quite frankly a significant part of me certainly hopes not.   Just to be clear, my reasons for hoping this is not the new wave of video poker machines is NOT any fear of being made less relevant to video poker strategy or fear of losing some revenue.   While most of my columns for Gaming Today deal with video poker, most of my income is derived from table games.  In the 10+ years that I've been analyzing games, I think I've left my mark in that arena and don't have to worry about being the video poker guru that my father was.

            No, my reasons for hoping that this is not a new trend is that I think it is bad for Players.  Well, bad for good Players.  I supposed it might be good for bad Players.  The problem with this is that it tends to move video poker machines a few steps closer to slot machines.  There will still be significant differences.  The biggest being that we will still be able to know the payback of a video poker machine by looking at the paytable.  However, if all Players begin to play very close to the theoretical payback because the casinos hand the Player the strategy, then there will be NO way that they will be able to continue to offer 99%+ paybacks.  Casinos can offer games with high paybacks because they know that such a small number of Players utilize these strategies.  They can rely on human error to drive profits while still (truthfully) claiming paybacks near 100%.  It is the best of both worlds for them. 

            That brings me to the reasons why I doubt this is going to be a new hot trend that will overwhelm the video poker market.  Why would the casinos want to mess with what already is such a great situation.  They get to advertise machines with paybacks at near or over 100%.  Yet, they know that the games are almost never played anywhere near this amount.  Just like blackjack with a 99.5% payback but holds 9-15%, video poker machines do about the same.   Given the speed that video poker can be played, the profits that can be gotten from even quarter machines can easily outpace blackjack. 

            Most casinos are well aware that people such as me exist.  We write articles trying to get people to play the proper strategy.  We sell books and software to make Players, well, better Players.  At the same time, casinos know that despite this wealth of knowledge that is out there, most Players either don't bother with it at all or make some half-hearted attempt to use it or use it and then abandon it when they don't break the bank.  I've often surmised that I could hand out free copies of Expert Strategy for Three Card Poker at the entrance of a casino and STILL 75% of the Players who would sit down at a Three Card Poker table would not bother to follow the strategy in the least.   So, on the whole, casinos are not very afraid of Players bearing strategy because they are such a minority.

            However, handing the Player the strategy and then daring them to pick a different one may be far more than casinos are willing to do where strategy is concerned.  It is one thing to question when a Player wants to stand on a soft 16 in blackjack.  It is something all together different when a big flashing light comes on to say STICK when a Player has a 16 vs. a Dealer 2, and then only way the Dealer can hit is if he is willing to turn off the stick sign and go out of his way to hit.  In the case of video poker, if a Player really wants to not use the house strategy, then he is likely to find a different machine altogether.  After all, who wants to have to turn off the machine's decisions before entering his own on every hand?  So, there is a good chance that the actual payback of the video poker machine is going to quickly approach whatever the theoretical payback is.  Since the casinos will never allow games to be offered at 99% in this case, there only choice would be to greatly reduce the payback of video poker, which in turn will scare off all the good Players while at the same time, probably increasing the payback of many of the bad Players, as their errors will no longer be a factor.

            So, the only way I can see casinos adopting this concept is if they have some crazy reason to scare off some of their most loyal Players and want to reduce profits.  Nope, I don't see this as a big trend.  At best, perhaps some casinos will use them as a great marketing ploy, but that is it.

            

Beware the Ides of March

            I have to be honest, I had to look up the historical significance and meaning of the "Ides of March."  I knew it occurred on March 15th, but I had no idea what it meant.  It turns out that Julius Caesar was assassinated on March 15th, more than 2000 years ago.  Not a good day for Rome.  2000 years later, it would be not a good day for Frome either.  It was 15 years ago, on March 15, 1998 that my father, Lenny Frome, passed away.  I say this somewhat tongue in cheek, but it is poosible that Las Vegas has changed more since my parents moved here in 1985 than Rome changed since Julius Caesar began his rule.

            In 1985, there was no Bellagio, no Treasure Island, no Excalibur, no New York New York, no Luxor, no Stratosphere and no Venetian.  The hotels that still stand looked quite different than they do today.  Today they reach right out to the Strip. Then, many were set back hundreds of feet.  I believe Caesars was the first to attempt to build a 'people mover' (a moving walkway) to bring people from the street 'all the way' to their front door.  It didn't take long to realize that the walkway only worked in one direction.  There was no assistance in leaving the building.  The overhead walkways that now exist at Flamingo and Tropicana didn't exist either.  Of course, those streets weren't quite as wide as they are now.  If I recall correctly, there were about 500,000 people living in Las Vegas back then as compared to over 2 MILLION today.

            When I tell my friends who live in Vegas that my parents lived on the East side, they want to know why not the 'newer' West side.  Well, the west side was mostly desert when they moved to Las Vegas.  Where I now live was only built in the early 1990's, several years after they moved here.  Some things have stayed the same.  There's still Harrie's Bagelmania (albeit without Harrie, who passed away a few years ago).  Ethel M is still here, although, I think their building got a bit larger in all these years.  The chocolate is still just as good!  Of course, the Hoover Dam is still here, but now it has an incredible concrete suspension bridge which overshadows it a bit.

            Truth be told, my father had little to do with these changes.  But that doesn't mean he didn't leave an incredible impact on Las Vegas.  What he changed was the INSIDE of the casino.  In 1985, if you walked through a Strip casino, you'd hear the clinking of coins from slot machines.  As you meandered through, you'd see almost exclusively Craps, Blackjack and Roulette tables, with an occasional Big Wheel or maybe Pai Gow Tiles game.  Somedays I wonder how the casinos thrived on such meager offerings. 

            Today, you don't hear the clink of any coins because the slots take in cash and give back paper tickets.  If you pay attention, you'll note that many of those 'slots' aren't even slots, they are video poker machines.  Slots got an upgrade and the Player got a fighting chance.  Instead of 92-93% slot machines that require no thinking or skill, a significant amount of the casino floor has become video poker machines, where strategy rules and paybacks can go up over 100%.  Nothing is hidden from the Player and Player's can make informed choices.

            On the table game side of things, the casinos went from effectively 3 choices to literally dozens.  It is a potpourri of games - Three Card Poker, Four Card Poker, Spanish 21, Blackjack Switch, Caribbean Stud Poker, Let It Ride, Crazy 4 Poker, Ultimate Texas Hold'em, Mississippi Stud Poker, etc....  If you are reading Gaming Today right now while still in a casino, please go down to the casino floor and take not of how many of the table games are NOT blackjack, roulette and craps.  Then think about how much more fun the casino is with all of these new games.   Back in the 90's, my father helped to develop Three Card Poker, Let It Ride, Caribbean Stud and Spanish 21.  These games opened the floodgates for all those that followed.

            His impact to the casino was absolutely immeasurable.  About 15 months ago, I nominated my father to the American Gaming Association's Hall of Fame.  Much to my disappointment, they did not pick him.  Two years ago, they elected Blue Man Group to the Hall of Fame.   I recently saw their show at the Monte Carlo.  It was quite entertaining.  But, has Blue Man Group really changed the make up of Las Vegas or casinos in general the way Lenny Frome has?  If not for my father, it is highly likely that Video Poker would never have become nearly as popular as it is today.  Games like Three Card Poker and Let It Ride might not have succeeded, and all the games that followed may never have been given an opportunity to succeed if not for the impact one 'retired' electrical engineer had on the industry.

            Many of you have written to me over the past decade telling me how much you enjoyed reading my father's column in Gaming Today way back when.  If you're one of those people who recognize the impact Lenny Frome had on the casino, then I'm asking you to send an e-mail to Brian Lehman at the American Gaming Association (blehman@americangaming.org) and let him know that you think it's time to induct my father into the Gaming Hall of Fame!

It's YOUR Money

            Over the years, I have frequently written about the value of comps.  Comps generally come in two different versions.  One is cash back.  The casino returns a percent of the total amount wagered in the form of additional play.  They do this because the odds are that any Player who plays that much is likely to play the additional money more than a minimal amount and will in the long run lose that money back to the casino, along with more of his own money.

            A second type of comp is that the Player can earn free items, meals or entertainment.  Sometimes, these may be earned on top of cash back and sometimes they are instead of cash back, meaning that a Player can essentially use his cash back to 'buy' something else. 

            Since both of the aforementioned comps are based on the amount a Player plays, you can really look at this as a form of rebate and that in many ways the Player has actually paid for these items.  There is another form of 'comp' which is an entirely different category.  This would be 'free play' that the casinos send out.  While there may be some correlation between how much they give each Player and his actual play, this is not a direct mathematical computation.  Casinos may throw a Player $5 or $10 or $20 just to entice you to come into the casino. 

            The question now is what you choose to do with these 'free plays'.  Unlike 'match plays', they do not require that you put up ANY of you own money.  A 'match play' coupon will pay you an extra $5 when you wager at least $5 on an even money wager (i.e. a hand of blackjack).  This still requires you to wager your own $5.  It is a great play if you are a good (or at least decent) Blackjack Player.  You'll win $10 if you win and lose $5 if you lose.  Again, the hope is that the Player will play the match play coupon and then stay and play for a while.  If you're planning on playing anyhow, that is fine.  If, however, you are not a knowledgeable Player and wind up sitting for an hour at a game that you don't know, the casino will more than get its $5 back.  Also, a match play coupon is generally only worth about half of its face value.  The coupon is surrendered whether the Player wins or loses.  Since most even money wagers are approximately a 50-50 shot, the Player will win about half of the time and lose half the time.  So, a $5 coupon will only be paid out half the time, making its value $2.50.

