SCIENCE FICTION: BELIEVING YOU CAN WIN AT SLOTS

            When I tell people that I help develop new games for the casino industry by doing the math behind them, I'm invariably asked if I work mostly on slot machines.  Ironically, I've never worked on the math behind slot machines.  I try to explain that in my opinion slot math is amongst the easiest math in the casino. 

            Developing a casino game is really two parts.  The first is the creative half that determines the specifics of the game. The second part is the math behind the game, which can frequently cause some changes in the first part.  This dependency mostly evaporates with slot machines.  Virtually every slot machine is a clone of another game from a math perspective.

            I'm a big fan of science fiction.  So, if I wanted to invent a slot machines based on Star Trek, I merely need to come up with 20 to 30 symbols that are identified with the shows.  Maybe I use the characters (Captain Kirk, Mr. Spock, etc...) or I use the different shows (the original Star Trek and The Next Generation).  It really doesn't matter.  Most importantly, I simply have to decide what determines a winning hand.  I list out all the winning hands on a spreadsheet.  I add the amount each of these winning hands should pay.  I then determine the frequency that each of these hands occur.  I do a few simple computations and play with the numbers to get a payback to my liking and I'm done.

            Now I'd like to create a slot machine based on Star Wars.  I don't need to change any of the numbers.  I just simply need to swap out Mr. Spock for Hans Solo and Captain Kirk for Luke and I'm done.  In theory, every single slot machine could be based on a single spreadsheet of probabilities and payouts. 

            How can this be done?  because essentially, slot machines are rigged.  No, they don't know who's playing, so it's not like someone with a Player Card is going to lose and someone without one is going to win.  Nor can it tell the difference between a local and a tourist.  When I say it is 'rigged', I mean that nothing about a slot machine conforms to the notion of what you see is what you get.  When you spin the wheels, you may see more Captain Kirks than any other single symbol, but that doesn't mean the probability of lining them up is any higher. 

            In that little spreadsheet I mentioned earlier, I need to list out all the losing hands too.  The slot could simply be programmed to randomly pick a losing hand a certain percent of the time, but what fun would that be?  Instead it is programmed to give you Captain Kirk, Captain Kirk, Tribble more times than you can count.  Just for good measure there will be a Captain Kirk above or below that Tribble 50% of the time.  OH, you were SO CLOSE to winning!  In reality, you were just as far away as if the screen showed, Klingon, Romulan and Ferengi!

            To put it in more familiar terms, just because the screen showed you 7-7-orange with a 7 just below the orange doesn't mean you were any closer to winning than if it showed Orange-Plum-Banana.  If you kept drawing the fruit salad, you might get bored and leave.  But by showing you 7-7-orange, you get a false sense that you just missed.

            I would love to hear from those of you who are reading this column who continue to play slot machines.  Why do you do this?  The average slot machine in Las Vegas pays about 92.3% which makes it about the worse play in the casino.  I supposed it is fun to sit down and play a slot machine with your favorite tv show on it, but is it really worth all that you are losing?  Wouldn't it make more sense to learn to play video poker or blackjack and simply buy the complete series of your favorite show on Amazon with the money you're saving?

            Maybe Ballys and IGT should introduce video poker that is themed to tv shows and movies?  They just simply need to make the deck take on the theme of whatever show we are talking about.  Imagine Batman Joker Poker where the Joker is the actual Joker from the show.  Batman can be the King and Robin can be the Jack.  Batwoman can be the Queen!

            These characters won't change the game any, which is what happens in the slot versions too.  Maybe we can get more people to give up slots and become video poker Players if we simply put their favorite characters onto the cards? 

            As we head into 2012, I don't really care what gets you to break the slot habit, I simply implore you to do so.  In the end, I think you'll have a lot more fun and your wallet will definitely thank you!

The Details Behind the Advice

I’ve spent the last couple of weeks trying to get the beginners among you to make a relatively simple adjustment to your strategy. It involves four relatively common hands – high pair, 4-card flush, low pair and 4-card straight.

As I explained last week, they are played in this order because of their expected values. This week, I will walk through the calculation of the expected values for each of these hands.

HIGH PAIR

We start with the easy one first. It is easy because EVERY high pair has exactly the same Expected Value (EV). Since we already have a pair of jacks or better, we don’t have to worry about what are the specific cards discarded as they cannot help the hand nor interfere with other hands being formed.

When dealt a high pair, we will draw three cards. There are 16,215 combinations we can then draw from the remaining 47 cards in the deck (47 choose 3). Let’s look at the results of all of these draws:

45 will result in a four of a kind paying 25 each for a total of 1,125.

165 will result in a full house paying nine each for a total of 1,485.

1,854 will result in a three of a kind paying three each for a total of 5,562.

2,592 will result in a two pair paying two each for a total of 5,184.

11,559 will result in a high pair paying one each for a total of: 11,559.

The Grand Total is 24,915.

We divide the grand total by the number of combinations to arrive at the Expected Value of 1.5365. Every high pair has this exact EV. By itself, this number means relatively little in terms of our strategy.

Yes, it does tell us that we can expect to win about 1.5 units back when we have a high pair, on average, but it doesn’t tell us if we should play a 4-card flush or a high pair when we have both.

LOW PAIR

This will generate very similar results to our high pair. The only (and very BIG) difference is that all of those high pair hands at the end will now end up as low pairs and pay nothing. Thus, we will have a grand total of only 13,356, which when divided by 16,215 gives us an Expected Value of 0.8237.

4-CARD FLUSH / STRAIGHT

The 4-card flush and the 4-card straight each have 47 possible draws. The flush can result in nine flushes paying six each – for a total of 54.

The straight (NOT INSIDE) can result in eight possible straights paying four each for a total of 32. However, depending on how many high cards each has, it may be possible to wind up with a high pair as well.

