What is the Allure of Progressives

            There is a theory in physics that goes for every action there is an equal and opposite reaction.  In gambling, there is a similar theory.  For every table game there will eventually be a sidebet.  And, for every sidebet there will be a Progressive version of the sidebet.  The math behind Progressives is probably the least understood math of any type of gambling.  It really isn't that hard once it is explained properly, but I've worked with a lot of inventors on a lot of Progressives, and it is fairly obvious to me that few people, even in the industry, understand how a Progressive works mathematically.

            Generally speaking there are 3 components of a sidebet - the fixed pays, the seed and the contribution rate.  Normally when we calculate the payback of a sidebet, we simply multiply the fixed pays by the frequency of each winning hand and sum up these values.  For a Progressive, we have to alter one step slightly and add one.  For the jackpot event, we use the seed amount as the equivalent of the fixed pay for that event.  Each time it is hit, the casino is on the hook to put that money back on the meter, so it is similar to a fixed pay in that regard.  We then need to add the contribution rate - which is the amount of each dollar wagered that goes on the meter - to the total payback calculated.    I'll save more details for another day, as this is not the point of today's column.  What is the point is to discuss how a Progressive differs from other wagers.

            While the top pay for most sidebets are pretty large, the amount they contribute to the overall payback is usually pretty small.  If you pay 1000 for a 1 in a million even, the contribution rate is a meager 0.1%.   In video poker the Royal Flush contributes only 2% to the payback of the game.  If we were to look at most table game sidebets, we'd probably find that most top pays contribute about 1-2% (or less) to the overall payback.  But, when we switch to a Progressive, we find that the top pay frequently contributes 15-20% to the payback when we take into account both the seed and contribution rate.  What does this mean for the Player?

            As I said, the Royal Flush accounts for 2% of the payback of video poker.  What this usually means is that until you hit one, you're only playing at about 97.5% which can be a bit rough.  When you hit one - and if you are a regular player, you WILL hit one, you bring the theoretical payback back to 99.5%.  Hit the Royal more frequently than 'normal' and you're likely up money as you will be above 100%.  With Progressives, it doesn't quite work the same way.  That top hand is either more rare or you'll be playing a game that deals much more slowly than video poker, meaning that there are no guarantees that you will EVER hit it.  So, even if the sidebet were paying 99.5% like video poker, ONE PLAYER is going to wind up winning 15-20% of that payback and everyone else will be playing at 77.5% - 82.5%. 

            When you consider the fact that many sidebets have paybacks far lower than 99.5%, you realize that the picture for those that don't hit the jackpot is even more bleak.  So, why do people play Progressives?  There are two main reasons.  One is a bit emotional and the other a bit more practical.

            First, Players have always been willing to accept low paybacks for a chance to win a life-changing amount of money.  The Lotto has made a lot of money for a lot of states.  Most states payout only 70% on their lotteries.  This is lower than the legal minimum of any casino game here in Nevada.  But, for the chance, however slim, of winning millions of dollars, Players are willing to throw a few dollars in for the hope of getting struck by lightning. 

            The second reason deals with the way Progressives work and makes far more mathematical sense.  To the casinos, the payback of a game is the long-term payback, which is calculated as I described earlier.  You'll note that what I described completely ignores the specific value on the meter at any point in time.   This money is merely an accumulation of the contribution rate over time.  It really doesn't matter to them (mathematically), if a jackpot that is supposed to hit about once a year, doesn't get hit for 3 years.  However, to the Player, the payback of ANY wager is dependent upon the specific payouts for each winning hand at the point in which you make the wager.  It doesn't really matter if the contribution rate is 10% of 20%.  If a Jackpot which is supposed to average $250,000, goes all the way up to $600,000 then the payback at that point in time is WELL above the theoretical payback. 

            It is possible that at a particular point in time that the payback of a wager could be over 100%.  At this point, it makes sense to play the game mathematically.  The problem is, however, that it will be one person that will benefit from this occurrence and it may not be you.  Then again, it might!

Why Play Max Coins?

            Generally speaking, I advise players to play max-coins when playing video poker.  For most versions, this means 5 coins.  The penny Player puts up 5 cents, the nickel player 25 cents, the quarter player puts up $1.25 and the dollar player has to put up $5 per hand.  This is done for one simple purpose.  On most video poker machines, the top payout - the Royal Flush - changes from 250 for 1 to 800 for 1 when that 5th coins is put in.  If you are playing a Progressive, the only way to win that jackpot is to play 5 coins.

            A payout of 800 for 1 on the Royal is worth approximately 2% of the total payback of the machine.  A payout of only 250 reduces this down to about 0.65%.  So, the Player is giving up more than 1.25% of payback if he plays below max-coin.  In similar fashion, if the machine is offering a Progressive, which should push the Royal payout to above 800, then the Player would be surrendering even more payback by playing below the max-coin level.

            The notion of playing max-coin does NOT mean you should wager 5 times the amount you feel comfortable wagering.  Instead it means you should consider lowering your denomination to the next lower level and then play 5 coins.  So, rather than playing 1 quarter, you should play 5 nickels.  This, of course, assumes that all things are otherwise equal.  It is certainly possible that when you go to a nickel machine (or change to the nickel option on a multi-denominational machine) that the paybacks may change as well and you may find that the payback on the nickel machine is well below that of the quarter.   This makes things a bit more complicated.  If the quarter machines pays 99.5% at max-coin, then it will be closer to 98% if you play 1 quarter.  If the nickel machines pays 98.5% at max-coin, then you'll still be better off playing max-coin nickels.

            There are a few times when you may want to play less than max-coin.  The first is when you are first leaning how to play.  As you are more apt to make mistakes at this point, you might be better off simply playing 1 nickel at a time.  Yes, you will be playing at a lower payback, but at this point, your goal is to become a better player while playing on a real machine.  Ideally, you'd spend most of your 'learning' time playing on your computer (or phone or tablet) at home for free ,but I realize that playing for free may be a lot less exciting than even playing for a single nickel.

            Another reason that you may not want to play max-coin is your bankroll.  If your bankroll is not large enough to support playing max-coin then you might be better off playing single-coin.   Once your bankroll is gone, you're done and you need to make sure you have enough money available to ride out the cold streaks.  Of course, one solution to this issue is again to simply drop down in denomination.  So, this advice really only applies if machines of a lower denomination are not available.  Since the advent of the multi-denominational machine, finding machines that play the denomination you want to play has become much easier, however.   So, this second reason may have limited practical applications.  But, if you find yourself in a situation where your bankroll will support 5 nickel play, but you only have quarter machines available, you may want to consider playing a single quarter as opposed to five quarters.

            One critical point to consider.  Just because you switch a machine from quarter play to nickel play, do NOT assume that the paytable is the same even if you are switching to the same variety of video poker.  There are no requirements that state that a machine must use the same paytable when you move from one denomination to another.   In similar fashion, don't assume that a bank of similar (or identical) looking machines all have the same paytable.  Casinos frequently and presumably purposefully mix the machines up, making sure to sprinkle higher paying machines in with lower paying ones.  I dare say that you may find no rhyme or reason to the pattern of machines on the casino floor.