            That brings us back to the free play coupons.  While the mechanics of a free play coupon work differently in different casinos, the basics are the same.  You get a certain amount of money to play on a slot machine or video poker machine.  This money must be played at least once through the machine.  So, if given $5, the casino doesn't care if you play $1, quarters or nickels.   You can Play 100 nickels or 20 quarters.  You can play one at a time or max-coin.  Now, if you choose to play one round of video poker at max-coin $1, you'll play one hand.  For most games of video poker, the Player will 'win' about 45% of the time.  This means that 55% of the time, your $5 will result in absolutely nothing.   Another significant portion of the time, you'll wind up with a High Pair and you'll get to keep exactly $5.  The remaining times you'll win anywhere from 2 to 800 per unit and have a rather nice win.  If you had an unlimited number of these free plays, it wouldn't matter much how you choose to play.  But since you get only one of these every so often, it is my opinion that your goal should be to turn the free play into cash which then puts all the choices in your hand.   Unlike the match play, proper use of free play can result in the return of 95-100%+ of the face value most of the time.  Assuming identical paytables, I try to play the lowest denomination available, which allows for the most hands.  The more hands, the more likely you will approach the theoretical payback.  Thus, playing $10 on a 98.6% machine will on average result in a return of $9.86.

            If you are disciplined, at no time are you putting your own money at risk.  Thus, even if you are a bad video poker Player and play the same game at 94%, you should still expect to come out with $9.40 of the $10.00.  Not a bad deal.  I know some of you won't believe to hear me say this, but you'd be better of playing the money through Slots than not using it at all - again, assuming you are disciplined and don't keep playing the money until you lose it and then put more of your own money in.

            A friend of mine recently told me that every time he goes to Reno on a business trip, he stays in a casino that gives him some amount of money in 'free play'.  It doesn't expire for a year and in the past 12 months, he has amassed $400-$500 in 'free play'.  I asked him how come he doesn't play and his response was that he doesn't know how to play video poker and he knows that Slots are not a good play.  I did give him a copy of both "Winning Strategies for Video Poker" and "Video Poker: America's National Game of Chance" to help him along.  But, I also told him that it didn't matter how bad he played.  Even a basic understanding of Poker could probably earn him a 90-95% payback on a jacks or better video poker machine which means he should win back at least a few hundred dollars.  Better in his pocket than the casinos!

It is not about the Medium

            I don't think there is a game in the casino more misunderstood than video poker.  Even in the days when slots were mechanical, most people considered video poker to just be another slot machine, but one with a computer screen.  I think many people just think that it was too hard to create a mechanical machine using cards, so they digitized it all, but it still plays like a slot machine - all because the hardware looks roughly the same.  It is NOT the hardware that makes the game.

            This past week, I met a gentleman who told me he likes to play keno slots.  I have to be honest and say I had no idea what he was talking about.  He explained that he picks a certain amount of numbers from 1 to 80 and then the machine picks 20 numbers and he gets paid if the 20 picked includes at least some amount of the ones he picked.  I politely looked at him and said there is nothing 'slots' about what he just described.  He simply was playing keno in video version (hence it is called 'video keno').  He was playing the EXACT same game as if he was playing in a keno parlor marking the little pieces of paper and handing them to the scantily clad woman.  Ironically, the video version of keno tends to pay higher than the old fashioned version because the Player can play far more hands per hour.  I explained to this man that the machine pulls 20 completely random numbers and throws them onto the board.  It does NOT decide ahead of time that you will hit 3 of the 8 you marked and then decide which numbers to pull to make that happen.

            This is in essence the very difference between a slot machine and a video keno machine or a video poker machine or a video blackjack machine.  In the latter three games, the machine uses a random number generator to decide which card to deal or which ball to draw.  You win or lose based on the specific cards/balls it randomly draws.  In a slot machine, the machine first determines whether your will win or lose.  If you are to win, it will decide how much you will win and set the symbols in the appropriate fashion.  If you are to lose, it will decide exactly which symbols to show you - always a losing combination - but potentially set up to make you feel like you almost won. 

            Over the years, when I've been asked what I do for a living and explain that I analyze casino games, a frequent follow up question is if I do it for live games or electronic games.  Since the majority of my work is in table games my response is usually just that, but I tell them it really doesn't matter what medium the game is in.  As long as the game is using essentially a random deck of cards (or ping pong balls) where each card has an equal chance of appearing, it does not matter if you are playing a game with a real life dealer, at a casino on an electronic multi-player table, on a stand-alone machine in the casino or playing at home on some software.

            Video blackjack has existed for years in the casino.  They were not always easy to find, but many Players relished the idea of playing for only $1 per hand and having the same experience (well, mathematically) as playing at a live table.  I would certainly understand those that feel that playing on your own machine is not as sociable as playing at a table, but that's not a mathematical difference. 

            In the past few years, many casinos have added multi-player electronic versions of popular table games (i.e. Shuffle Master's TableMaster games).  These games play identically to the live games.  There are times when for one reason or another the casino chooses to employ different paytables, but the probabilities of winning a hand or losing a hand or being dealt a particular hand remains the same.  Any changes to the payback as a result of paytable changes cannot be sneaked past the Player.  These payouts must all be visible on the machine.   Because the digital cards are as random as real cards, we can always calculate the exact payback of any of these games based on the paytable. 

            While the name "Slot machines" presumably comes from the different slots the wheels are in (well, were in when they were mechanical), and there is a little bit of similarity in the notion that video poker cards are in 'slots' in the machine as well, this is where the similarity ends.  The critical difference between games like video poker and slots is that in video poker your cards are determined randomly and you win or lose based on the pattern of these cards.  With slots, whether your win or lose is determined by the machine and then you are presented with symbols to match the pre-determined outcome.   Slots could never be replicated on a live table, but games like video poker, video keno and video blackjack are (or could be).

Strategy is Underrated

          I can't stress enough the importance of using the right strategy when playing in the casino.  Over the years, I've heard all sorts of excuses for why people abandon strategy, ranging from it doesn't matter in the short run to some anecdotal story about how someone they know threw strategy to the wind and it paid off massively.  Yeah, that's nice.  If you're a sports fan, you know the importance of having a good coach or manager.  There are reasons why Pat Riley, Joe Torre and Bill Parcells are in such high demand.  Yes, it is because they win.  And they win because the utilize the right strategies for their respective sports.  This doesn't mean that once in a while their strategies won't fall apart.  Nor does it mean that there won't be times that they'll execute their strategy perfectly, yet still the other team will win due to a bad bounce.  I doubt any of these coaches would abandon their strategy over a bad bounce or a single loss.

            The same is true when you walk into the casino.  The coach/manager of your 'team' is you.  You decide which game to play.  This is the first key step in your strategy.  In fact, this leaves you with more power than any of the aforementioned coaches.  I'm sure many of them wish that they could pick their opponent on any given day, but they don't get to.  You on the other hand can decided whether to play slots, video poker or a table game.  If you decide on video poker (always a good choice), you decide which variation and to some degree, which paytable.  You can choose the short-pay paytable or make sure you find the full-pay paytable for the game of your choice.   Joe Torre isn't going to hit the field with only 8 fielders, why should you play jacks or better video poker that pays only 8 for a Full House instead of the full 9?

            Once you decide on your game and paytable, the real nitty gritty part of the strategy begins.  There are 52-cards in the deck.  There are 2,598,960 ways you can be dealt 5 cards from a 52-card deck.  There are 32 ways to play each of these deals, ranging from discarding none of the cards to discarding them all.  You have to make a decision on each of these hands which ones you will keep and which ones you will discard.  Fortunately, in about 75% of the cases, it is fairly obvious which ones you want to keep.  The other 25% is the challenge.  Back to our baseball analogy.  Most of the time, there isn't a lot for the manager to do.  He doesn't really have to tell his leadoff batter to 'get on base' every time he comes up.  I think it is fairly obvious that's what he will be trying to do.

            Unlike the baseball manager who has to outguess the opposing manager and players, the video poker Player doesn't need to outguess anyone or anything.  Video Poker is a game of pure math.  For each of those 32 possible ways to discard, there is a finite number of ways the hand can be completed.  Using computers, we can determine the final hand rank of every one of those hands and determine, on average, how many units the Player can expect to have return to him.  It is true that we don't know exactly which cards will come up this time, but we do know that over time, the actual results will approximate our expected results.  Based on this, we learn that the best play for the Player is to play the hand whichever way results in the highest expected return of units.  We call this 'expected value' or EV for short.

            This concept is used for EVERY single decision made in the casino in every game with any strategy.  The decision to hit or stick in blackjack is decided by which of these two decisions results in the higher expected value.  We Fold on Q-6-3 in Three Card Poker and Play on Q-6-4 because in the case of the Q-6-4, Playing has a higher Expected Value than Folding.  The opposite is true for Q-6-3.