For each high card that is in the 4-card flush or 4-card straight, three additional hands can wind up as a high pair instead of a losing hand. These additional three units when divided by 47 possible combinations means that each high card adds about 0.0638 to the Expected Value of our 4-card flush or 4-card straight.

So, a 4-card flush with zero high cards has an expected value of 1.15 (54 divided by 47). If there is one high card, we add .064 to this to get to about 1.21. With two high cards it climbs to about 1.28.

With three high cards – well, we would have a 3-card royal and that’s a whole different hand! So, a 4-card flush has an EV of somewhere between 1.15 and 1.28.

Since no other hand has an EV in between these two, we don’t bother separating these hands out on our strategy chart. Instead, we take the average of ALL 4-card flushes and say that its Expected Value is 1.22.

With regard to a 4-card straight, the Expected Value with zero high cards is a paltry 0.68. With one high card it goes up to 0.74. With two high cards it goes 0.81 and with three high cards to 0.87. Technically, a 4-card straight with 4-high cards is an inside straight (only one way to complete it) so its EV is much lower.

Because numerous other hands, including our low pair have an Expected Value in this same range, our strategy table shows each of these hands separated out.

So, when we look at all of these hands and rank them from high to low in terms of their Expected Values, we come up with the following:

High Pair: 1.54

4-Card Flush: 1.22

4-Card Straight with three high cards: 0.87

Low Pair: 0.82

4-Card Straight with two high cards: 0.81

4-Card Straight with one high card: 0.74

4-Card Straight with zero high cards: 0.68

It is based on these Expected Values that our strategy is derived. I’d like to raise two final important points. First, note that the 4-card straight with three high cards actually outranks the low pair – which is in conflict with the simple rule I gave two weeks ago.

While you should play this 4-card straight OVER the low pair, this particular combination is so rare that ignoring it while you work on learning the strategy will not cost you much. The ONLY way this hand can occur is 10-10-J-Q-K.

This leads to the second important point. For the purposes of this part of the strategy, ALL of our 4-card straights are outside – meaning they can be completed on either end. The other type of straight is an "inside," which has a gap in the middle or has an ace on one end or the other.

These can be completed only one way and have a much lower Expected Value. In Jacks or Better, most inside straights are not even playable.

I’d like to take this opportunity to wish everyone a Happy and healthy New Year and remind everyone to make their resolution to break the slot habit in 2012!

Clarity on a Little Advice

Last week’s column gave some simplistic advice to beginners who are not yet ready to sit down and really learn the strategy for video poker. It discussed the relative rankings of four of the most common hands – high pair, four-card flush, low pair and four-card straight.

While I gave the expected values for each of these hands, along with some explanations as to why the rankings are what they are, this week I want to stress that these explanations are not the critical part of the process.

The strategy for video poker is based on one thing – math.

We don’t keep a high pair over a 4-card flush because the high pair is a sure winner. If this were the case, we’d keep a high pair over a four-card straight flush, too (but we don’t!). The fact that the high pair is a sure winner explains why its expected value is as strong as it is, but it is the actual value of this expected value that puts the high pair where it does.

So what is this "expected value" I keep talking about?

It is the average amount of coins we expect to win over the long run from that hand.

How is it calculated?

It is calculated by looking at EVERY possible draw given the 5-cards already dealt.

Say what?

There are 2,598,960 ways to deal five cards from a 52-card deck. For each of these ways, there are 32 different ways to play each – ranging from discarding all the cards to discarding none of them. For each of these 32 ways to play a hand, there is a varying number of possible draws.

If we discard one card, then there are 47 possible draws (each of the 47 remaining cards). If we discard three cards, then there are 16,215 possible draws (choosing three cards from 47). A computer program goes through every possible draw and tallies up the winning hands for each of the 32 ways to play a hand.

It then computes the average number of coins returned for that way. This is the expected value for that particular way of drawing. It compares the expected values for each of the 32 ways and whichever has the highest one is the proper play for that deal and is deemed the expected value for that deal.

An example usually helps to shed some light on this process. Assume you are dealt: 4 of clubs, 5 of hearts, 5 of clubs, 5 of spades, 7 of diamonds.

We recognize the three-of-a-kind (5’s), the EV of which is calculated as follows:

Drawing two cards from the 47 remaining in the deck will create 46 four-of-a-kind winners (a five combined with each of 46 remaining cards). Sixty-six draws will end as full houses (six pairs in all ranks but 4, 5, and 7; 3 pairs of 4 and 7) while the remaining 969 draws do not improve the hand but instead leave it as a three-of-a-kind.

In summary we have:

46 4-of-a-Kind paying 25 each,

66 Full Houses paying 9 each,

969 3-of-a-Kind paying 3 each,

We calculate the total payout as 4,651, which is an average of 4.30 for each of the 1,081 possible draws. Therefore, the expected value of this deal/draw combination is 4.30.

As should be fairly obvious, if we try to play this hand in any of the other 31 ways, the expected value will NOT be any higher than 4.30 and thus this is also the expected value of this deal.

As all three-of-a-kinds have exactly the same expected value, this is ALSO the expected value of all. We will find this value on our strategy table.

Next week, I’ll walk through the four hands (high pair, low pair, four-card flush and four-card straight) I used in last week’s column. This will explain why the strategy I described last week doesn’t just make some sort of logical sense but is the right play mathematically.

I’d like to take this opportunity to wish everyone a happy holiday and a very happy and healthy 2012!

A Little Advice

            Last week's column was a gambling related philosophical debate about perfect vs. good enough.  This week, I'm going to the other end of the spectrum.  It is nearly impossible to define a 'bad' strategy as there really is no end to how bad a Player can play most games.  Playing every hand in Three Card Poker would probably meet the definition of a bad strategy, but is it worse than Folding every hand below a Pair?  Probably not, and I'm not going to waste my time to try to find out.