          

Better is Better than Best

            A long time ago, I remember reading an article about product marketing in which it stated that you'll never (rarely?) see a company say that there product is better than a similar product.  Why?  Because if you say something is better you have to prove that it is better.  If you, on the other hand, say your product is the 'best' product then it is possible for the other product to be 'best' too.  Best, in marketing parlance, simply means as good as, whereas, better means superior.  So much for those Run, Spot, Run books which talk about good, better and best.  In marketing it is more like good, best and better.

            As bad as it is in the English language, I think it gets even worse when it comes to math.  You can make numbers say just about anything you want them to.  In the past couple of years, much has been made about the 1% (or is it 2%) of the country that is the wealthiest members of our society.   Then there are those that focus on the remaining 99% (or is it 98%).  I don't get political in this column, so please understand I am making no political commentaries here - only mathematical ones.  A friend of mine posted up on Facebook the other day some statistics about what happens if you look at the top 1% of the world instead of just the U.S.A.  All of a sudden a very significant portion of the country is in the top 1%.   Which statistic is more relevant?  I know people who are millionaires who think they are doing 'ok' and I know people who make very modest salaries who are as happy as can be.   The relevance is more likely in the message that someone is trying to send rather than anything absolute. 

            In the case I just discussed, I'll assume that all data presented was reasonably accurate.  A such, no lies were told.  No misinformation was disseminated.   Data was simply presented in a way to try and get some particular message across.  A few months ago, I wrote a column in which I asked if the U.S. has had a Democrat or Republican President more.  In the past 5 years, it has been a Democrat.  But in the last 8 out of 13 years, we had a Republican.  But, in 13 of past 21 years, a Democrat.  In 20 of Past 33 years, a Republican.  I can keep going backwards through the 20th century.  Someone attempting to make a political point is likely to use whichever statistic backs his point the best, even though it may have only minor relevance to the point.

            When it comes to gambling, the numbers can be manipulated just as much, if not more so.  If I had to take a guess, I'd say that the average video poker machine in Las Vegas probably has a payback of 97%.   Now, if I'm a casino whose average video poker payback is only 96%, I might put together some advertising that simply says 'come to Vegas where the video pokers pay an average of 97%!' .  The implication is that the casino pays this as well, but that's not what they said.  On the other hand, a locals casino that likely has a significantly higher average payback is much more likely to say 'come to the XXX casino, where OUR video poker machines payback 98.5%'.  Of course, we don't really know how they calculate these averages.   With slot machines they simply can present how they paid in the prior month because there is no human error involved.  With video poker machines do they simply take a straight average of all their video poker paytables?  Do they weight $1 machines more than nickel machines?  Maybe there is a uniform method for doing this or maybe they have enough wiggle room to give you whatever number they feel will send the right message. 

            Of course the 'average' payback has very limited value to an Expert Player.  In the simplest example, let's assume we have 2 casinos with 2 video poker machines each.  One casino boasts a 98% average and the other a 97% average.  So, should you head over to the one with the higher average?  What if their 2 machines each have a 98% payback.  But the other casino has one paying 94.5% and the other paying 99.5%.   The only machine out of the bunch worth playing is this last one, even though the casino's average is lower than the others.

            One of the local casinos here boasts of having the most machines paying over 100%.  I'll assume that they are telling the truth with this, but that doesn't mean that their machines don't pay 100.01% and that all of the machines below 100% pay 96%.  Now, to the experienced Player you will still happily seek out the 100.01% machine, but this doesn't mean that you can just show up and sit down at any machine and know that you are playing 100.01%.  At the same time, you would be better off finding a 101% machine at another casino that may have only 3 machines of this type and whose average machine pays 96%!

            So, what's my point?  Don't be sucked in by numbers that can be made to say anything they want.  The payback of a machine is an absolute number, calculated with mathematical certainty.  It doesn't mean that every time you play (even if it is for a few hours), that you will experience this payback.  It does mean that over time, your experience should begin to approximate this theoretical payback, assuming you are using the right strategy.  When you look at the paytable on a machine, that tells you the payback of the machine.  This is all that matters.  Marketing numbers that the casinos produce are just that - numbers they produce.  After all, why trust the group that has actually made better, better than best?

Think Loss Rate

            How much of a difference is there in terms of payback from one casino game to another?  Most table games have a payback between 97 and 99.5%.  Video Poker can range from about 95% to 101%.  Slot machines probably range from about 85% up to 95%.  Sidebets, quite frankly are all over the place, ranging from just over the legal limit of 75% and going up to the low-mid 90%.  While there is a lot of overlap, one of the largest determining factors is strategy.  More complex strategy means a combination of more human error and/or Players not even trying to follow it.  Simple strategy is much easier to learn and follow.  Three Card Poker has one simple strategy rule.  Follow it and you should approach the theoretical payback of about 98%.  Don't follow it and you can only do worse.

            Video Poker has paybacks considerably higher.  Not all of the versions, but you can still find plenty of them well above 98%.  Video Poker's strategy, however, is far more complex than Three Card Poker's strategy.  The average Video Poker machine has more than 30 different strategy items that need to be memorized and in the appropriate order so that you know how to play the hand.  So, first you need to review the hand and determine the realistic ways the hand can be played and then you have to know which of these ways has the highest expected value, which tells us which way the hand should be played.

            In most games, many of the hands are pretty obvious even if you knew little.  If you're dealt a 6-7-8 in Three Card Poker, I don't think you need to have read a book to know what to do.  What if you are dealt K-3-2?  What about Q-8-2?  What about Q-3-2?   For each hand, the Player is really asking himself if he is better off Playing or Folding.  Those are the only two options in Three Card Poker.  The answer is pretty obvious for the Straight and a good deal less obvious for the other three hands.  The strategy is determined by the math behind the question of whether the Player is better off Folding or Playing.  By Folding, the Player forfeits his original wager (one unit).  By Playing, he wagers an additional unit.  If Playing can return at least that additional unit (on average), then the hand is worth Playing.   The Player does not have to perform some complex calculation on each hand.  The decision is to Play or Fold and the math works out very neatly.  For every hand stronger or equal to Q-6-4 the Player is better off Playing.  For Q-6-3 or less, he is better of Folding.  You've just become an expert at Three Card Poker strategy.

            Video Poker is not nearly this simple.  First of all, there is no folding and no additional wagers.  You make an original wager and your only goal is to maximize the amount of money you get back on average for each hand.  If you're dealt a Straight off the deal, there isn't much to think about - unless of course it is also a 4-Card Straight Flush or a 4-Card Royal - then what?  What if you're dealt Three of a Kind and 3-Card Royal?  How about a Pair and a 4-Card Flush?  Does it matter if it is a High Pair or a Low Pair?  (Yes, it does!)  