            You are in complete control of how to play these hands.  In the case of video poker, the decisions you make are ones that can result in the machine you are playing having a 100.5% payback or a 96% payback.  One payback means you will win in the long run and the other means you will lose (and lose a lot more) in the long run.

            Does playing the right strategy mean you will win every session?  Absolutely not.  It just means your chances of winning increases greatly.   In today's world, the manager that utilizes matchup charts that show how hitters have done against certain pitchers is likely to be far more successful than one who just feels that now is the right time for a certain pinch hitter - he's due to get a hit.    Utilizing the right strategy is important in a variety of situations.  I can't stress enough that the casino is most definitely one of these situations.

Quads are the Key

For those of you who read my column regularly, you are probably now well aware that a full-pay jacks or better video poker machine pays 99.5%.  Many people are still confused, however as to what this means.  It does NOT mean that if I start with $100 I will walk away with 99.5% or $99.50.  It means that in the long run, you could take the total amount you wager (NOT your bankroll) and multiply it by 0.5% (the 'loss' rate or 100% minus the payback) and this should be the amount you have lost over time.  So, if you play 10,000 hands over the course of a year (or a month or a decade) and you play max-coin $1 machines, you would have wagered $50,000 and can expect to lose about $250. 

            In video poker, however, 10,000 hands isn't really the long run.  Don't get me wrong, it is certainly approaching the long run.  But, given that a Royal Flush should occur about every 40,000+ hands, it would be hard to declare 10,000 hands to be the long run.  If you've hit at least one Royal, you would be ahead of the game.  If you haven't, it would be totally fair to say you are behind because you still have 30,000+ hands to go.  Royal Flushes account for about 2% of our payback.  So, if you were to NEVER hit one, you'd theoretically be playing only a 97.5% game.

            With a hand frequency of 1 in 40,000+, Royals sort of march to their own drummer.  You might hit 2 or 3 in 40,000 hands or you might go 100,000 hands without hitting one.  When you hit one, you're going to have a very good month and when you don't, well, it will be harder to even break even.

            Four of a Kinds, on the other hand, should occur about 1 in about 420 hands.  With the average Player playing hundreds of hands per hour and perhaps thousands in a session, this hand becomes critical to our chances of success over a session or two.  It accounts for 6% of our overall payback.  Relative to the other hands, this is not necessarily large, but it is a hand that is frequent enough that you expect to hit it over a session, but not frequent enough to be sure you'll hit your fair share over a few nights.   If you were to play 10,000 hands, you'd probably find that the frequency of High Pairs and Trips and Straights are very close to what they should be.  Royals will by very definition have to be either more frequent or less frequent than expected, but Quads can be just about anywhere over that period of time. 

            In theory, you should hit about 24 of them over that time.  The math says you very likely could hit only 12 or as many as 36.  If you hit 12, you're about 3% short in payback.  Assuming you haven't hit a Royal and you're now 5% short.  The odds of coming up a winner over that span is very unlikely as you'll be playing at 94.5% and hoping the other hands come up big - which simply isn't very likely.

            Conversely, if you've hit36 of them, you'll be at 100.5% EVEN if you haven't hit a Royal.  A winning session is not guaranteed but certainly more likely.  Over time, the frequency of the Quads will slowly head towards that 24 per 10,000 hands, but your results in the short or medium run is heavily dependent on hitting your four of a kinds.

            As with anything video poker, the number of Four of a Kinds you get is at least partially attributed to luck.  We've all played for hours and been dealt dozens of Three of a Kinds to watch NONE of them turn into Quads.  We've also all sat there and drawn 3 Kings to a single King.  Nothing that happens is truly out of the ordinary.  However, you can increase your chances by playing the right strategy.  If you hold a 4-Card Straight OVER a Low Pair, you are going to greatly reduce your chances of Quads.  If you hold 3 High Cards instead of just the 2 that are suited, you will lower your chances for getting Quads.  The reason why we hold only the 2 suited cards is both to give us a chance to hit the Royal AND to increase the chances of Quads.  Both of these hands are reduced to ZERO CHANCE if you hold 3 off-suit High Cards!

            Of course, if you choose to hold a Low Pair OVER a 4-Card Flush you may increase the frequencies of Four of a Kinds, but you'll do so at your own peril.  Quads are important, but not so important that you should be throwing the proper strategy out the window.

Eyes Wide Open

            I finally discovered something that has a lower payback than slot machines – New Jersey Turnpike tolls!  As I write this, we’re back on the East Coast for personal business.  After landing at Newark, we had to drive up to the Boston area.  I couldn’t believe the toll from Newark airport to northern end of the Turnpike.  It was $3.60 to go about 20 miles.  Throw in the $12 toll to cross the George Washington Bridge to cross into New York and I was out more than $15 after only being on the road for 25 minutes!  It takes quite a bankroll to drive on these roads, and with NO chance of winning.  We had only left NJ less than a year ago and all these tolls had gone up considerably since we left!

            On a more serious note regarding slots, I received a very good question from a reader this past week.  He acknowledged what I had written several weeks ago that the average slot machines paid only 92-93% and that video poker generally paid 97-100+%.  He asked that given that casino gambling is just a form of entertainment, what is so bad about the idea of taking $100 of your bankroll to go for a huge jackpot on a slot machine, especially given that winning a similar amount at video poker would take a long time with smaller wins along the way.  I have to admit, that it took me a little while for me to come up with a response.

            I think the best I can come up with is that if you go in with your eyes open as to what you are doing then I can’t really say there is anything wrong with it.  Gambling is entertainment and if it brings you enjoyment to take part of your bankroll and put it into a low payback slot machine with a jumbo-sized jackpot, that is your choice.  If I have any issue with the concept it is that it is very hard, if not impossible to go into this with your eyes truly open.  Yes, you can know the size of the jackpot, but you don’t know the probability of actually hitting it. 

            The other issue is that it is standard practice in casino gaming that if the game has a huge jackpot (usually Progressive) then the payback of the game tends to be even lower.  This is true for both slot machines and even table game sidebets.  Outside the casino, this is even truer for things like Lotto.  Most state lotteries have paybacks in the 50-60% range.  Players are willing to play games with very low paybacks in hope of winning that life altering prize.   Again, however, in the case of Lotto, we are able to compute the probability of winning the top prize.  This is not the case for slots.

            While the low payback of regular slots is concerning, and the presumed even lower payback of a Progressive slot is even more concerning, the biggest concern still belongs to the notion that there is no way to know anything about a slot machine.  We don’t know the probability of the jackpot spin or any other result.  We have no way of knowing the overall payback of the machine by a simple glance at the glass.  In a place like Nevada, the payback can be no less than 75% so that is about all we really know.

            So, that all said, if you feel that you want to play a game that has a life-changing jackpot with a portion of your bankroll, I can understand the desire to try your hand at a slot machine.   It is probably the only chance you have for a multi-million dollar prize.  If you are looking for a gigantic jackpot, I would personally recommend a Pai Gow Poker sidebet or the Six-Card sidebet for Three Card Poker.  The prizes will only be in the few hundred thousand to $1 million, but you’ll still be playing games with higher paybacks.

            In the end, it is your money and you have to decide how you want to spend it and what provides you the most enjoyment.  If chasing a mega jackpot on a low paying machines with a portion of your bankroll is what brings you joy, I won’t stop you.

            

Player Friendly

            This past week, I met someone who was visiting Las Vegas from California.  I told him about my work with video poker and he asked me what is the best game to play.  My natural reaction to that is to just laugh.  How am I supposed to answer that?  Besides the fact that 'best' is a very subjective term.  Admittedly most people want me to answer which games are the best mathematically.  But, as this guy was stating on the strip, the odds (pardon the pun) that the best game is anywhere near is rather slim.  In fact, I'm a bit scared to tell him to play a particular type of machine in fear that he'll find it, but not at anything near full-pay.

            As the conversation continued, he told me that he likes to play Double Double Bonus Poker.  I was certainly not surprised to hear this.  It is a very popular game and he cited the biggest reason that it is - the extra chance to get a huge jackpot with the Four Aces and a kicker.  He also told me about the time that he was playing a ten-play Double Double Bonus machine and was dealt Four Aces plus the kicker on the initial deal.  Multiply that by 10 and it is a NICE payday even if you are playing a relatively small denomination or not max-coin.

            When you get dealt a hand like that, you might just be hooked for life.  It reminds me of the day I was playing golf with a friend.  Neither of us are all that good.  I still had a great time, but he wasn't happy with how poorly he played.  Well, until we got to about the 17th green and he rolled in about 30 foot putt.  Then he wanted to know when we could play next. 

            I suggested to the man that he try to find some Double Bonus machines, which at full-pay have a 100.1% payback.  Double Double Bonus has a payback of only 98.8%, also at full-pay.  I then told him that the best paying machines were variants of Deuces Wild, but only if he played proper strategy.  I really didn't know if he had a clue as to proper strategy for even Bonus games, yet alone Deuces Wild.  I figured that he would still be better off sticking to what he was familiar with than trying to play a game like Deuces without the benefit having attempted to learn the strategy.  While there are differences between Double and Double Double, at least he is still in the same general universe with those two.