            This is not to say that every strategy that isn't perfect or as per last week's column 'good enough' would necessarily meet the definition of 'bad'.  I don't consider playing Three Card Poker with the strategy of Play any hand with a Queen to be good enough, but I can't really call it a bad strategy either.  With a game like Three Card Poker, there isn't really much to learn so you draw your line in the sand where you do and that's how you play it.

            A game like video poker is far different.  For anyone that doesn't use Expert Strategy, you might be hard pressed to find two people who used identical strategies.  In reality, they may be TRYING to use Expert Strategy (or some other particular strategy) but due to its complexity, they make a variety of errors along the way.  Then there are the multitudes of Players who just play by the seat of their pants, pretty much oblivious to the math that should be guiding them.  To these Players, getting them to even good enough will be quite a challenge.

            But, no matter what level they play at, if they just learn a few simple strategy points that might help them get a little closer to Expert Strategy then at least it is a step in the right direction.  So, today's column is for these Players.  I would like you all to consider learning just this small part of the strategy and trying to implement it.  You may still be a long ways away from playing Expertly, but hopefully, we can save you just a few bucks along the way and add to your enjoyment too.

            Here goes:

            1)  High Pair

            2)  4-Card Flush

            3)  Low Pair

            4)  4-Card Straight

            This strategy only means something on the hands that are either a 4-Card Straight or a 4-Card Flush and are also a Pair.  Approximately 25% of all 4-Card Straights and Flushes fall into this category, so these hands are fairly common.  This is why it is imperative that these hands be played correctly.  Let's take a closer look at why you should play the hands as described above and learn how these are NOT close calls.

            The High Pair is the only sure winner in the bunch, but this is NOT the reason it is at the top of the chart.  The determining factor is always the expected value of the hand, which is the average amount we expect to win with that hand over the long run.  Sometimes, the sure winner is not the right answer, but in this case it is.  The expected value of our High Pair is 1.54 which reflects the opportunities to turn this into Two Pair, Trips, Full House and Quads. 

            Next up is the 4-Card Flush which will win for us in the long run.  This is NOT to say that we will have more winning hands than losing hands.  With 9 opportunities to complete a Flush and perhaps a few more to complete a High Pair (depending on the exact makeup of the 4-Card Flush), we can expect to win with this hand only 20-30% of the time.  But since many of these will win with a Flush, the wins will be significant.  The expected value of a 4-Card Flush is 1.22.  It will be a smidge higher if you have 1 or 2 High cards and a bit lower if you have none.  If you have 3 High Cards, you have a 3-Card Royal and that takes precedence over the 4-Card Flush, but not the High Pair.

            While the Low Pair has the exact same probabilities as the High Pair of winding up as Two Pair, Trips, Full House or Quads, the fact that it starts as a losing hand is enough to bring its expected value all the way down to 0.82.  That means in the long run, this is a losing hand.  It is the second strongest losing hand (behind the relatively rare 10-J-Q-K Straight, which is also the ONLY exception to the rule I'm presenting here as you hold this 4-Card Straight over a Low Pair, which can only happen with a Pair of 10's).  The Low Pair is also BY FAR the most common hand in video poker, accounting for nearly 30% of all hands.

            Lastly, we have the 4-Card Straights.  While a 4-Card Straight with 2 High Cards ranks only slightly below the Low Pair with an expected value 0.81, it is still below it.  It only gets worse with 4-Card Straights with 1 High Card or 0 High Cards with expected value of 0.74 and 0.68, respectively.  These may not seem like big differences, but they will eat at your bankroll over time.

            It would still be far better for anyone reading this to become a truly Expert Player, but any improvements in your strategy are still better than none.  To help you on your way, we continue with our holiday special.  We are offering Winning Strategies for Video Poker, Video Poker: America's National Game of Chance and Expert Video Poker for Las Vegas for $5 each, which includes postage and handling.  Feel free to order as many as you'd like as they make great stocking stuffers!  Send a check or money order to Gambatria, P.O. Box 36474, Las Vegas, NV 89133.  We'll do our best to get them to you before the holidays.

            

Perfection is the Enemy of Good Enough

            Recently, while my teenage son and I were debating something, he responded with "perfection is the enemy of good enough."  My initial response was to shoot back "good enough is the enemy of perfection."  Since this highly philosophical discussion, I've given both of these phrases a lot of thought.

            I'm very well aware that I am a perfectionist who was raised by a perfectionist.  If you brought home a 99 on a test, my father wanted to know why you didn't get a 100.  If there is such a thing, however, as a realistic perfectionist, I think both by dad and I would qualify.  We strive for perfection, but also realize that it is often not realistic to truly attain it all the time.  I think this is why I found the aforementioned quotes to be both interesting and a little befuddling.

            My initial reaction that good enough is the enemy of perfection goes to my basic notion that we should always strive to be perfect.  Over the years, I've been asked many times regarding the strategy for Three Card Poker and if it really matters if you go with Q-6-4 or just Q-High.  The impact to payback is barely noticeable.  You might play for hours before getting a hand that Plays under one strategy but not the other.  Yet, the notion of settling for the easier Q-High frustrates me so.  Clearly the strategy is 'good enough.'  But, is remembering Q-6-4 SO hard that you one needs to go with Q-High?  To me, this is a case where good enough became the enemy of perfection.

            There were times my father's work on video poker was criticized (mildly) by other analysts for being less than perfect.  On one hand, my father was not prone to doing things less than perfectly - especially math work.  On the other hand, he taught himself how to program a computer at age 60, so this was not totally his comfort zone.  In a nod to that realistic perfectionism I mentioned earlier, my father's strategies for video poker were not designed to be 100% perfect.  They were designed to be played by humans.  And, not a bunch of rocket scientists, but the masses.

            The process that my father used to analyze video poker was rather similar to the same one I use, which is most likely not all that different from the ones created by anyone else.  We all have different degrees of shortcuts we use to speed up the process but the basic idea is the same.  We look at each of the 2,598,960 possible initial 5-card deals from a 52-card deck.  We then analyze each of the 32 possible ways to discard and review each of the myriad ways to draw to each of these 32.  Whichever of these 32 ways results in the highest expected value is the proper way to play the hand. 