            In Video Poker, the hands are categorized into about 30-40 different hand ranks and partial hand ranks.   Each of these is assigned an expected value.  This expected value is calculated by looking at ALL the possible draws for that hand and tabulating the total units won for each final winning hand.  We then divide this total by the number of possible draws so that we can compare apples to apples.  So, to look at a simple example.  Suppose you are dealt the following hand:

4♥        5♥        6♥        7♥        8♦

            The decision here should NOT be driven by your favorite Clint Eastwood line ("are you feeling lucky, punk?").  It should be driven by the math.   The straight has an expected value ("EV") of 4.00.  There is no draw in this case and the EV is simply the payout of the hand.  If you decide to discard the 8, there are 47 possible draws.  2 will result in a Straight Flush, 5 will result in a Straight (remember that you would have discarded a card that could also have made it a Straight) and 7 that will result in a Flush.  All other cards result in a losing hand.  So, do you throw away the sure 4 units to go for the Straight Flush?  When we add up the payouts of the winning hands, we get 162 units (2 x 50, 5 x 4, 7 x 6).  We divide this by 47 (the number of possible draws) and get 3.45.  As this is less than the EV of the Straight, we keep the Straight.  In the long run, this will be the better move.

            While most Player would play this correctly (I guess?), the simple reality is that except for those that learn the right strategy, there will be a significant number of Players who will NOT play this correctly.  Throw in the roughly 25% of hands that require a real decision and the casinos can count on Player error to help pad their winnings.  This is why they can offer the 99.5% paybacks on so many full-pay jacks or better Video Poker.   Someone like myself might sit down and get the 99.5%, but the vast majority of Players will play well below this level.   They are likely to play in the 97-98% range if they have some idea of what is going on and perhaps as little as 95% if they just 'wing it'.   The difference between 99.5% and 96% may not seem like a lot, but I always suggest you turn that around to the loss rate - 0.5% vs 4%.  Now there is a 700% increase from one to the other.  The impact to your bankroll could be staggering.

Frustration

            I consider myself to be a very competitive person.  Anybody who has ever played against me in a board game or on a sports field is pretty aware of this.   I play fair and hard.  I'll never cheat and don't throw tantrums.  But I really hate to lose.  So, you can only imagine what I feel like when I'm having 'one of those nights' while playing video poker.   Gambling isn't exactly the type of thing one does if they hate to lose.  Even if you're playing video poker or blackjack, games that are near 100%, you're still going to lose more than 50% of the time over short sessions.  Not a bad record if you're the Marlins, but I prefer to win, well, closer to 100% of the time.

            When I'm on the sports field, I have a significant amount of control in the outcome.  If I'm playing tennis, well, it is just about all on me.  If I'm playing softball, I can do my best to get on base when I'm at bat and make all the plays that come to me.  I can't help my right fielder catch the ball, however.  In this regard, gambling is more of a team sport than a single Player sport.  I'm an expert at just about any game in the casino that I will sit down to play.  So, I can make sure that I'll play each hand the way I should to maximize my overall payback.

            Unfortunately, luck still plays a significant portion of casino gambling (kind of like my right fielder catching the flyball?).  I can't control which hands I'm dealt.  In the long run, I know I will get my fair share of each type of hand.  In a given night, the difference between winning and losing is about getting your fair share of key hands.  You're not going to make money off of 4-Card Straights, so you don't usually keep track of how many you got. 

            When we look at the final paying hands of video poker, it should be no surprise that most of the payback comes from the bottom 3 hands.  Jacks or better gives us about 21-22% of our payback.  Two Pair gives us 26%, and Three of a Kind gives us another 20-21%.  This is almost 70% of a total of 99.5% payback.  Straights give us over 4%, Flushes over 6% and and Full Houses around 10%.  That brings us to 90%.   Four of a Kinds give us about 6%, Straight Flushes a mere 0.5% and Royal Flushes the remaining 2%. 

            The more common a hand is, the more likely no matter how weird your session is going that at the end of it, you're going to have very close to the number of those hand that you are supposed to.   So, if you play 3000 hands and the average shows that you should have about 650 High Pairs, you're not going to find out that you only had 500 of them.  Maybe you have 630 on a bad night and 670 on a good night, but you'll get very close to the 21-22% payback you are supposed to.

            On the other end of the spectrum is the Royal Flush.  If you play 3000 hands, you're well below the roughly 40,000 hands it takes to play to catch a Royal.  If you play a session and miss the Royal, you're inherently playing at 97.5%.  If you hit one then, well, you're assuredly playing well over 100%.   As a result, there really isn't a lot to discuss where the Royal is concerned.  It is literally hit or miss.  Straight Flushes simply don't add enough to the mix and are also so rare that you can't really look to them for a good or bad night.

            The critical hand is the Four of a Kinds.  Earlier I said that they make up 6% of the payback.  That is on a jacks or better game.  Move to Bonus or Double Bonus or Double Double Bonus and these number goes way up.   You win or lose in these games based on two key factors.  Do you get your fair share of Quads and which Quads do you get (when playing the bonus games)?   If you play 3000 hands, you can 'expect' to hit about 7 Four of a Kinds.  It would not be uncommon to play this many hands and get only 2 or 3.  If you have one of these nights, you're not likely to walk out a winner.  Quite frankly, you may not walk out with any of your bankroll left.  Fortunately, it is just as common to get 10 or 11 of them.  In these cases, you are very likely to walk out a winner.  If you're playing Double Double, you'll also want to hit some of the bonus Quads and/or the 'double' bonus quad with one of the kickers. 

            Playing the right strategy is, of course, a critical component of getting your fair share of Four of a Kinds.  But, the right strategy does only so much to make the 5th card in Quad 3's also be a 2, 4 or Ace.  Sometimes it just takes luck to have that good night.  Sometimes my right fielder actually catches the ball.  All I can do is hope.

Nutritional Labels for Casino Games?

            Today's column topic comes from my Freshman college roomate.  He posted a question to one of my old columns on my blog (gambatria.blogspot.com).  He wanted to know if I thought if the casinos would ever have to disclose all the key statistics about each game - a sort of 'nutritional label' for each game.  My response was that I didn't think so for 3 reasons.  The latter 2 were more political than mathematical.  This column is about that first reason.  With the exception of slot machines, all that information about each game is already fully known.

            While admittedly, if the average person were to walk up to a game that he has never seen before, he isn't going to know what the payback or win frequency is.   I'm an expert and I couldn't necessarily tell you these key stats about a game I've never seen before.  I might be able to take a good guess about it, depending on whether we are talking about a complete game or a sidebet.  There isn't a lot of variation in table game paybacks.  There are probably very few that are below 97% and, of course, none above 100%.  Sidebets can have a much larger range, as some are as low as 75% and others go up to the mid 90's or even a smidge higher.   If I were to walk up to a video poker machine that has a foreign paytable, but is based on one of the better known games, I can probably peg the payback to within .25% by doing some quick math in my head.