            Of course, the real problem with answering his question is that he was going to be playing on the strip, which isn't exactly know nowadays for having too many full-pay machines.   Much to my surprise, I checked my source for video poker inventory - www.vpfree2.com - and found that the casino he was staying in (I won't name it), DOES have a some full-pay machines, but all at denomination of $1 or more.  It took me a second to fully comprehend this.  Usually casinos only put out full-pay machines for low denominations.  If you want to play at nickels they'll allow some winners.  Then it hit me,  NONE of their full-pay machines were over 100%.  If you want to play Double Double at full-pay, they'll be happy to let you at $5 per hand ($1 max-coin).  With a payback of 98.9%, the casino can expect to clear more than $30 an hour!  Of course, they may have some quarter machines to play, but those will be short-pay and you may find the same loss rate as a result. 

            I'm not naive.  I fully realize that most video poker machines have paybacks below 100% and that means that you will lose over the long run.  I have stated many times that gambling is just a form of entertainment for almost everyone.   But given the nature of gambling is that the cost is variable and that sometimes you can win money, your goal should be to minimize the losses and give yourself the best chance to win.

            To do this, you need to find games that have paybacks as close to 100% (or over) being played at a denomination that you feel comfortable with.  If you are okay with playing a $1 machine, that's great, but make sure you have enough bankroll for it.  Don't expect to walk over with $100 and play all night.   If you start with $100 don't be surprised if it is gone in a hurry and once your bankroll is gone, there is no coming back from it. 

            If you don't feel comfortable playing $1 machines or you don't have enough bankroll to do it, make sure that when you step down in denomination that the paytable doesn't take a big step down too.  Or, as I told this gentleman, if he really wants to find good video poker options, he might have to venture to one of the 'locals' casinos where the paytables are known to be a bit more Player friendly.

The Penalty Box

            In last week's column, I analyzed a particular hand that could be played multiple ways.  The hand was as follows:

J♠        8♦        Q♦       3♥        9♦

            From a quick glance, one might think to play the hand as a 4-Card Inside Straight with 2 High Cards, a 3-Card Double Inside Straight Flush with 1 High Card or simply as Two High Cards.  As always, the decision comes down to which of the hands has the highest Expected Value (EV).   In last week's column, instead of simply relying on the EV in a strategy table, I used a program that I created that allows me to put in the EXACT 5 cards and tell it which ones I'm holding and which ones I'm discarding.  It then gives me the exact EV of the hand in question.  Why do I do this instead of just using the value in the strategy table?

            The values in the strategy tables are averages of all hands of that particular type.  The accuracy is thus dependent on a few factors, ranging to the nature of the specific hand to the specificity of that hand.  For example, we list the Expected Value of a 4-Card Flush as 1.22.  In reality, there is not a single 4-Card Flush that has that EV.  While there is always the same number of possible ways to draw the Flush (9), the number of High Cards in the hand will impact the exact expected value because it changes the number of ways we can pick up a High Pair.  If we have 0 High Cards, the EV is 1.15.  With 1 High Card it is 1.21 and with 2 High Cards it is 1.28.   We could just as easily list these three hand separately on the strategy table, but it wouldn't change the strategy we would employ at all.  There are no other hands that have an EV between 1.15 and 1.28.  So, in this case we lump all the 4-Card Flushes together and show the average EV for all 85,512 possible 4-Card Flushes.

            In a similar fashion, we have a single entry on our Strategy table called the 4-Card Royal which has an expected value of 18.66.  but not all 4-Card Royals are created equal.  We might have 10-J-Q-K which allows for pulling the suited 9 and picking up a Straight Flush.  Or we can pick up an unsuited 9 for a Straight.  However, we also only have 9 ways to pick up a High Pair.  Thus the EV of this hand is rather different from that of J-Q-K-A which has no way to pick up a Straight Flush and also has only one way to pick up a Straight (both ends are NOT open).  But, we get 3 additional cards that will give us the High Pair.  

            But, there is another item that can affect the specific Expected Value.  What happens if we are dealt a Flush 3-J-Q-K-A.  The Flush has an EV of 6.00 while the 4-Card Royal has an EV of 18.66.  But, when we discard the 3, we lose one opportunity to draw the Flush.  This will certainly NOT drop the EV of the 4-Card Royal to below that of a Flush, but we should recognize the impact of the specific card we discard.  When we discard a card that could help improve the final hand, it is called a 'penalty card'.  In this particular case, there is no impact to our strategy as a result of discarding the 3, so we are safe to lump all 4-Card Royals together.

            However, as we go down further on our strategy table, we begin to break apart the hands into smaller groupings.  We don't have all the 4-Card Straights listed together the way we do the 4-Card Flushes.  Because a Straight only pays 4 and there are only 8 ways to complete them, the EV of Straights drops to the point where it is very close to many 3-Card Straight Flushes, 2-Card Royals and even High Card hands.  Many of these hands also tend to overlap a lot, as in the example at the beginning of this article.  The hand is 2 High Cards, a 3-Card Straight Flush and a 4-Card Inside Straight all at the same time.  Slight changes in the hand make up could make it other hands all at the same time.

            When a hand overlaps as this one does, there is usually at least some penalty card situations.  In this case, if we choose to play the hand as 2 High Cards, discarding the 8 and 9 create the penalty card situation.  We wouldn't want to draw an 8, 9 and 3, but we wouldn't mind drawing an 8, 9 and 10.  While this may not be the most common outcome, it is one that would complete the Straight and give us one of the highest possible payouts for the 2 High Cards.  So, discarding them may reduce the ACTUAL Expected Value slightly from the one we may find under 2 High Cards in the strategy table.

            Likewise, when we hold the 8, 9 and Q, we are discarding the Jack which is a penalty card.  It can be used to complete a Straight or we might pick up another Jack to make a High Pair.  So, I calculate the exact Expected Value in last week's column to make sure the result was 100% accurate.

            As I've said many times in my column, you don't need to memorize the Expected Value of any hand because the value itself is meaningless.  What matters is the relative value.  You need to know which hand has the higher EV.   Once in a while, a penalty card situation will cause a hand as it is shown on the strategy table to have an ACTUAL Expected Value that actually drops it to below that of another playable hand from that same 5-card draw.  This in essence creates an exception condition to how the hand should be played when using a strategy table.  The hand should STILL be played according to which has the higher Expected Value, but because we are using the 'average' shown on a strategy table, we don't actually do this.

            When my father, Lenny Frome, developed Expert Strategy, he was well aware of this situation.  He felt that the impact on the payback of these exceptions was too small to be concerned with relative to the idea of listing out what could be several to dozens more lines on the strategy table.  Learning Expert Strategy can be enough of a challenge.  He didn't want to complicate it further by trying to list out hands that might look something like this:

·         4-Card Straight with 2 High Cards, EXCEPT if there is a 3-Card Straight Flush, but ONLY if the 2 High Cards are part of the 3-Card Straight Flush

            I tend to agree with my father and learning these extra rules are only for diehards and even then, the risk of error might be more than the extra 0.001% it might yield in payback.

Rare Gems - Straight Flushes

            One of the ironies about video poker paytables is that they don't always reward hands more for being more rare.  If I were to ask you which occurs more often in video poker - a Flush, a Straight or a Full House, I'm guessing most of you would say a Straight, followed by a Flush and lastly a Full House.  It is really a trick question.  Without knowing what the paytable is, there is no way to answer the question accurately.  The only thing we know is that, in general, a Full House outranks a Flush, which outranks a Straight. 

            On a full-pay video poker machine, assuming you use Expert Strategy, you will actually hit more Full Houses than either of the other two.  A Straight will occur just slightly more often than a Flush.  Upon close inspection, we realize that this is by far a product of the payouts for each hand than it is a product of the hands themselves.   If we take a look at the game of All American Video Poker - which would appear to now be obsolete - we will see a very different pattern develop.  In All American, a Straight, Flush and Full House all pay 8.  With no reason to go for one or the others, the pure probabilities of hitting each hand begin to show up.  As a result, the frequency of Straights and Flushes increase dramatically, to the point where they occur nearly twice as often as a Full House.

            A similar phenomenon occurs with a Straight Flush.  Generally speaking, it occurs just about 4 times as frequently as a Royal Flush, while paying only 1/16th of the amount.  Or we can look at it the other way and say that it is more than 20 times as rare as a Four of a Kind while only paying twice as much.  When we throw in the Bonus Video Pokers, it only looks worse.  This far more rare hand might actually pay LESS than many of the Quads we can hit, which are far more common.

            Of course, I'm wondering how many of you have hit nearly as many Royal Flushes as you've hit Straight Flushes.  I doubt you remember your Straight Flushes as vividly.  Winning $62.50 on a max-coin quarter machine isn't quite as memorable as a cool $1000, but that isn't my point.  If you use Expert Strategy on a jacks or better machine, you should hit a Royal every 40,400 hands or so and a Straight Flush every 9200 hands.  The key phrase is "if you use Expert Strategy."  Since most Players, at best, use pieces of strategy, I'm guessing that the Straight Flush shows up far less often because the partial Straight Flush is frequently overlooked when the Play.

            If dealt the following, what's the right play?

J♠        8♦        Q♦       3♥        9♦

            Do you play the 4-Card Inside Straight with 2 High Cards, the 3-Card Double Inside Straight with 1 High Card or the 2 High Cards?  As always, there is just one way to determine the right play.  We go to the Expected Values of each.