            The calculation to do the above is absolute and assuming no error in the process will be 100% accurate.  In other words, it will be PERFECT.  So, in a perfect world, a Player could sit down at a video poker machine, press the Deal button and then enter the five cards he was dealt into an APP on his phone, which would run the process I just mentioned and tell him exactly which cards to discard.

            Unfortunately, the casinos are not too keen on this idea.  In fact, I was recently sitting at a Blackjack table and pulled out my phone to check e-mails while the Dealer was shuffling and got reprimanded.  I knew you couldn't use such devices at the table, but I assumed this meant while the game was in progress, not while waiting for the shuffle!  So, sitting at a video poker machine with your tablet in your hand will probably not be allowed.

            Because of this, the next best thing is that the results of analyzing all of these hands need to be summarized a bit.  This is what we call a strategy table that lists the rankings of all the hands in order of their expected value.  Certain hands become essentially 'exceptions to rules' when we try to summarize the hands.  These exceptions could be listed as their own rows on the strategy table, but what would the impact be if the strategy table grew to be 50 or 60 rows instead of the usual 35 or so?   By ignoring these exceptions we cost ourselves MAYBE 0.01% or 0.02% of payback, but we greatly simplify the strategy table, thus reducing the probability of errors.

            In this case, my son was right as perfection could be the enemy of good enough.  My father could have put together a perfect strategy table, but if learning it became that much harder so that the likelihood of errors increased to the point where an average person would lose more in errors than he would gain in playing 'perfectly' - would this still really be 'perfect'?

            At the end of the debate, it would appear that my father had already resolved the issue for us - and we were both right!

            As we are approaching the holiday season, Gambatria would like to offer to all of our readers a deal that may not be perfect, but is certainly better than good enough.  We are offering Winning Strategies for Video Poker, Video Poker: America's National Game of Chance and Expert Video Poker for Las Vegas for $5 each, which includes postage and handling.  Feel free to order as many as you'd like as they make great stocking stuffers!  Send a check or money order to Gambatria, P.O. Box 36474, Las Vegas, NV 89133.  They'll ship 1st class mail (or priority mail in some cases) so you can get them in time for the holidays.

Vintage Lenny Frome - Video Poker is NOT Slots!

This article was first published in about 1992 by my father Lenny Frome.  Keep that in mind as you read through some of his comments and realize just how much has changed in the nearly 20 years since!

Video Poker is NOT Slots!

by Lenny Frome

            Every time we write a column for a new publication, we do so with a great deal of uneasy feeling.  After all, the readers who pick up this journal after a session at the poker tables or in the Bingo parlors look at Video Poker players with disdain.  No matter how special we consider our machines, they look at them as "just slots".

            In 1988 Las Vegas had a poker room paper called of all things, POKER ROOM. Within days of accepting our very first Video Poker article, the publication closed its doors. Imagine our guilt feelings as we contemplated that just planning to put Video Poker into print could cause a gambling paper to close. Maybe they were "just slots" then.

            In the four short years since , Video Poker has come of age.  From just a handful of game versions, there are at least 50 unique versions, which with their various pay-tables, create literally hundreds of different games.  Today, the term "Video Poker" doesn't hardly give a clue as to what kind of game we're referring to.

            The public by and large has learned to respect this family of games for several reasons. Most analysts attribute its popularity to the man-machine interaction--the decision making by the player which affects the outcome.  Others claim the players enjoy their privacy and are never intimidated.  Those reasons don't satisfy me because for a long time Video Poker languished in Las Vegas.  When the machines paid on on two-pair or better, they were a drug on the market.  Nobody knew how to play them and even when they did approach expert play, the payback of 90% disenchanted the public.

            When the pay-table was revised to pay on Jacks or Better, the public flocked to them.  Nobody, including the casinos really could explain this phenomenon because it took quite a while before the 99.6% payback on expert play was proven.  Meanwhile, the public could sense that they won much more often and played longer.  In the long run, players still left money in the machines but they enjoyed the time on them.  Today, one-third of casino revenue is derived from Video Poker.

            Outside of Las Vegas the payback is necessary lower which makes it even more important for players to learn how to play correctly.  To become a good player is easy once becomes be aware of several key factors:

          ELEMENTS OF EXPERT VIDEO POKER PLAY

(A)  The game is governed purely by known mathematical probability;  if you don't believe that, you cannot become a good player.

(B)  Once the deck is defined and a pay-schedule displayed, the optimum strategy for hold/discards on every hand is known, along with the payback percentage and the average number of each level of winners.

(C)  Unlike reel-slots, which can have their payback altered almost at the whim of the casino with absolutely no warning to the players, Video Poker payback is not variable unless the posted rules and/or pay table is revised.  Stated another way, all machines which play the same game and have the same pay table, must have the same payback.

(D)  It follows that players can tell which machines are the most liberal and can learn the strategy to optimize the payback.

  

(E)  The essence of Video Poker strategy is that every hand must be played (cards held) in the way that the hand has the maximum win-potential.

(F) The win-potential of a hand is indicated by a numerical value known as EXPECTED VALUE (EV). Players do not have to remember exactly how EV is derived  or even what the EV of any hand is, but they have to know the proper way to hold/discard so that the EV is highest.

(G)  Once the deck and paytable are defined, a ranking table is available in Video Poker books which shows the way to play every hand that can be dealt and played in that version.

            Learning the ranking tables is a lot easier than you might imagine since most hands are playable in only one way, which is obvious.

            We'll continue this treatise soon; in the meantime, practice on the kitchen table by dealing out 10 cards, five down and five up on top of them. That's how the machines do it. Rember that the caveat "Play With Your Head" translates into "Learn How First".