            There is little doubt that putting the key statistics on each machine would make this information far more readily available than the way it is currently done.  But, I wouldn't equate this to a can of soup without a nutritional label.   The list of possible ingredients and the exact quantities in the soup is nearly endless.  Throw in the fact that there are hundreds of thousands of food products (or more?) and it is completely impossible to make a choice based on nutritional content without these labels.  When you walk into a particular casino, you have perhaps a dozen or so choices of which table game to play.  Yes, each casino may have its variation of rules.  One may offer a 6-deck shoe for blackjack and the other may have a single-deck game.  One may hit on soft 17 and the other may stop on all 17s.  But, if you spend time reading a book or two on gambling, you'll quickly learn and likely remember the paybacks of most of these rule variations.

            For many games, there is almost no variations available - especially for the base game.  Want to play Three Card Poker?  It has a 97.98% payback for Ante/Play.  While there are some variations of Pair Plus, the overwhelming number of them have the same paytable, paying 92.72%.   These numbers are not known because Shuffle Entertainment published them, they are known because any mathematician/programmer can calculate these numbers using a variety of techniques.  In the case of Ante/Play, there are a total of 6 cards dealt to the Player and the Dealer (3 each).  There are 22,100 possible Player hands and 18,424 possible Dealer hands for each of the Player hands.  Thanks to the speed of today's computers, a program can run through ALL of these hands (numbering well into the Trillions), determine the right strategy for each Player hand and tell us absolutely everything we would ever want to know about the game - the payback, the win fequency, the probability of winning given any Player hand, how often the Player folds, how often the Dealer doesn't qualify, etc... 

            Unlike food, casino games are, well, gambling.  Part of gambling is rewarding those people who are more prepared and more knowledgeable about gambling.   The strategy for Three Card Poker doesn't take a PhD to learn.  It takes about 20 seconds (or less).  Play a Q-6-4 or better.    You could read this just about anywhere on the internet.  If you want to know the details about the strategy (how and why), you can read a booklet on the game (I suggest my very own Expert Strategy for Three Card Poker, but that's just me!)  Armed with this strategy you are very likely to do better than someone who has no idea what to do over the short run and almost assuredly so over the long run. 

            For years, people have asked me if I'm banned from casinos because of my in-depth knowledge of table games or if I'm 'hated' by the casinos for arming people with the strategies for how to play the games.  I'd like to think that I've had at least some influence on how people play.  But, I don't think the casinos care one bit.  Even with the best strategies, all casino games (except a few video poker variants) have house advantages.  The casinos are totally fine with a few people playing near the theoretical payback as results are all relative.  A few people who are winning in the short run or who are doing better than the rest can keep the rest of the Players in the game.  After all, if the other guy can win, why can't I?  Of course, this is far more true IF you know the right strategy. 

            I've often surmised that if I were to stand near a Three Card Poker table, handing out my booklet for free that only 20-25% of the Players would actually use the strategy.  Half of these people would probably give it up within the hour when the results don't match the theory - ignoring the time factor that is required for this to happen.  What this really translates to is that I don't think it would matter one bit if the casinos were to put a little sign on each table that had the payback and win frequency of the game.  Most Players would probably ignore them.  After all, how many people really read those nutritional labels on food anyhow?  And that's about what actually goes INTO your body!

            

The Nature of the Game

            My elder son has finished up his year in college and came home the other day.  As we do our best to keep him entertained while in Vegas, we went to the Laugh Factory at the Tropicana the other night.  Invariably, when comedians are in Las Vegas, they will tell jokes about the dry heat and about losing money while gambling.  I think I've been very honest about the odds of long-term winning while gambling.  With the rare exception of some tough to find video poker games and/or the ability to count in blackjack, you're simply not going to win in the long term.  But, this doesn't mean that you have to 'lose your shirt' either. 

            A few weeks ago, I showed how playing blackjack for an hour, a $5 Player should expect to lose only a little over $1/hour.  This, of course, assumes playing properly.  If you are too timid to double down on soft hands, or don't like splitting 2's looking into a 7, then, well, all bets are off as to what your payback will really be.  The comedian was hopefully joking when he talked about struggling to add up his cards while playing blackjack.  If you're really struggling with this, maybe you should try Casino War or Three Card Poker.

            In that same column where I talked about the average you can expect to lose while playing blackjack, I also spoke of the average you can expect to lose while playing full-pay jacks or better video poker.  As the two games have similar paybacks, the only real difference is the average amount you wager in an hour of each game.  Much to many Player's surprise, a max-coin quarter video poker actually wagers more in an hour than a $5 blackjack Player.  That said, however, the game of video poker is far more volatile and while the average loss rate by only be a couple of bucks an hour (depending on speed of play), actual results will wind up all over the place.  Blackjack is a much less volatile game and we will find that our actual results will really tend to be very close to the theoretical amount.

            To help illustrate this point, I ran 100,000 multi-hour sessions of blackjack, each consisting of 100 hands.  I then tabulated the amount won or lost, rounding to the nearest dollar.   First of all, the Player had a winning session nearly 46% of the time.  He lost 49% of the time, with the remainder being breaking even.  Around 32% of the time, the Player will wind up within $20 of his starting point, with only a slight slant towards the losing side.    He will wind up within $40 of his original bankroll more than 55% of the time.   He will wind up losing $100 or more only 5% of the time.  To be clear, this is NOT the same as saying that if he starts with $100, he will go 'bust' only 5% of the time.  The simulation I ran does NOT take into account a Player who may have at some point been down more than $100 and then came back to lose less than $100.  This will not be a huge number, but it will add to the total.

            I'm not downplaying the impact of losing $100.  This is not a small amount and could be considered to be a high cost for 2+ hours of entertainment.  At the same time, we are only talking about a 1 in 20 chance.  At the same time, the Player has a 4.4% chance of WINNING $100 or more.   That's why it is called gambling.

            But, the overall point is that the notion that everytime you gamble you're going to lose your shirt is simply not accurate.  If we assume that 'paying' up to $25 is a fair price for the 2-3 hours of entertainment value, then we find that the Player will meet this goal 62% of the time.  In fact of this 62%, he will actually wind up winning money nearly 75% of the time. 

            As stated earlier, this all assumes playing properly.  This tends to be what trips up Players far more often that the basic nature of the game.  Blackjack has a payback of about 99.5% when played properly.  Played improperly, the payback could drop dramatically,  If you drop it to 98%, which is still a respectable payback for most table games, this may not seem like a lot.  However, turned around, it means the casino advantage increases fourfold.  If I were to simulate such a strategy, we would find that the numbers are not so generous to the Player, and the likelihood of losing one's shirt will go up considerably.

            Thus, while the nature of the game it still one where the Player will lose in the long run, the Player can still greatly control (within reason), just how much will be lost by learning to play using the right strategy.