            Calculating the Expected Value for the 4-Card Inside Straight is fairly easy.  We can draw the Straight with 4 cards and we can draw a High Pair with 6 more.  This will return 22 units to us.  Divide by 47 and we get a result of just below 0.47.  For the other two, I ran them through a program I have that calculates the exact Expected Value given the specific discards.   The Two High Cards have an Expected Value of just below 0.50 and the 3-Card Double Inside Straight Flush has an Expected Value of just below 0.53.  This is the proper play. 

            While the odds of hitting the Straight Flush are 1 in 1081, this is still far greater than hitting it with either of the other two hands (it is zero in these cases).  Ironically, it is not the tremendous payout of the Straight Flush that causes us to play the hand this way.  By holding a 3-Card Straight Flush, we give ourselves numerous chances to hit just Straights and Flushes - a combined 1 in 20 (roughly).  Throw in opportunities for Three of a Kind and Two Pairs and this hand simply beats the others.

            Now, no one expects you to calculate the Expected Value of even the 4-Card Inside Straight on the fly or to carry a small computer to run my program that calculates the exact Expected Value for each hand.  It is much easier to simply use a strategy table that lists out each playable hand.   If we look up the three hands in a strategy table, we find a 3-Card Double Inside Straight Flush has an Expected Value of 0.54, the Two High Cards have an Expected Value of 0.49 and the 4-Card Inside Straight with 2 High Cards doesn't even make it onto our strategy table because the Two High Cards always outranks it.  These values are the average of all hands of that type so they don't always equal the exact Expected Value taken into account the exact discards.

            In the end, the frequency of a hand occurring is a product of the paytable and following the right strategy.  If you want to get your share of Straight Flushes, you can't do a lot about the former, but the latter is fully in your control.

What to Play

            Last week, I wrote about Four Card Poker and mentioned how I would cover it's 'crazy' cousin - Crazy 4 Poker in an upcoming column.  I started to work on this column this past week when I got to the point of discussing why a Player would choose to play one of the games over the other.  The overall paybacks are fairly similar.  The reality is, that I can't really suggest to Players to play one of these games instead of the other.  This is because casino games are (or at least should be) a form of entertainment and we can't overlook this factor in our choices.

            So much of what I write is all about the math.  Years ago, my father, Lenny Frome, described Expert Strategy as a three-legged stool, with each leg equally important.  After all, we know what happens if one leg of a stool is shorter than the other two!   These three legs were:

·         Know which game to play

·         Know how to play that game

·         Know what to expect

            The first of these legs essentially referred to the payback of the game.  Don't play short-pay machines when you can find full-pay machines.  On the surface, it might mean play only the game(s) with the absolute highest payback.  But, if that were the case, everyone should be clamoring for the one type of video poker machine in the casino with the highest payback - probably some Deuces Wild variant. 

            If this were what my father intended, why did he bother to write about all the other games in detail - not just video poker but all of the proprietary table games too?  This is why a few years back, I added a concept to my father's three-legged stool.  I called it the comfy cushion.  It means you have to ENJOY playing whatever game you choose as well.  There are two significant reasons why I added this explicity to Expert Strategy.

            The first reason is because, as I said earlier, gambling should be a form of entertainment.  By this definition, you should enjoy it your time doing it.  Yes, I fully understand that it is a somewhat unique form of entertainment in that you might walk away with more money than you started, but with rare exception, these are not life-altering amounts of money we are talking about.  I'm sure no one minds being miserable while they are winning thousands (or hundreds of thousands of dollars), but more often than not, your win will be far smaller than this and you will lose more often than you will win.  No one likes to lose, but if you're absolutely miserable while you are losing $20 over 3 hours, something is very wrong.   When you go to a movie theater, there is a good chance you'll spend $20 too.  You'll have no chance of getting that money back.  You probably won't mind if the movie was good.  If the movie was a rotten tomato, it might bother you a bit more.  This is the same attitude you should take with you to the casino.

            The second reason is that if you're not having any fun while playing, there's a pretty good chance you are going to forget all about the other two legs of the stool.  You may know how to play a game, but in your frustration you'll start doing things you shouldn't be doing.  You may know what to expect, but while you're not having fun, you'll start imagining the cards are all against you or that the casino must be cheating and again, you'll go away from the strategy that you are supposed to be using.  So, on a theoretical level, you might be playing a game with a higher payback, but if you don't adhere to the strategy you may find that on a reality level, you've lowered the payback to the point where you'd be better off playing a different game.

            Undoubtedly, some of you may take what I'm saying as carte blanche to now go off and play any game in the casino.  In the end, of course, it is your decision.  But, please don't take this as my endorsement of playing slots or sitting down at a Craps table and simply playing the Hardways bets for hours at a time.  The other two legs of Expert Strategy remain full in force, so I suggest you certainly know what to expect in these cases.  Your chances of a winning session is greatly reduced.  It is one thing to pick a 99.2% video poker machine over a 99.6% one.  It is quite another to play a 91% payback proposition bet for hours.  If this is the only thing you enjoy in the casino, it might be time to pick a new form of entertainment

Still Wild About Deuces Wild

            A few weeks ago, I wrote about full-pay deuces wild video poker and it's 100.6% payback.  It has gotten harder to find 100+% payback machines, but this one can still be found in many of the casinos that cater to the locals (i.e. OFF the strip!)  People are still amazed to find that such machines exist at all.  As I've written many times, the casinos don't mind leaving a few of these around in lower denominations.  This way they can say that they have positive payback machines, but they don't really have to worry about the professionals swarming on them.

            Even if you are an Expert Player who can play at 800 hands per hour, you're dropping $1000 in the machine every hour.  At 0.6% advantage, you can expect to win $6 per hour.  It certainly beats losing, but no one is getting rich at $6 per hour.  If you're willing to sit in a casino for 40 hours per week just as you would any other job, you might be able to clear $12,000 per year.  Of course, you won't be collecting a regular paycheck.  Some weeks you're going to lose and others you're going to hit the big payout.  But, at the end of the year, should be fairly close to that $12,000.  This will be your reward for playing roughly 1.6 million hands of video poker and putting into the machine a mere $2 million!

            I'm not going to recommend you quit your day job and try this.  In fact, I won't even recommend you give up looking for work, if you currently are, and become an professional video poker Player.  For almost everyone reading this column, you are a recreational player and video poker is a form of entertainment.  Some nights you win, some nights you lose.  Depending how long you play for per session, you'll lose roughly 2 out of every 3 times you play.  But, if you pick the right machines and learn the right strategy, your night out might cost you $20 and you can get some entertainment and a few drinks.

            With a 100.6% payback, you would definitely be picking the right machine with Deuces Wild.  So, the only other thing for you to do is to learn the right strategy.   At first glance, the strategy table for Deuces Wild might look daunting due to its size, but when you look closely, you'll see it is broken down by the number of Deuces.  If you make sure to learn it this way, you'll find it much easier to learn AND you'll be doing yourself a huge favor in terms of learning to play properly.  Deuces is not a hard game to learn.  It is just so vastly different from any other game, that people make lots of mistakes.

            One of the most important things to learn is when to hold just the Deuces when drawing.  it is so tempting to want to hold the best possible portion of a hand, but sometimes you simply box yourself into a corner by doing so.  For example, if you are dealt the following:

2          2          6D       7C       QD

            You may be very tempted to hold the 4-Card Straight figuring that there are so many possible cards to complete the Straight (a 3, 4, 5, 8, 9 or 10).  If you pick up a 6 or a 7, you'll have Quads.  This is clearly superior to going for the 4-card Flush, which would require one of the remaining 11 (or 10 if the 2 was a Diamond) diamonds to make a Flush or a 6 or Q to complete the Quads.

            The problem with either of these is that they completely eliminate the possibility of any of the bigger payouts while in essence targeting some of the lower paying hands.   Further, we the two Deuces, we can do no worse than wind up with Trips, so it is not like we are giving up a sure winner.  Proper strategy says that unless you have a Royal, Five of a Kind, Straight Flush, Four of a Kind or a 4-Card Royal, you hold ONLY the two Deuces.

            When we take a closer look at the strategy, we find that we ONLY go for a 4-Card Straight or 4-Card Flush IF we have NO Deuces.   Be very prepared when dealt Deuces in Deuces Wild to frequently play them 'bare' (hold only the Deuces).  Of the 2,598,960 possible 5-card initial deals, 48 will consist of 4 Deuces (obviously, you're done when this happens).  Three Deuces will occur 4,512.  About 90% of these will be played as just the three Deuces.  Two Deuces will happen 103,776 and nearly 75% of these will be played as just the two Deuces.  A single Deuce will be dealt 778,310 times.  About 45% of these will be played as the single Deuce.  This is the 3rd most common hand in Deuces, following a Pair and a Razgu. 