Giving Thanks

            I apologize to those of you who have been looking for my column the past couple of weeks and couldn't find it.  As some of you may have heard by now, my mother (and wife of Lenny Frome), passed away two weeks ago.  After the funeral, my brother recounted a story to me that I had never heard before.

            When my father passed away in 1998, my brother was the first one who headed out to Las Vegas to be with our mom.  It took a day or two before all the arrangements were made for them to come back East for my dad's funeral.  Yet, of course, they still had to eat.  My brother asked my mom where she wanted to go to dinner and she responded with Hugo's Cellar at the Four Queens.  My family had already made that a regular dinner spot when anyone came to town - and it is a tradition that carries through until today. 

            As they walked through the casino from the parking garage to the restaurant, they passed by two women playing video poker.  They were each holding a copy of one of my dad's books.  My brother said he could not have staged it any better if he tried.  This was clearly a sign.  My father's impact to the industry would continue long after he was gone.

            My father was informally called "the Godfather of Video Poker" by many in the industry.  To be sure, he played NO part in the invention of the game.  At the same time, no one can deny the impact he had on popularizing it.  Even if you are not a video poker expert or even a regular, I can't help but imagine that your play isn't just a tiny bit better from having read his articles - or any of the numerous writers who came after him - including me!  Would video poker have had the staying power if there wasn't someone telling the early Players how to play it?  Would video poker have eaten up as large a percentage of the casino floor as it does today?

            Of course, my father could just have easily been called "the Godfather of Proprietary Table Games".  He had a hand in the development of Let It Ride, Three Card Poker, Spanish 21 and Caribbean Stud Poker.  At their respective peaks, there must have been a combined 2500-3000 of these tables.  As I consider myself an extension of my father's work, we can add on Ultimate Texas Hold'em, Mississippi Stud and a host of smaller games to the total.  This brings the total to perhaps as high as 4000 proprietary tables that my father directly or indirectly had a hand in.  Imagine the casino floor without any of these games.

            While my father was the public face of everything that went on, everyone that knew them (both personally and professionally) knew that my parents were always together.  My dad brought my mom to business meetings to size up the potential client.  My mother was the proofreader for all of my dad's books and booklets.  She was responsible for shipping orders and for the accounting.  In fact, it was my mother who was always listed as the "President" of their company. 

            With the help of Catherine Jaeger, the editor of Midwest Gaming and Travel, we have launched a campaign to get my father into the American Gaming Association's (AGA) Gaming Hall of Fame in 2012.  No disrespect to Blue Man Group (one of the inductees for this past year), but I truly believe Lenny Frome's impact on the industry has been far greater.  To this end, we are asking people to write to the AGA and urge them to induct my father into the Hall of Fame in 2012.

            There are a number of ways to make your voice heard.  You can copy the sentence below or use your own experience to explain why you believe the time has come for Lenny Frome to be inducted into the Gaming Hall of Fame. "Because of his many significant contributions to casino gaming, I respectfully request your consideration of Lenny Frome for induction into the Gaming Hall of Fame."

Mail it to:
American Gaming Association
Frank J. Fahrenkopf, Jr., President/CEO
1299 Pennsylvania Avenue, NW, Suite 1175
Washington, DC 20004

Online:
E-mail to:
Brian Lehman/Communications Manager-AGA
blehman@americangaming.org
Facebook: www.facebook.com/AmericanGaming

            Over this Thanksgiving weekend, my family and I one again dined at Hugo's Cellar.  This time, for the first time we toasted the memory of both my father and my mother.  My dad may have been the "Godfather of Video Poker", but most importantly, they were the "Father/Mother and Grandfather/Grandmother of the Frome family."  Once again, they are "always together."

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 Godfather of Video Poker

The November issue of Midwest Gaming and Travel is a tribute to my father, Lenny Frome.

I'd like to thank Catherine Jaeger (the editor) for coming up with this idea and using it as a means of launching a campaign to have my father inducted into the American Gaming Association's Gaming Hall of Fame.  Here is a little bit more about this campaign - Make 2012 Lenny's year!

My father changed the landscape of every casino in the world by helping to make video poker as popular as it is.  He also provided the original analysis for games like Let It Ride, Three Card Poker, Caribbean Stud Poker and Spanish 21.  Imagine the casino floor without any of these games.

Below is a link to the article I wrote for Midwest Gaming and Travel about my dad.

The Godfather of Video Poker

Video Poker Progressives

            A couple of weeks ago, I described in detail how the math behind Progressives work.  In that column, I mentioned how video poker progressives works just a little different.  There are still two paybacks to be concerned with - the long term theoretical that the casino is concerned with and the specific payback at any point in time that should be the attention of the Player.  The majority of the calculation is still the same in that we multiply the payout of a winning hands by the frequency of the winning hands  and sum up these values.

            What is different about video poker is that the frequencies of the different winning hands can vary as the amount on the meter changes.  For those of you who are video poker Players, this should be no surprise.  For years, I've been telling you that a single unit change in the payout of a hand not only changes the payback but can change the strategy.  Each time you change the strategy you potentially increase the frequency of some hands at the expense of others.

            As a very simple example of this, imagine how the strategy changes as we go from a standard full-pay jacks or better machine to a Double Double Bonus machine.   Because the payout for Four Aces is so high, we actually find that the Player should discard Two Pair in favor of a single Pair of Aces.  This will obviously reduce greatly the frequency of Two Pairs and Full Houses and increase the frequency of Three of a Kinds and Four of a Kinds. 

            So, it should be no surprise that as the jackpot for a Royal increases above 800 that the strategy will begin to shift.  Hands with the potential to be a Royal will have their expected values increase.  This will lead to more Straights, Flushes and of course Royals and the expense of Pairs, Trips and Quads.  Of course, we will also throw away a variety of partial Straights or Flushes to go for the Royal, so this will work against the Straights and Flushes and might increase the number of High Pairs. 