The Cheap Cost of Entertainment

            I received an e-mail this week from a loyal reader who was questioning some of the numbers from my recent column.  The column was discussing the definition of payback and had the amount of the buy-in is irrelevant to the discussion of the payback.  The example I cited was discussing someone who sat down to play 100 hands of $5 blackjack.  With a payback of 99.5%, a Player can expect to lose $2.80.  The point of the column was to discuss how this $2.80 will not change no matter how much the Player buys in for.  If he buys in for $20 or $100 he will still lose the same $2.80.  All that changes is the percent of the Player's bankroll that he will lose.  The $2.80 is a fixed amount.

            My reader questioned this calculation.  Not so much for its pure math, but because I 'ignored' the situation where the Player might lose his first 4 hands be 'bankrupt.'  My reader is quite correct.  The situation I described ignored the numerous circumstances in which the Player will actually lose his entire buy-in before reaching 100 hands.  With a buy-in of only $20, this is fairly likely to occur.  Roughly 1 in 16 times, he will lose the first 4 hands and be done right then and there.  This doesn't even include the times he may double or split in the first couple of hands and go broke before even 4 hands. 

            That said, this was not really the purpose behind my calculation.  Since the point was to show how the expected loss rate does not change based on the buy-in, I could have just as easily used a $100 and $500 buy-in in my examples.  With a $100 buy-in, it is far less likely that the Player will go broke before 100 hands.  However, my reader does bring up a very, very important point about the importance of being properly bankrolled for any game.  The amount will vary greatly from game to game, mostly dependent on the volatility of the game.  Blackjack is a relatively low volatility game so $100 would be good enough most of the time.

            The second part that the reader questioned was my math regarding the anticipated loss while playing 1000 hands of full-pay jacks or better video poker at max-coin quarters.  I said that it would be $6.25.  My reader wished that his expected loss was only $6.25 and that this would make it 'cheap entertainment'.  Well, I stand by this number.  On a max-coin machine, the Player will wager $1.25 per hand.  Over 1000 hands, he will wager $1250.  A full-pay jacks or better machine pays about 99.5%.  Losing just 0.5% of his total wager brings us back to $6.25.

            Of course, this is the long term average.  Unlike blackjack, video poker has a much higher volatility.  Blackjack is a lot like a coin toss.  You win about half the hands.  You lose about half the hands.  Except for actual blackjacks, splits and double downs, all  payouts are even money to the original wager.  There tends not to be huge swings in how you will do.  After 1000 hands, you'd probably be very close to the theoretical 99.5% for blackjack. 

            Video poker is quite different.  You 'win' about 45% of your hands, but an overwhelming majority of these are really pushes (High Pair).  The rest of the payouts range from even money all the way up to 800 for 1 for a Royal Flush.  That Royal accounts for about 2% of the total payback.  This means that until you hit the Royal, you're only playing a 97.5% game which means the loss rate over 1000 hands would be closer to $20.  Eventually, you will hit that Royal and for that 1000 hands, you will have a significant win.  When you add up the TOTAL amount you wager and multiply it by 0.5% (the loss rate), the total amount you've lost should be very close to this number.  At the same time, if you hit more Royals than 'average', you'll probably be up significantly.  If you hit less than average, your loss rate is likely to be quite a bit more.

            When we tie together the two thoughts that my reader brought to me, we realize the importance of being properly bankrolled when playing video poker.  Given the volatility of the game, it becomes even more important to make sure you are in the game until you get to one of the big hands.  In jacks or better, this mostly means the Royal.  In double double bonus video poker, you have the luxury of a few of the Quad payouts AND the Royal. 

            I had an opportunity to experience this first hand twice this past week.  I ventured out on 2 separate occasions to play video poker.  In one case, I was down about $40-$50 when I hit two solid hands and came all the way back and left even.  In the other case, I hung around even most of the night.  I was down about $5 when I hit I was dealt 3 Aces on a five-play double double machines.  Short of being dealt quads, this is about all you can hope for.  Now all you have to do is hit the Quads.  On the fifth hand, I was dealt an Ace and a 3.  Not only did I hit the 4 Aces, I hit the bonus 4 Aces.  About 5 hands later, I left up with a nice victory.  In the case of my first night, if I had brought only $40 with me, my bankroll would've been gone and I never would've made it to the big hands.  Also, if I weren't using proper strategy, my losses up to that point would have been that much larger, and even a $60 or $80 bankroll might not have lasted as long as it needed to.

            Proper strategy and proper bankrolling are keys to achieving the theoretical paybacks of a casino game.  In turn, this is what can lead you have 'only' that much of an expected loss rate and get a cheap night of entertainment.

Customer Power

            There were two different articles that appeared today that on the surface appeared only marginally related.  Yet, to someone like me, I found that they were far more important to one another than meets the eye.  The first article discussed the upcoming building boom here in Las Vegas.  Several major casino building projects are in the planning stages and Las Vegas may, in a few years, welcome its first major new casinos in several years.  One of the sub-plots of this article was some local columnists discussing what they felt was needed to build a perfect casino.

            In reading these suggestions, I can't say that I have a lot of hope that many (any?) of them would be implemented.  One of the suggestions dealt with the idea of putting the attractions near the front of the casino and the casino way in the back.  Another dealt with moving the restaurants closer to the self-parking garages.  Yet another suggested that casinos go smoke-free (I'm all for this one!).  The one that got my attention was the one that requested that casinos do away with blackjack that pays only 6 to 5 (instead of the traditional 3 to 2).  This one also mentioned better paying slots, but the focus was on blackjack.

            For those who have read my column over the years, you know I'm all for 3 to 2 blackjack and do my best to warn people about playing 6 to 5.  Roughly, 1 in 21 hands will be a blackajck.  That's about 2 hands per hour.  If you're a $5 player, this will cost you about $3/hour.  This may not seem like a lot, but it will increase your loss rate by about 300%!  A 99.5% game quickly becomes a 98% game and now you're playing a game that requires a great deal of strategy with a payback that is in the same range as many of the table games with little strategy.

            That brings me to the 2nd article I read today.  It talked about how gaming revenue in Las Vegas was WAY UP compared to last year, for the month of February.  A significant portion of this was due to the Chinese New Year occurring in February of this year vs. January of last year.  But, even when this is accounted for, revenue was still up.  Revenue on the strip was up even more than the rest of the city.  It is on the strip that we find virtually all of the 6 to 5 blackjack tables.

            6 to 5 blackjack was created because over time blackjack Players were getting better and better and the hold at blackjack tables was dropping.  Casinos have a lot of overhead to cover - from Dealer salaries to the massive electricity bills.  While every business should run efficiently, this is not exactly the case of they should keep the customer happy at all costs even if it means eking out a small profit.  Casinos are expected to make huge profits at the tables and slots to help offset many of the things they provide at low cost or free.  I have no idea what the cost is to present the pirate ship battle at the Treasure Island, but they've been doing for about 20 years for free every night.  The money to do these performances comes from the gambling side of things.

            So, the casino decided to come up with a way to greatly increase the house edge on blackjack.  They could have tweaked the rules a bit - use larger shoes, limit when the Player can double, etc..  But, these have limited practical impact to the house edge.  One of the most common Player errors is not doubling on soft hands when they should.  So, eliminating this as an option doesn't really help the casino at all.  So, they chose to pay blackjack at 6 to 5 and take a bit out of the bankroll of the good and bad player alike.