            If you want to learn to play Deuces Wild, we have three different products that can help you.  You can find the strategy tables for full-pay Deuces Wild in our book Expert Video Poker for Las Vegas ($5).  We have the strategy table for full-pay Deuces Wild plus a variety of variations of full-pay Deuces Wild in Winning Strategies for Video Poker ($5).  Lastly, we have our Deuces Wild Tipsheet ($2.95) which contains the strategy tables for 3 different Deuces paytables and has the most detailed information on the full-pay variety of any of our 3 sources.  You can order any or all of these directly from us.  Send a check or money order to Gambatria, P.O. Box 36474, Las Vegas, NV 89133

Jackpot Power

            As we get deep into the political season, we're all going to be frequently reminded how it is possible to make numbers say just about anything we want them to.  Quite frankly, it is not just the arena of politics this happens in.  It can be done with all types of math - casino math, included.

            By now, many of you well know that a full-pay jacks or better machine pays about 99.5%, which is a very solid number for a casino game.  Many of you may even be aware that the Royal Flush contributes 2% of this amount.  But what does this really mean?  It means that if the machine was defective and NEVER dealt a Royal Flush, but dealt all the rest of the hands in the frequencies we would expect, the payback of the game would be closer to 97.5%.   This is about the same payback we would get from a short-pay (8/5) jacks or better machine so should we expect roughly the same experience?

            ABSOLUTELY NOT!  One of the measures I like to use is what I call a 'session simulator'.  This process simulates a session of play for a particular game.  For video poker, I use 3 hours of play at 700 hands per hour.  For this particular demonstration, I ran 1000 of these sessions under 2 conditions.  The first was a full-pay jacks or better machined that NEVER paid a Royal Flush.  To be clear, the only way this could ever really happen would be if the machine was broken or rigged.  As I don't believe the latter happens in any reputable casino, nor would a broken machine likely stay on the floor for this many hands - this is merely for illustration purposes and to prove a point.

            In this scenario, the Player still managed to walk away a winner about 28% of the sessions.  This compares to about 29% when a regular full-pay jacks or better is played.   Why is there such little impact to this?  Under normal circumstances, the Royal would hit only about every 20 cycles or so.  Some of these cycles would already be winners, so the Royal Flush doesn't change this.  It only changes the magnitude of the win.  In the cases where the session was about to be a loser, the Royal most likely flipped ONLY these into winners.  However, when we look at the long run, the overall payback of ALL the sessions put together was where we expected it to be - at about 97.5%

            When we put the 8-5 jacks or better machine (with the Royal occurring as it should), we find that the Player wins only 14% of his sessions.  His winning sessions are cut by half!  The overall payback of all the sessions is also what we would expect it to be at 97.5%.

            So, why do two different machines paying about the same amount create such different short-term results?  This goes to a concept of volatility.  There is a mathematical formula for volatility, but I'm afraid if I start explaining it at that level, you're all going to turn the page.  That is why I like to use the session simulator as a means of explaining what volatility does and is.  When a large amount of the payback is concentrated into a very infrequently occurring hand, there is a larger degree of volatility.  In the case of the full-pay jacks or better game without the Royals, I removed a large degree of the volatility.  This is why a game with a considerably lower payback that the original version can still have a not very different short-term result.

            So, what does this all mean for you?  There are two points I'd like you take away from this week's column.  The first is to realize how important the Royal Flush is to your long-term results in video poker.  If you are on a cold streak of Royals, your short-term results may not look all that different from 'normal', but you may find that your larger bankroll is suffering.  If you play for 3 hours at a time, you may find that you're still leaving the casino a winner 3 out of 10 times, but for some reason your wallet still seems a lot lighter than it should.  The good news is that in the long run, those Royals will show up as often as they should (assuming you are playing Expert Strategy).  Ironically, when the Royals are running hot, you'll still walk away a winner about 3 out of 10 sessions.  But, a few more of those sessions will be big winners.

            The second point I want everyone to think about is if a 'mere' 800 unit payout occurring roughly every 40,000 hands can make this type of impact to a game, imagine what happens on a slot machine that can pay hundreds of thousands or millions of dollars for a 'hand' even more infrequent.  The average payback on a slot machine is ONLY 92-93%.  If we consider that many of them will have a massive top pay that might occur only every few hundred thousand hands (or million hands), what % of the overall payback does this account for? 

            With these occurrences being so infrequent (and COMPLETELY unknown as to how frequent), the payback of the machine without the jackpot could easily be 80-90%.  I'd put this through my session simulator but as it is not possible to know the frequency of all the payouts, there is no way to do it.  Just for fun, I built an 82.5% video poker paytable and put it through the process and it showed that the Player will walk away a winner only 5% of the time.  As we've already shown, it would then be possible to create an infrequent, very high paying jackpot which will push the overall payback up, while barely changing the short-term results. 

            The end result is one that we know all too well for slots.  Very few people walk away a winner even in the short run, which pays for the handful of people who win the big jackpots.  I'll take video poker any day!

Deuces Gone Wild

            I love getting fan mail and/or e-mails from readers.  There are two reasons for this.  The first is that it is always nice to know that someone is actually reading my column.  It is especially gratifying when someone tells me that they ALWAYS read my column.  The second reason is that a question from a reader can frequently become the basis for a particular week's article.  There are times I sit down to write my column and I simply don't know what I want to write.  I think of a topic and realized I covered it at some point.  Of course, being that I have now been writing for Gaming Today for more than 8 years, it is possible that I last wrote about the topic in 2005 and by now there may be some new readers.

            This week, I received an e-mail from someone who was questioning some of the strategy for Full Pay Deuces Wild.   Full Pay Deuces can be found in several casinos in Las Vegas.  As is the case for most 100+% machines, you won't find them on the strip.  You're going to have to head to some of the local casinos (such as Station Casinos) if you want to find them.  My source (www.vpfree2.com) shows that there should be 100+ machines scattered about at a variety of denominations up to a quarter. 

            While I've never been a big fan of Deuces Wild, this is just a personal choice.  Any game that pays 100.6+% is hard to criticize and is a good game for the regular Player to learn and master.  The strategy table is rather long, but when you break it down by the number of wild cards, you realize that it is not really a hard strategy to learn.  With a paytable that begins paying at Three of a Kind, you don't have to worry about counting High Cards.  The one thing, I strongly advise the beginner to learn is how to recognize hands with lots of wild cards in them.  It can become very easy to not realize that 2 6D 9D 10D KH is a 4-Card Inside Straight Flush with 1 Wild Card. 

            The question I received this week was specifically about holding a 4-Card Inside Straight (presumably with no Wild Cards) versus throwing all 5 cards as a Razgu.  The strategy table tells us that we hold the 4-Card Inside Straight.  If you look at the strategy table in Winning Strategies for Video Poker, however, it lists both hands as having an expected value 0.3+ - although it does list the 4-Card Inside Straight higher meaning its "+" is greater than the Razgu "+".

            While I write extensively on Video Poker in Gaming Today, I spend most of my time analyzing table games.  Many years ago I did write my own video poker engine that allows me to analyze most video poker paytables.  One of the limitations is that it does NOT do wild card games.  Fortunately, I have both other resources available to me and the ability to quickly create a program to help determine exactly how much those "+" are worth.

            Calculating the expected value of the 4-card Inside Straight was very easy.  There are 8 ways to draw the Straight (4 Wild Cards plus 4 of the 'natural' way to complete the Straight).  Each pays 2 units so we have a total return of 16 units.  Divide this by 47 ways to draw and we have an expected value of 0.3404.

            The Razgu is a bit more complicated.  As I've written about in the past, the overall expected value as shown in a strategy table for a hand like a Razgu is the actually the AVERAGE of all the possible hands of that type.  Often, no single hand will actually have EXACTLY the expected value shown. 

            About 20% of all hands in Deuces Wild are classified as a Razgu, each with their own subtleties.  The exact make up of suits and ranks will have some impact on the exact expected value.  For each 10 through Aces that is in the hand, there will be less chances to make a Natural Royal.   The exact suit composition of the initial deal will impact the number of possible Flushes that can be made if we discard all five cards. 

            In this particular case, however, the reader was talking about a 4-Card Inside Straight, which does limit the possibilities.  In order to get a more exact expected value, I quickly set up a program that had the initial deal set to 3D 4C 5H 7S 8S.  I figured that by leaving in all of the High Cards I would leave the expected value about as High as it could go and we could see just how close of a decision this really is.

            The expected value of this specific Razgu came back at 0.3267.   So, it would be more accurate to say that a Razgu is about 0.33- and a 4-Card Inside Straight is 0.34+.  It is not exactly a canyon between the two expected value, but there is a clearly superior choice.

            To help me prove my work, I realized that we also sell a Deuces Wild tipsheet that my father created a long time ago.  It has more detailed numbers on it.  It actually lists the expected value to two decimal places.  It lists the 4-Card Inside Straight 0.34 and the Razgu at 0.32.  (When all the possible Razgus are considered, the average must wind up at below 0.325).   It was good to know that my quick and dirty program was able to produce accurate results!

            If you're interested in learning the strategy on Deuces Wild, we have the tipsheet for $2.95.  It includes the strategy tables for Deuces Wild, Double Pay Deuces Wild and Triple Pay Deuces Wild.  Or you can order Winning Strategies for Video Poker which includes these 3 paytables plus dozens more for only $5.  Send a check or money order to Gambatria, P.O. Box 36474, Las Vegas, NV 89128.

Sometimes, Is Less More?