            Thus, pinpointing the exact frequencies can be a bit tricky.  Fortunately, the far easier of the paybacks to determine is the payback at any point in time.  This is because at any point in time, we can know the exact amount of the Progressive jackpot and use this number to determine the exact strategy and in turn the exact frequency of each hand.

            The most common video poker Progressive is an 8-5 machine, meaning it pays about 97.3% when the jackpot is reset to 800 (per unit wagered).  At this level, the frequency of the Royal is about 1 in 40,200 hands.  If the jackpot were to climb to 1600 (per unit wagered) then the payback of the game will go up to about 99.5% and the frequency of the Royal goes up to 1 in 32,700 hands.

            Of course it is rather unlikely that you're going to see a Progressive for a Royal get this high.  With only 1% of the amount wagered (at most) going to the meter, the average amount that will be added to the Progressive Jackpot is somewhere between $327 and $402 (1% of the previously mentioned frequencies).  Of course, something that can occur 1 in 40,000 hands or so can easily occur every 10,000 hand or 80,000 hands.  So, it is not impossible to see the progressive meter go to 1600.  It would have to go to about 1800 for the game to become positive (payback over 100%).  This is not impossible, but not very likely.

            As the payback goes up, the strategy changes and the frequency of the Royal increases, making it harder and harder for the jackpot to keep increasing as the likelihood that it gets hit goes up.  Because of this, it is a bit harder to calculate easily the long term theoretical payback.  It is reasonable, however to approximate it using the same process used for regular progressives.

            In this case, I would take the frequency of each hand using the reset value of the jackpot and multiply each by the payout of the hand and sum these up.  Lastly we would add the percent of each wager going to the jackpot to the total.  This means that the long term theoretical payback of a Royal paying 8-5 with an 800 unit reset amount is about 98.3%.

            I have to admit, if I were designing a paytable for a video poker progressive, I would probably make the likelihood of the game going over 100% a bit more common.  I think it would be a lot of fun to the frenzy that would/should occur each time the payback at any point in time goes over 100%.

            

Vintage Lenny Frome - A's and 8's

When I have time I'm going to try and post up some of my father's (Lenny Frome) articles here as well.  The following article is about a rarely found (but I'm told there are still a few 50-cent machines at Circus Circus) version of video poker - Aces and Eights.  Its payback is about 100.25%.  This article is probably 15-20 years old, so some of the information may be dated:

Aces and 8's--From Green Felt to Video  

             Long, long ago before the world played Video Poker, the story of Aces and Eights, the dead man's hand was abroad in the land. It always conjured up a mental image of evil-- a hand that brought fear into the hearts of men, even the roughest, who made a living with the pasteboards and reckless gun slinging.

             Leave it to the enterprising folks at CircusCircus to capitalize on this theme and then carry it out in high-tech fashion under their big top. They have come up with a sure winner in Aces and Eights, a 100% payback machine featuring four progressive Jackpots as added attractions which will frequently push the payback into positive territory.

            The pay schedule  is very straight-forward for a multi-progressive (or is it just that we are getting adjusted to the new regimen in such lengthy tables?)  It is an 8/5 schedule Jacks or Better with these four bonuses to offset the 2.3% shortfall vis-a-vis full-pay 9/6ers:

·         Four 7's pay 50 for 1 on 1 to 5 coin-play non-progressive.

·         Four 8's or Four Aces pay on a single progressive which resets at 80 for 1 (5-coin play only).                

·         A Royal Flush pays on an 800 for 1 minimum progressive jackpot.

·         Sequential Royals (either way) pay on a 10,000 for 1  minimum progressive

Looking at the payback situation, these bonuses work into the picture this way:

            Four of a Kinds in any one specified suit occur on average only  once in 5,500 hands; a regular Royal once in 40,000 and in either    sequence once in 2,400,000 hands.  The extra 25 on the 7's adds .47%. The extra 55 on the 8's adds a  minimum of 1% as does the extra 55 on Aces. The Sequential Royal gives us an extra 9,200 which is worth .38%. As the meters climb  upward the value of these jackpots further increases the payback. Together, these bonuses,  take the payback up from 97.3% to 100.15%. With some minor changes in strategy, we can pick up a little bit more.

            The first time we saw this machine, the Sequential was posting $13,204, the Royal  $1,030 and the Four Aces or Eights a whopping $154. The game was close to 102% payback. While watching it, the jackpot was hit on 8's by one of the players seated at about 50 machines on the floor.  The Aces/Eights progressive had gone an unusually long time since the last hit. We cannot expect many such generous jackpots. Frankly, we were genuinely surprised when the meter reset at $100, since that is more than three times the 25 for 1 normally paid on quads.

            Even with this liberal machine we need all the savvy we can muster to play the game expertly. The extra value of Aces and 8's dictates these modifications in the ranking order of 8-pairs: Even at minimum meter value of $100 on a quarter game (80 for 1), the pair of 8's is better than a 4-low-card flush and at $120 beats those 4-card flushes with two high cards.

            Incidentally, the player who hit the $154 would have been right in breaking up 8's full to go for the quads. I'm happy to report that it wasn't necessary to wrestle with that problem--but if it were you, what would you have done?

 

Progressing

            Last week, I alluded to the seemingly complex math associated with games that offer progressive payouts (i.e. "progressives").  Progressives are games where the top pays are not fixed dollar amounts or odds payouts, but rather have variable payouts that increase as more wagers are made since the last time the prize was won.

            Progressives have become very popular for table games sidebets.  They have long been used for some video poker machines for payouts on Royal Flushes.  Most commonly they are found on slot machines, which love to use a progressives ability to create a very large payout for a very rare occurrence.  As is always the case with a random event, the cycle between hits can frequently become far larger than 'average' and thus create an even larger than normal jackpot.

            As I described last week, Progressives essentially have two different paybacks.  The first is the long-term payback which is what concerns the casino.  The second is the payback of the wager at any point in time which is what should concern the Player.  Let's take a closer look at how these are calculated and why there are two different paybacks.