            Now, if you've been going to a buffet on the strip that give you free drinks included with the price of the buffet and all of a sudden they tell you that they're going to start charging you for your sodas, you might think twice about where to eat.  Yet, for some reason, paying 6 to 5 didn't have much of an impact to the amount of money people wagered on blackjack. 

            However, if we look at the report about Las Vegas gaming revenue for February, we find that the biggest spike occurred on the Strip.  If you head out to the casinos in the 'suburbs' where you find more local Players, you'll find almost NO 6 to 5 blackjack.  Local players tend to be better players (or they don't stay local very long) and the better player knows that playing 6 to 5 blackjack is very hard on your wallet.   You need to learn a complex strategy just to be able to earn a 98% payback?  A Player can sit and play a relatively simple game like Three Card Poker and earn the same payback and have a chance for a larger single payoff (with Trips of a 3-Card Straight Flush).  And, if you're not an accomplished blackjack Player, your real payback could easily drop to 95-96% which leaves a Player with very little chance of having a winning session.

            But, if nobody complains about having to pay for the soda, AND they have the same number of customers this month as they did last month (or more!), then there is little reason for the casino to go back and give out free drinks at the buffet.  This is even more true at the tables.  If a Player is just going to sit and take his 6 to 5 payout with little regard to the impact to his wallet, who can blame the casinos for making this their basic offering.

The Definition of Payback

            I never get through a holiday without a serious discussion of what I do for a living with someone I've never met before.  Family (and friend) functions tend to bring together people for a large meal leaving them with loads of time to discuss all sorts of things.  As I have one of the more unique jobs around, my vocation tends to take up a larger than proportionate amount of the time we spend together.  This past holiday season was no different.

            First I listened to one person tell me how he has a system for roulette.  Admittedly, he didn't get a chance to explain it to me in much details when I had to tell him that it doesn't work.  No system does.  He told me how each time he came to Vegas, he would use this system and invariably walk away with a few hundred dollars.  Of course, his sample size was about 6-12 sessions, which isn't exactly statistically significant.  Based on what he told me, I commend my new found friend for his discipline which can be an important part of any successful gambling story.  Know when to get out when you are ahead.  But, that said, if you really have a system that nets you $400 in an hour or two, it is forever repeatable, which means you do it every night and then you send out a team of people to repeat your system.  No 'real' system could work only if you use it once every few weeks.

            Next up in the discussion came my favorite topic (ha!) - slot machines.  The system here was to attempt to outguess when the machine was going to pay off by altering the amount wagered for each 'pull'.  It was hard to keep a straight face when we got to this point.  I've heard of people varying their bet when playing blackjack in an attempt to guess the next cards.  If you do this well, it is card counting.  If you simply try to outsmart the shoe, you're just guessing.  If you try it with a slot machine, you are definitely guessing. 

            We've all seen the disclaimer that says 'past performance is not an indication of future returns'.  Nothing could be more true with slot machines.  What happened in the last spin has absolutely no bearing on what happens in the next one.  A slot machine is programmed to have a winning spin some percent of the time.  Every time you spin the wheels, the chance of winning is this exact percent.  With some combinatorial math we can also say that the probability of having X winning hands in Y spins will be some percent (assuming we know the probability of winning in any given spin).  But that is only true for the next Y spins.  We absolutely, positively CANNOT use any of the past spins in our calculation.  If the past 100 spins were losers, the probability of winning on the next spin is still whatever it is.  If the past 100 spins were winners, the probability of winning on the next spin is the same percent. 

            When I suggested to my new friend that he might want to avoid slot machines due to their 92+% payback, which makes them some of the worst payers in the casino.  Of course, when you look at the machine you have no way of knowing if it is programmed at 98% of 85%, which is as much as part of the problem as the average of 92+%.  My friend wanted to know how this payback was calculated especially when taking into account the way he plays - altering his wager from spin to spin.

            I explained that the payback used for any game is the highest payback that can be obtained by a Player assuming he plays using the best possible strategy he can.  For a game like video poker this means he uses perfect strategy to play each hand and that he plays max-coin in order to get the benefit of the 800 for 1 payout for Royal Flushes.  For slot machines, there is no strategy, so that does not impact the payback.  With slots, the impact of max-coin can frequently be even greater than with video poker.  Not only do you buy additional lines with additional wagers, you sometimes also buy additional combinations of winning hands.   As a result, playing less than max-coin can be even more punishing to your bankroll.  The payback of a slot machine thus assumes a max-coin play on each spin.

            Payback (for any game) is the amount that a Player can expect to have returned out of the TOTAL amount wagered.    The amount you buy-in for is completely irrelevant to this definition.  If you sit down at a blackjack table for $20 and play 100 hands of a $5 table, you'll wind up wagering about $565 (when you account for splits and double downs).  With a 99.5% payback, you can expect to lose about $2.80.  This works out to be 14% of your buy-in, but if you had bought in for $100 it would've been 2.8%.  Just further proof that the buy-in is not relevant to the payback discussion. 

            If you play 1000 hands of video poker (quarter machine, max-coin), you'll wager $1250.  If you're playing full pay jacks or better with a 99.5% payback, you can expect to get back $1243.75.  No matter how much you put into the machine, you should expect to have lost $6.25.  If you play less than max-coin, your expected loss will be higher.

            Slot machines are no different.  If you spin the wheels 1000 times on a nickel machine with 27 lines, you'll wager $1800.  You won't know the exact payback of that machine, but if we use a generous 95% payback, you can expect to get back $1710 of that $1800 wager and sustain a $90 loss.   If you choose to vary your bet from spin to spin, your payback might be even lower, raising your expected loss.

            In all these cases, the paybacks are expected 'long-term' paybacks.  Long-term can mean different things to different games.  In a 2-3 hour session of playing, your results can and will greatly vary from the examples shown here.

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.

            

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.

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.

Is the Search for Perfection Overrated?

            

            One of the traits I inherited from my father, Lenny Frome, is that I am a perfectionist.  This is not to say that I am perfect (far from it).  The joke in our family was always that one of my sister's brought home a '99' on a test and my father, not missing a beat said "why not a 100?"  Fortunately, for me, by the time I came along, he learned to temper his ways a bit.  I try to focus most of my perfectionism inward.  Nobody takes it harder when I find a mistake in my work more than I do.

            At the same time, I try very hard to be practical about things too, where strategy is concerned.  Us mere mortals do have limitations to our ability to memorize dozens of video poker game strategies.  It is why I strongly recommend that you learn one or two different games and do your very best to 'perfect' the strategies to those games.  But, what are you to do if the games whose strategy you memorized are not available when you go to the casino or if you're just in the mood to try something different?