            This week, I received an e-mail from a reader who was interested in a game called Triple Bonus Poker.   He enjoyed playing the one and only machine he could find of it in Las Vegas, but was unsure of the payback and strategy.  Not familiar with the game off the top of my head, I went to check my copy of Winning Strategies for Video Poker and found the game the reader was talking about.  He had actually found a Full-Pay version of the game and its payback was a very respectable 99.6%.

            What also quickly struck my eye was that the strategy table was much shorter than most others.  Then I noticed the top of the page which said "KINGS or BETTER".   Triple Bonus Poker doesn't pay on Jacks or Better, it only pays on Kings or Better.  Yes, the payback is still 99.6%.  It does this by paying well for Quads (240,125,75 - no kickers required) and VERY well for Full Houses and Flushes - 11 and 7 respectively.   It should be noted that it only pays 1 for a Two Pair, so this game is going to be VERY streaky.

            So, why play this wild game?  Well, that very short and easy to learn strategy table is what intrigues me.  I've often wondered what the error rate is for many Players given the intricacies of the standard jacks or better strategy table.  Keeping track of those High Cards makes for a long strategy table with subtle differences between 4-Card Straights and 3-Card Straight Flushes.   Looking at the strategy table for Triple Bonus and most of it is fairly intuitive.  Yes, it helps to know for sure that you throw a Full House if you have Three Aces and you dump Two Pair if you have a Pair of Aces, but these are easy things to remember. 

            The strange part is that despite having a respectable payback and a relatively easy strategy table, my source for games in Las Vegas tells me that NONE of these games exist.  As this source is user maintained, it is on occasion incorrect as it is in this guess.  There appears to be at least ONE table in Las Vegas.   Easier to find is a game called Triple Bonus Plus or Triple Play Plus. 

            One has to be very careful to not confuse these two games as their names have more in common than the actual games themselves do.   First of all, the latter game is a Jacks or Better game.  This means a full-length strategy table.  The Straight Flush is upped to 100 from 50, but the Quads pay of 75 is lowered to 50.  Most noticeable is that the payouts for Full House and Flush are the more pedestrian 9 and 5, respectively.   The end result is a payback of 99.8%.

            A game that pays 99.8% can actually be profitable for a Player when you include cashback and comps.  Or, at the very least, it can be a neutral game which you can play for very long periods of time with a relatively small bankroll.  I'm not one to dismiss this idea.  Also, while 99.8% and 99.6% might seem very similar, I am frequently the one to point out that you should at this from the other side.  One has a 0.2% house advantage and the other a 0.4%.  In other words, Triple Bonus Poker has TWICE the house advantage of Triple Bonus Plus.

            That all said, Triple Bonus Poker offers the Player a relatively easy game to learn without all of those pesky High Cards.  I have little doubt that for the average Player, the error rate will go down and the gap between the two games will be reduce to below the 0.2%.  If you are truly an expert Player, this will matter less to you.

            Of course, it would seem that the casinos have taken the choice away from the Players anyhow.  While there is perhaps a single machine of Triple Bonus Poker in all of Las Vegas, my source states that Triple Bonus Plus can be found in moderate abundance - at least in some casinos that target locals.  This part isn't a surprise because the best paying machines are generally found in the locals casinos.  What we don't know is whether the casinos removed the Triple Bonus games because Players didn't like the very streaky (and lower hit frequency) Triple Bonus or because the real paybacks were higher due to a lower error rate.  If this is what happened, it may have been a case where less was more for most Players.

There is Such a Thing as a Free Breakfast!

             Last Friday morning, my wife and I went to see one of the first showings of The Hunger Games at the Red Rock Station.  She had read the book a couple of months ago and has been very excited about the movie coming out.  I can't remember the last time we went to see a movie on opening day.  Maybe on the Sunday of opening weekend, but at 9:30 a.m. show on Friday?  We got there by about 8:30 a.m. to make sure we got tickets.  Fortunately, the 6 people ahead of us didn't buy them all and try to scalp them!  So, by 8:31 a.m. we had our tickets and now had tome to go get some breakfast.

            We walked over to the buffet and found out that if you have one of their Boarding Pass frequent Player cards, they'll take $3 off the cost.  I didn't have mine on me, but I knew I had one, so we walked over to the Customer Service area, got a new card and saved our $6.  While we were getting our new cards, I noticed a promotion that they were running today.  If you earn 300 points, you get a free box of Girl Scout Cookies.  Limit 2 per person and they DON'T take any of your points for the box of cookies.  If we were looking for a place to play, this might have swayed us to stay - all other things being equal.  We usually buy Girl Scout Cookies every year.  They cost about $4 per box, so there is some real value to us.  If we were diabetic, or I found they only have the one variety of cookies we don't like, then the value of this promotion has to be discounted from the $4 price.

            I'm a firm believer in taking advantage of any/all promotions that the casinos want to throw at the Player.  But, you have to be smart about deciding the value that each has to you.  If your local supermarket runs a half-price sale on cold breakfast cereal, but you like oatmeal in the morning, the sale has little value to you.  If you're the type of person who is going to stock up anyhow - just in case - well, you're going to be doing the casino a big favor by chasing everything. 

            After the movie was over, we stopped at the Rampart Casino on our way home.  It is completely on the way to our place.  They are running a promotion that gives me $10 in free slot play - which of course, includes video poker as the casinos continue to erroneously equate the two.  The rule is you have to play the full $10, but you get to keep any of the return.  I sat down at a nickel Bonus Poker machine and played max-coin.  40 hands later, the machine said $12 and I left.  It took about 5-10 minutes.  Am I that hard up for $12?  Certainly not.  But for 5 minutes of my time, the Rampart picked up the tab for breakfast for me and my wife!  If I had sat down for an hour and played their short-pay machines and lost the $10 AND another $20, I would've played right into the casinos hands.

            These are the little benefits the casinos give to Players to try to bring them into the casino.  They'll give you a discount on meals.  They'll give you some free play.  It is no different than what the supermarkets do.  They put milk on sale and hope you'll pay full price for bread, pasta and cheese.  No one has ever complained about the supermarkets doing it, so no one should be surprised that the casinos do it as well.

            Just like the supermarkets, the casinos now give you points when you play.  I've heard some Players voice concern that the casinos use your Rewards card in less savory ways.   Some are worried that the casino will have you win less often if you use your card because they are in essence paying you to play.  From a computer perspective, this is certainly possible.   But, do people really believe that the casino will cheat (aka. break the law) to not give the 1/4% back to the Player that they are telling the Player they can have.  Caesar's Entertainment (formerly known as Bally's and Harrah's) has a market cap of over $1.5 BILLION.  I don't think they are going to risk that type of money so that they can cheat some Player out of his $5 cashback!

            The lesson for today is get the Rewards card.  Get everyone you can.  Keep a little box of them with you when you head out to the casinos.  When you play in a casino, ALWAYS use your card.  That said, be smart when determining the value of the rewards when you decide where to play.  Are you better off playing at a casino that gives 50% more rewards, but has lower paybacks?  If there is a promotion running that allows you to get a free meal at a steakhouse, but you're a vegetarian, it has no value.  If it is a steakhouse you love to eat at, then it is worth its face value. 

            Especially for video poker players who are (hopefully) playing at 99% paybacks and higher, taking that extra 1/4% - 1/2% from the casino can put you very close to an even game.  It will certainly cut the house advantage down considerably and your bankroll will certainly notice.

Back to Video Poker

            I've spent 3 out of the last 4 weeks discussing Soft Hands in the games of blackjack, Spanish 21 and Blackjack Switch.  I did this for two reasons.  The first is that it is nice to write about something other than video poker once in a while.  The second is that it is frequently easier to illustrate important concepts by using games with more straightforward differences.  If you read my column this past month, you probably can understand why you don't use the same strategy for Soft Hands for these different games.  While they may be all blackjack based games, the differences created by removing the 10's (Spanish 21) and by having a Dealer Bust of 22 (Blackjack Switch) pushing against Player hands change the math, which in turn changes our strategy.

            One thing that these games have in common, for the most part, is the payouts.  A win is a win and you get paid even money.  Spanish 21 has its bonus hands and its Charlie payouts (which also effects strategy), but you don't have to worry about looking for a paytable to know what to do.  You just have to know which game you are playing.  I must admit that a very, very long time ago, I sat down at a Spanish 21 table not realizing for about 30 minutes that I wasn't playing regular blackjack!  When it finally hit me, I'm sure I turned a nice shade of red, something I don't do very often.

            The bottom line is that from my little detour on blackjack we learn that rule changes can and will change our strategy.  What we have to learn directly from video poker is that paytable changes can do the same thing.  One could argue that there really are no rule variations across virtually all video poker machines.  You are dealt 5 cards.  You decide which ones you want to replace.  You draw that many cards.  Games like Multi-Strike and some of the attempts at a 7-Card Stud game do manage to cross the rule line, in my opinion.  In the gray area are the games that use Wild Cards (Jokers and/or Deuces).  Are these really rule changes or paytable changes?  It really doesn't matter once you realize that both can have the same impact to our strategy.

            If I pick up a copy of Winning Strategies for Video Poker, I will find 27 different paytables JUST for jacks or better.  Admittedly, some of these paytables are pretty tough to find these days, but these paytables were considered to be the 'full-pay' paytables in a number of jurisdictions when the book was revised 15 years ago.  It purposefully left out many of the short-pay machines that are some of the most common both then and today.  There are probably 50-60 paytables in use today just for jacks or better.  