            Normally, to calculate payback, we take the frequency of a winning hand, multiply it by the payout of this hand which gives us the contribution rate for the hand.  We then sum up these contribution rates to arrive at the overall payback.  For most wagers, the frequency of a particular winning hand is fixed as it is unaffected by strategy.  So, if we are playing Caribbean Stud Poker, we don't have to worry about the strategy of Folding and Playing for the sidebet because you would never Fold a hand that is strong enough to earn a bonus.  Video Poker presents an additional challenge in that you can alter you strategy depending on the payouts and thus alter the frequency of winning hands.

            So, to calculate the payback of a Progressive at a particular point in time, we follow the calculation I just described.  For example, let's assume the following paytable at a particular point in time for a $1 wager:

Hand	Pays (For 1)
Royal Flush	$113,473
Straight Flush	250
Four of a Kind	50
Full House	10
Flush	7
Straight	5
Three of a Kind	3
Two Pair	2

           

            If we perform the calculation described, we get the following:

Hand	Frequency	Pays (For 1)	Contribution Rate
Royal Flush	0.00015%	$65,473	10.07680%
Straight Flush	0.00139%	2500	3.46292%
Four of a Kind	0.02401%	250	6.00240%
Full House	0.14406%	50	7.20288%
Flush	0.19654%	20	3.93080%
Straight	0.39246%	15	5.88697%
Three of a Kind	2.11285%	10	21.12845%
Two Pair	4.75390%	5	23.76951%
Total	7.62536%		81.46074%

            So, if you were to walk up to a table and see these payouts, the payback of the game at that very point in time is 81.46%

            But, the payback to the casino could be vastly different.  Let's assume that the Royal Flush is seeded at $50,000.  This means that every time someone wins the jackpot, the prize for the Royal Flush will be reset to $50,000.  Further, let's assume that for every $1 wager that is made, the Progressive increases by 10 cents (i.e. 10% of the wager).

            There are two changes that we must now make to calculate the payback for the casino.  The first is that we always use the seed amount as the payout for that hand.  Thus, we repeat the calculation shown above but we use $50,000 as the payout for the Royal Flush.  This is the amount that the casino itself directly paying out each time the jackpot is won.  When we do this, we find that the payback of this wager is 79.08%.

            However, we must now ADD to this payback the amount of each wager this added to the Progressive meter - in this case 10%.  Eventually this 10% will go back to a Player.  It might happen while the jackpot is at $50,000.10 or it might happen when it is at $120,000 or more.  From the casino's standpoint, it doesn't matter.  That 10% belongs to the players.  Essentially all the Players that don't win the jackpot are handing those dimes to the person who finally does.  So, when we add that 10% to the 79.08% we find that to the casino this wager really has an 89.09% theoretical payback.  Over time, the casino will keep 10.91% of every dollar wagered.

            So, if you were to play this wager while the Jackpot is $65,473, you would actually be playing it on the 'low side' of the average jackpot.  How big is the average jackpot?  To calculate that, we take the average number of hands between jackpots (in this case 649,740) and multiply it by that 10%.  On average the jackpot will grow by $64,974 before it is hit.  We add this to the seed amount and find that the average jackpot will be $114, 974.  At that point, the payback of the wager is the same as theoretical payback of the wager. 

            If the jackpot grows to be above $185,930 (which is very likely at times), then the payback of the wager at that point will actually be OVER 100%.  The only problem with this is that it will only be over 100% for the ONE person who actually wins the jackpot.  Everyone else will just be feeding dimes to the one person who wins.

A Game Changer?

            For more than 20 years, my father and I have implored our readers to kick the slot habit.  The biggest reason for this is twofold.  First, the paybacks on slots are just too low.  If I recall correctly, the State of Nevada reported that the average payback on a slot machine last year was in the 92% range.  You just don't stand much of a chance.  The second reason is that you have no clue what the payback is of any given machine.  So, even though 92% is an average and there might be some games paying even as high at 98% (not very likely), you have absolutely NO WAY of knowing which machine is doing this.  For the moment, I'll leave off that playing a game with absolutely no strategy is not one that I find very appealing to spend my time at.

            Well, this past week at the Global Gaming Expo, I had a conversation with the founder of a company who appears to be trying to change some of these problems with slots.  I find his attempts extremely noble.  I'm not necessarily convinced that the casinos are going to support what he is suggesting - but time will tell.

            The company trying to revolutionize the slot industry is called "Pharos Gaming" out of New York City.  The gentleman I spoke to was Frank Abramopoulos and he is a Director there.  The concept is rather simple.  Every one of their "Open Label" machines is given a unique digital code that is on the screen.  A Player can then access a 'app' on his smartphone and enter this code.  This app will return to the Player significant information about the slot machines.  Most importantly, it will tell the Player the payback of the slot machine.  As the company's slot machines are all single-machine Progressives, it will use the current size of the jackpot to calculate the precise theoretical payback of the machine. 

            With this single concept, Pharos Gaming has eliminated at least one of the basic problems with slot machines.  Any player can now know the payback of a machine instantaneously.   This is certainly progress.  But, even if you know the payback of a game, I don't recommend that you start playing games at 92%.  However, because Pharos Gaming's Open Label machines are stand alone progressives, the true payback of the machine to a single Player is fully dependent on the size of that jackpot at any point in time. 

            So, in theory, a Player can walk up to a bank of machines, punch in each of the special codes and then only play the game that shows a current payback of over 100%.  This has been going on in the video poker world for years.  The only difference is that for video poker, you don't really need a smart phone, you just need to remember the payback of a few base paytables and learn how to approximate the current payback based on a simple formula (I'll cover this again in a future column).  But, progress is progress.