            In these cases, you just have to use some common sense.  If you try to bring your Jacks or Better strategy over to Joker Poker, you may find yourself in deep trouble.  But, what happens if you use your basic full-pay Jacks or Better strategy on a full-pay Bonus Poker machine?  What will this really cost you in theory?  Calculating this - with the help of some of my video poker analysis programs - is relatively easy.

            We simply run the numbers on a full-pay jacks or better machine using Expert Strategy for jacks or better.  From this program, we extract the frequencies of all of our winning hands.  We then use these frequencies against the Bonus Poker paytable to get a theoretical payback of Bonus Poker using jacks or better strategy.  We then run the numbers on Bonus Poker using Expert Strategy for Bonus Poker and compare the results.

            The theoretical payback for Bonus Poker using Expert Strategy for Bonus Poker is 99.16%.  The theoretical payback for Bonus Poker using Expert Strategy for jacks or better is 99.15%.  If you were to play all 2,598,960 possible 5-card deals using jacks or better strategy you would find that you cost yourself about 200 coins.

            In other words, while it is still preferable to learn the right strategy for Bonus Poker, if you use your jacks or better strategy, your bankroll will not take a big hit.  However, this should not give you free license to play jacks or better strategy on any game you want.  If you were take your jacks or better strategy to a DOUBLE Bonus Poker game, you would find that it will play at about 99.6%.  This might sound good (after all jacks or better itself plays at a bit less than this), but you have to remember that Double Bonus Poker is one of the few positive games out there.  If you play it using the proper strategy, it can afford you a 100.1% payback.

            So, what's the point?  Good question.  Nobody should expect perfection when they head to the casino.  The simple mathematical fact is that every deviation from perfection, however, will cost you.  It might be peanuts as in the case of playing Bonus Poker using jacks or better strategy.  If you play a hundred hours a year as a $1 max-coin Player, you'll cost yourself $30 per year.  We'd all rather have that $30, but we're not talking a significant amount of money.  Do the same on our Double Bonus scenario and we're talking about $1500 per year, which I dare say is QUITE significant.

            So, while we shouldn't shy away from video poker because we might make a few mistakes, we should still be prepared to learn the right strategy for each game and to do our very best to utilize it every time we play.  This is the very essence of Expert Strategy - Know which games to play, know what strategy to use and know what to expect.

            For those of you who want to learn the subtle differences between jacks or better strategy and Bonus Poker strategy, both strategies can be found in Expert Video Poker for Las Vegas and Winning Strategies for VideoPoker.

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!

Beating the Casino

            

            A couple of weeks ago, I discussed how a blogger lamented how the last good table game invented was blackjack because none of the games invented since gave the Player a chance to beat it.  I would argue that blackjack is hardly 'beatable'.  It requires an incredible amount of discipline and knowledge of card-counting schemes in order to eke out even the slightest edge.  With the continuous shufflers and regrettably 6 to 5 payouts on blackjack, even with the most sophisticated counting scheme, beating the game is almost impossible.

            There is only one game on the casino floor (barring the occasional game that accidentally makes it to the floor) that is readily beatable.  That is video poker.  There are games all are over Las Vegas with paybacks of over 100%.  If you learn the proper strategy you can earn these paybacks.  I will not, however, promise that you will become filthy rich off them.  Unlike card-counting schemes which would allow you to bet $5 when the count is against you and perhaps $5000 or more when it is in your favor, video poker machines essentially have a constant wager and there are no known counts for you to track.  Each hand is completely random and no matter how many hands you have won or lost in a row, the next hand is still random.

            Over the years the casinos have caught on to this idea and this is why many are still willing to put machines on their floor with paybacks over 100%.  They simply don't put them on the floor with high denominations.   If you are willing to play video poker 40 hours per week (like a job), are able to play 700 hands per hour, you would play 1,456,000 hands per year (approximately).  If you played a quarter machine, you would wager the staggering sum of $1.82 Million per year.  If you can play the entire time on a full-pay Deuces Wild machine paying 100.76%, you'll earn about $13,800 per year.  This doesn't account for any taxes and doesn't account for any cash back and/or comps.  

            Of course, some of you will just suggest playing a higher denomination.  Even playing dollars, the annual 'salary' will get to only $55,000 or so.  This is certainly not a bad income.  Of course, this most certainly doesn't mean you can count on any sort of regular 'paycheck'.  There are going to be weeks you lose and there are going to be weeks you win far more than average.  And, as I said earlier - the casinos have caught on to this.  According to my research, there are no $1 machines playing full-pay Deuces Wild in the Las Vegas area.  So, the casinos are willing to let the resourceful Player make some money, but not enough to really entice large numbers of Players to do them harm. 

            This is also further proof that video poker machines are not slot machines.  Casinos would NEVER allow banks of 100+% slot machines to exist.  Slot machines require no strategy.  Thus, as long as the slot machine were to be played for 40 hours per week the casino would be paying out the $13,800.  To the casino it doesn't matter if this is one person, 10 people, 100 people or 1000 people who wind up winning this money.

            Video poker requires that the Player learn the proper strategy to earn this money.  So, if 52 people took turns playing for 1 week and played using Expert Strategy, then the casino would still be paying out the $13,800.  But the casinos know this is highly unlikely.  Despite strategies for virtually every imaginable game being available for 10-20 years, the overwhelming percent of Players simply choose to ignore the proper strategy.  The reality is that 50% of the Players probably know of no real strategy and just muddle along - playing a Deuces Wild game at no better than a 95% payback.  Perhaps another 25% play using some rudimentary strategy that they learned somewhere and play at 97%.  Another 15-20% have made real attempts to learn strategy but haven't really mastered it and can play at 99%.  The final 5-10% have learned the proper strategy and make a significant attempt to play properly.  Perhaps half of this group truly attains a payback of 100.5% or better.

            The result for the casino is that their machine probably pays out at no more than 96.5% in total.  A number that they can definitely live with.  However, just as the casino doesn't care if it is 1 or 1000 Players that win the $13,800, you do not have to be concerned with how any other Players do.  The casino is very happy with that machine that pays back 96.5% and will net them more than $65000 per year - EVEN if it means one of the Players made a few hundred or thousand over the course of the year.

            But, if you want to be this Player, you have to learn how to play video poker using the proper strategy.  To help you along the way, we're offering up our two full-length books for just $5 each (which includes postage and handling).  Winning Strategies for Video Poker includes strategy tables for 61 of the most common games found anywhere.  America's National Game of Chance: Video Poker is 200 pages of Lenny Frome's best articles, stories and quizzes and is an excellent way to learn how to play video poker in an easy to understand way.

            Send a check or money order to Gambatria, P.O. Box 36474, Las Vegas, NV 89133 and you'll be on your way to becoming an Expert Video Poker Player.

The Payback Mirage

             The battle between the short-term and the long-term, where gambling is concerned, is an epic struggle and so totally misunderstood by most.  Why is this a problem?  Because it is critical to understand what to expect when you’re playing.  If you don’t, you may begin to believe that something is wrong about what you are doing and this can lead you to deviate from proper play.  When you do that, you may help yourself in the short-term, but this will eventually give way to damage done in the long run.