            Of course, in an ideal world, none of you reading this column would actually play any of the inferior paytables if given an opportunity to play one of the better ones, but that is not likely the reality.  Also, in order for this to happen, each of you would have to know how to determine which are the better paytables to actually play.  I'll save that for another column.

            Today's column is about understanding how the strategy changes as a result of a paytable change.  With dozens of paytables out there, each game could potentially have its own strategy.  This doesn't mean that if you bring your strategy from one game to another that you'll be committing bankroll suicide, but  you won't be helping yourself either.  In some cases, you might add another 1-2% to the house advantage by using the wrong strategy for any particular paytable.

            So, what is a Player to do?  First, you can't try to master every paytable out there.  I'm guessing there are not a lot of Experts who play regular blackjack, Spanish 21 and Blackjack Switch on a regular basis.  It is too easy to get parts of the strategy confused and then you start making mistakes.  Very quickly, 3 games each with paybacks of 99%+ become not nearly as strong for the Player.  The same is true of video poker.  After a while you're going to forget which games a 3-Card Straight Flush with 1 High Card outranks a 4-Card Inside Straight with 2 High Cards. 

            The key is to target a single game.  It should be a full-pay machine with a strong paytable.  Then, go out and learn the strategy.  Read a book.  Buy some software.  Practice at your desk.  ONLY when you have mastered the strategy should you venture out to the casino and play using real money.  Before you jump to play a different game, repeat the entire process all over again.

            

Hot Streak or Cold Streak?

          I've written many columns in the past several years about how our minds can play tricks with us regarding odd results.  We have a tendency to remember what appears to be very rare events and all but forget the routine.  The end result is that we begin to think that all that occurs are those strange occurrences.  This eventually leads many to believe that a game is either broken (if we are winning) or rigged (if we are losing).  The most likely real answer is two-fold.  First, we're not correctly remembering what actually occurred and second, most people really aren't aware as to how rare or common some event actually is.

            How much does it matter if our memories are a little faulty?  In the grand scheme of things, perhaps not much.  But, from a math perspective, it can make a great deal of difference.  Several months ago, a friend of mine relayed to me his experiences while playing Let It Ride.  He claimed that in a five-hand span he was dealt a Four of a Kind, a Full House, a Straight and TWO Three of a Kinds.  He must have been able to read the expression on my face as he kept telling me that it "REALLY" happened.  I was a bit skeptical. 

            When I got to my computer I did some computations and discovered that the odds of being dealt those 5 hands in a row (in any order) was about 27 BILLION to 1.  Okay, I wouldn't call it impossible, but I wouldn't call it very likely.  But, what if his memory was a little flawed?  What if he was dealt those 5 hands in a block of 10 hands?  What if his memory just 'forgot' about the five losing hands?  In this case, the odds would drop to a 'mere' 492 MILLION to 1.  At least we're back down into Lotto territory.  So, did my friend get these 5 power hands in 5 deals?  10 deals?  20 deals?  I have no clue. 

            This past week, I had the opportunity to do my own research.  Family is visiting from out of town, which usually means I'm playing in the casino a bit more often.  On one evening, I sat down at a five-play machine.  In the first 31 hands, I was dealt 5 Three of a Kinds (on the first 5 cards).  I know these numbers to be true not because I sit there and count how many hands I've played, but rather I was able to see the point counter on the machine and specifically took notice of how many hands I had played after being dealt my 5th Trips. 

            This made me wonder about just how rare is it to be dealt 5 Three of a Kinds in 31 hands.  So, when I got home and went to work on the calculation.  Before you read any further, I'd like you think about this and come up with how often you think this happens?  1 in 100? 1 in 1000? 1 in a million?  This is one of the cases where I think many people would guess rather wrong if they don't know how to do the actual math.  Until I did the calculation, I didn't really know what to expect.  I knew it wasn't astronomical, but I figured it was a bit more rare than it turned out to be.  In the end, the number was 562.  The odds of having 5 Trips in 31 hands is in the same ballpark as the odds of being dealt a Flush on the deal.  It didn't seem like such an odd occurrence anymore, but at the time, I figured the machine was on fire.

            Of course, I didn't draw a single Four of a Kind out of any of these hands.  Five times I had five chances to get those Quads and I couldn't hit a single one.  So, maybe the machine was actually cold, not hot.  How cold was the machine that I couldn't hit a single Four of a Kind from my 5 Trips?  In reality, not at all.  I had an 80% chance of not hitting any Four of a Kinds from these trips.  So had I actually hit one (or more), it would've have been the more rare occurrence.

            There are many things to take away from this column.  One is that it is hard to rely on anecdotal stories.  If you didn't witness the event yourself, you don't even know if the story is true.  And, even if you did witness it yourself, we necessary learn a lot because once upon a time something rare happened.  We need to look at all the stories everywhere in order to learn what to expect.  This is best done by computer programs and computer simulations.  From this, we learn that virtually everything that happens when we play in a casino is just part of the normal ups and downs that happen 'randomly'.

Smackdown! Video Poker vs. Slot Machines

            

            This past week, I received an e-mail regarding last week's article about slots.  In that article I talk about how casinos can legally and do make sure that slot machines are created so that they produce a large number of near misses to make the Player feel like he almost won.   A reader wanted to know if the same is true of video poker.  He wrote:

             I'm always interested in the little things casinos do to try and influence how a player thinks.  Your article spells out an excellent example of how a slot machine display can create the illusion of coming close to a big win. I was wondering if the same thing applies to some extent to Video Poker.  If I'm holding 3 to a royal flush and my 2 new cards don't create a winning hand, but one of those 2 cards is one of the cards I need for the Royal, then I might be influenced to think that I was close to hitting a royal, even though the hand is as much of a winner as any losing hand.  Do you think that VP machines are set up this way as well?

            My answer depends on the definition of "set up".  Are video poker machines specifically programmed to have Player get more near misses than one would expect to occur randomly?  Absolutely not (in most jurisdictions).  In places like Nevada the law requires that any game that uses a real life object (like a deck of cards or die) in digital form must play as random as the real-life object.  In other words, if the game uses a deck of cards, every card must have exactly the same probability of being dealt as every other card. 

            Thus, the casino CANNOT program the video poker machine to have one of the two remaining cards for the Royal Flush be drawn just so it looks like the Player came close to winning - EVEN if it doesn't change the overall outcome of the hand.   So, if the Player is dealt a suited 10-J-Q and the two cards that are supposed to be dealt are the 8D and 5C, the machine cannot change the 8D to the suited King just so the Player comes closer, but still loses.

            What makes Video Poker so superior, in my opinion, to slots is that there is no need for the casinos (or the manufacturers) to do this.  One of the beautiful things about almost any game being played with a deck of cards is that the suspense is built into the game by the very fact that a deck of cards is being used.  True, once in a while a hand is so bad, there is no suspense, but this is infrequent.  How many times have you played a hand of video poker where the first 2 cards are a Pair or 2 cards of a Royal Flush?  Your heart skips a beat as you begin to be believe you're about to be dealt Four of a Kind or maybe a Royal.  That suspense turns to much when the final 3 cards are a mess and help your hand not at all. 

            Conversely, how many times have you been dealt very little (a single High Card) and you wind up being dealt a Flush, a Straight or even a Four of a Kind?  Nobody is forcing these hands to come out of the machine.  They occur because of the nature of the random deck of cards which generates are near misses for us.

            When we look at my reader's question about a 3-Card Royal being dealt one of the necessary cards, we find that it is not such an unusual occurrence.  For a simplistic way to approximate the likelihood of this, we simply have to know that we are going to be dealt 2 cards and we are looking for one of 2 cards to appear.  So, this is roughly equivalent to giving us 4 chances to be dealt 1 card from 47 cards in the deck.  This works out to be about 8+% of the time, hardly making it a rare occurrence.

            I think this leads to an interesting question.  Does it really matter if near misses are occurring because of the nature of a random deck of cards or if it is purposefully being programmed in by the manufacturers.  Quite frankly, by itself, I don't think so.  However, I believe what this tells us about video poker machines and slot machines is the critical part. 

            Everything about a video poker machine is the result of using a random deck of 52 cards.  So, while it is random, we also know all of the probabilities with 100% certainty and thus we can calculate a payback, determine a strategy and know what to expect over the long run.  We can look at the paytable and know everything there is to know about the machine.  We KNOW that if we see 2 machines with identical paytables, they have identical paybacks.

            With slot machines, we know NOTHING.  We can look at 2 slot machines standing side by side with identical paytables and still know absolutely nothing about either of them.  We have no idea how often winning hands will occur.  We have no idea which losing hands are programmed into it and how often it will 'tease' us with near misses.  A moment ago I gave a rough estimate of how often we can expect to get a near miss when drawing on a 3-Card Royal.  This can be calculated with absolute precision too (8.3256%).  You can't do this with a slot machine just by looking at it.

            I guess in the end it comes down to the difference between NFL Football and WWE wrestling.  I don't know who will be the next Champion, but I prefer the NFL version where it comes down to the best team and not the WWE where someone decides who should win and then puts on a good show to make it happen!