            To try and prove this point, I ran some video poker simulations.  I played 100,000 3-hour sessions of video poker.  I assumed each session consisted of 2100 hands of video poker (700 hands per hours).  I started with a full-pay jacks or better game.  What did I find?

            Well, in total, 210 million hands of video poker were played.  At the end of all these hands, the payback was essentially exactly where we would expect it to be – 99.52%.  If the simulation used max-coin quarters, the result would be a loss of about 1.26 million dollars.  Of course, based on 210 million hands, it would also take 34 years of 24 hour/day play to get to this point.  Quite frankly, this is MORE than a lifetime of play.

            When we look at some short term results, we find that the Player will lose about 68.5% of the session and win 31.5% of the time.  So, even when playing a full-pay jacks or better machines, the Player can expect to lose 2 out of 3 times when playing for 3 hours.  Even though the edge is less than 0.5% for the house, the Player will walk away a loser far more often than a winner.

            So, is it any wonder that I advocate playing games with a 100% payback or better.  To prove this point, I created a fictitious machine whereby the payouts are the same as full-pay, EXCEPT the Four of a Kind pays 30 instead of only 25.  The simulation showed that after 210 million hands, the overall payback was 100.70%, which is what we would expect.  So, this game is a bit more positive than full-pay is negative.  Thus, the results of our sessions should probably be flip-flopped from our full-pay version, right?

            Not exactly.   We find that even with the payback of 100.7%, the Player will STILL lose 58% of his sessions!  That’s right.  The Player will still lose nearly 6 out of 10 sessions while playing a game that is significantly in his favor.   Despite this 1.2% turnaround (from 0.5% negative to 0.7% positive), the Player will wind up winning only an additional 1 session out of 10 and still lose a significant majority of his sessions.  How can this be?

            These results occur because when playing video poker, our wins will, on average be larger than our losses.  Of course, even this is a bit deceiving.  What really happens is that every so often we have a HUGE victory, while our losses tend to be more moderate.   In sessions where we hit a Royal Flush, our winnings will be far larger than virtually ANY loss we would ever have.  As a result, we lose more sessions than we win, but those big winning nights tip the scale back in our favor.  When we play a 99.5% game, it only is enough to bring it back closer to even.  If we play a game with a payback of OVER 100%, those big wins are enough to turn the game positive in the long run, even if in the short run we are losing more than winning – in terms of sessions, not dollars.

            As I said earlier, it is critical to understand how this all works.  Otherwise, it is way too easy to simply give up on playing the right strategy if you feel you are losing too often.  While we all play in ‘sessions’, in the end, all that matters is how we are doing over the long run.  In the second example (the 100.7% game), would you really be upset to lose 58% of your session, but  wind up winning 1.85 million dollars over a lifetime?

            One last point for those of you who would try to use the information here as ‘proof’ that the long run is really too long.  I ran each machine for a mere 1000 sessions or 3000 hours of play.  This could be 3-5 years of play for a local in Las Vegas.  While there is a bit more deviation from the long term expectations, on the whole the numbers still prove my point.  The overall paybacks for the games were 99.26% and 100.49% respectively.  The win frequencies for a session were 70.8% and 58.7%, respectively.  So, even over a much shorter period than multiple lifetimes, we will begin to see a pattern develop whereby the Player loses more sessions than he wins, but can still end up a winner in the long run.

Take A Stroll Through the Casino

It has been more than 20 years since my father, Lenny Frome, began writing about video poker. I think he had two goals when he started. The first was to tell people about this relatively new casino game which had paybacks about as high as any in the casino – and in some cases over 100%. The second goal was to get people away from slots which have arguably the absolute worst paybacks in the casino. Two decades later, it would appear that while much good work has been done, much more is needed.


The most common question I’m asked by friends is “what is the ‘best’ game to play in the casino?” In this case, ‘best’ means having the highest payback. Usually, most people start to answer the question before I can and start with blackjack – which is essentially a correct answer. With a payback of 99.5% (give or take, depending on the rules), blackjack must be described as being one of the ‘best’ games to play. Of course, the original version is a bit slow and requires a significant degree of strategy, but that really isn’t part of the equation at the moment.


Frequently, the next answer that comes up is Craps. This is a bit tougher to size up. Craps is really dozens of different independent wagers so determining the ‘payback’ of Craps is not only difficult (if not impossible), it is also meaningless. Avoid all the proposition wagers with horrible paybacks and you’ll have a much higher payback than the guy constantly buying ‘hard ways’ bets. Craps can be a really fun game with a lively table and when a shooter gets hot. Playing with just a couple of Players and/or during only cold or slightly warm streaks and it I prefer games where you can sit down!


After blackjack and Craps, the person who asked the question finally goes silent. It is almost as if the casino still only has about 4 options – blackjack, Craps, Roulette and slots. Well, I guess the good news is that the silence means the most people have figured out that you’re not going to win money playing slots. As for Roulette, well, it is a bit like Craps, but almost every wager has the same so-so payback. But what about the rest of the casino? Over the past 20 years, the casino floor has changed tremendously. Many of the people who ask me the question do go to the casino. Have they not noticed all the other games?


I don’t know who is more surprised. The person I’m talking to when I say “video poker” or me when they respond “what’s that?” I guess if you’ve always been a table game person maybe you haven’t noticed that not all the ‘slot machines’ look alike. Of course, this was truer when slot machines still had handles and video poker machines didn’t. With the advent of video slots, the casual observer may just see lots of lights and colors on a computer screen and think they are all the same. I’ve spent many columns explaining the vast differences between slots and video poker to need to do so again today.


Once I explain what video poker is to the person who asked the original question, they are even more surprised to find out that a ‘routine’ payback can be about the same as blackjack and that there are still a fair number that can be found that have paybacks over 100%. This, of course leads to an explanation of what it takes to exploit such a Player advantage. Yes, you can probably make 30k-40K a year playing quarter video poker, but it would take playing 40 hours a week in a smoky casino, playing very disciplined and it would be a lot like having a very streaky commission job. You might earn nothing one year and earn 50-60K the next. This is not necessarily an easy job or one suited for anyone. The ultimate irony comes when I find out the person I’m talking to is an attorney, here in the NYC area, who is probably pulling down at least a few hundred thousand a year. I don’t think he’s giving up his day job!


So, I guess after more than 20 years of trying to get people to break the slot habit, we can confidently say we have achieved some success. I think the number of people who think that they have a shot at the slots has gone way down. At the same time, the campaign to keep teaching people about all the other games in the casino goes on. From video poker to blackjack to many of the newer table games that offer higher paybacks than the traditional casino games – many while offering a good deal more excitement too. The next time you head out to the casino, before you sit down to play, just walk the casino floor and check out all the games you may not have known existed. Then, to learn more about it, head over to my website and there’s a good chance I already have written about it. If not, feel free to drop me a line and I’ll do my best to cover it in the near future.