            Explaining the math behind Progressives has always been a tricky proposition.  I have worked on many sidebets for table games that utilize Progressives and I've been amazed at how few in the industry fully understand how it works.  I won't go through the details here, but the short version is that you essentially have two paybacks.  One is the long-term payback which is the one the casino is worried about.  The other is the specific payback at any point in time that the Player should be focused on.  In the end, all the people who play on the Progressive but don't win it are playing below the long-term payback and the person who finally wins the Progressive is playing above it - IF the jackpot grows to be larger than average (which will happen roughly half the time).

            In the case of Open Label, the Players that are oblivious to the feature that allows you to check the payback are essentially feeding the machine so that those that are 'in the know' can come along when the game goes positive and win the jackpot.  This works so long as you have the two classes of Players - oblivious and in the know.  If EVERY Player who ever plays these games became an 'in the know' player, the model would fall apart.  NO ONE would ever play the slot when the jackpot is near the reset value, as the machine would probably be playing at 92% or less.

            So, how does this entire system differ from video poker and its progressives?  From what Frank told me, the Progressives on their open label add a large amount of each wager to the jackpot (he didn't specify specifically how much).  Mathematically, this can increase the likelihood that the game will go positive - assuming the hit frequency of the jackpot is low enough.  The bad news is that the only way to accomplish this is for the base payback at reset to be fairly low.  This requires that they continue to get those oblivious players even while they are marketing towards the more knowledgeable ones.

            In the case of video poker, the payback at reset is considerably higher than its slot machine counterpart and the amount of money added for each wager to the jackpot is relatively small.  Thus, video poker machines do not often get much above 100% (if at all) unless the base game is very close to 100%.  At the same time, this means that the Player who doesn't hit the jackpot is not giving up quite as much to the one Player who does.

            I tip my cap to what Pharos Gaming is trying to accomplish.  Any means by which Players can gain more information about the game they want to play is a good thing.  Also, there is some merit (and profit) in chasing games with paybacks over 100%.  However, a slot is still a slot and your chances of hitting that jackpot will be based 100% on luck.  With video poker, an Expert Player can gain advantage over other Players by modifying his strategy as the jackpot goes up and increase his chances of winning it.

            Despite this change, I still implore you all to kick the slot habit and try video poker instead.  To help you along this path and to celebrate our arrival in Las Vegas, we're offering up some specials!  You can order any or all of our top video poker titles for just $6.95 each - Expert Video Poker for Las Vegas, Video Poker: America's National Game of Chance or Winning Strategies for Video Poker.  Send a check or money order to Gambatria, P.O. Box 36474, Las Vegas, NV 89133.  All prices include shipping and handling.

Total Opposites: Slots and ATMs

I’m writing this article from my new place in Las Vegas! I’ve got boxes everywhere and can’t find half of my stuff, but none of that will deter me from writing my weekly column.

I figure my new beginning here in Las Vegas is a perfect idea for a topic. What should you do when you’re just beginning to go to the casino?

I know one thing you shouldn’t do – play the slot machines. No game requires less knowledge than slots, so that’s why a lot of beginners wind up there. Few, if any, games give you less of a chance to win.

That’s why I think a good place to begin is with video poker. No, video poker is NOT a slot machine. It may look a little like a slot machine, but just because it has a computer screen and some buttons doesn’t make it a slot machine.

Perhaps we should consider ATM machines to be slots as well?

Video poker machines work on a totally different premise than slots. Video poker machines use random number generators to simulate dealing actual playing cards. Slot machines use random number generators to simulate nothing – they simply use it to pick which symbols will appear, but none of it is based on any actual anything.

You see 20 different symbols but that doesn’t mean they will appear with equal frequency. With video poker, you have 52 cards and each one should appear with equal probability.

It is this difference that makes all the difference. Because we know that a video poker machine simulates an actual deck of cards, we can create computer programs and math models to tell us absolutely everything about the machine.

Of course, we don’t know exactly which card will show up when, but we use probabilities to tell us the likelihood of any given card and, in turn, any given hand from showing up. It is from this we are able to develop actual strategies for which cards to hold and which cards to discard.

To start with, we know there are "only" 2,598,960 possible initial 5-card deals from a standard 52-card deck. Each one of these combinations has an equal likelihood of being dealt to the player. For each of these, we know there are 32 different ways to play the hand, ranging from discarding no cards to discarding them all.

Obviously, many of these ways would make little sense. If you are dealt three 6’s, a 10 and a 2, you’re not going to discard the 6’s. But, to be absolutely sure, our computer program takes a look at all 32 ways and determines which is the best way to play the hand.

The value it assigns to each is called the "expected value" or EV for short. The EV is calculated by looking at every possible draw that can occur given which cards were initially dealt and which ones were held.

The program sums up the payouts for each of these hands and divides by the total number of draws. We then look at the expected value for each of the 32 possible draws. Whichever has the highest EV is the proper way to play that hand.

By looking at the results of all 2.6 million hands, we are able to summarize the strategy into what is called a strategy table. This is what a player must learn in order to play each hand correctly.

As some of you are reading this, you may think this all sounds very complicated and not very beginnerish. But, it really is far less complex than it sounds. Most of the hard work is done by people like me.

Your part is to learn the strategy table and to use the information from it to play each hand. About 75% of the hands will be fairly obvious and the remaining 25% may take some memorization to get correct.

I suppose the alternative is to just keep playing slots. As I questioned earlier, if you think video poker is slots, you might as well consider a slot machine to be an ATM – even if they are complete opposites. The ATM gives you your money and the slot machines take it away!

Deja Vu All Over Again!

            How many times does a person move from northern New Jersey to Las Vegas in a lifetime?

            It was the summer of 1985 and the plans had been in the works for months.  My parents called me in my dorm one night to tell me that they’ve decided they were retiring to Las Vegas that summer.  At the time, they thought that I might transfer to UNLV or one of the UC schools.  But, having made many friends and in the middle of pursuing my degree, transferring just didn’t seem prudent.  I decided that I would stay at SUNY@Albany. 

            When I got home for summer break, I found much of our house already packed up.  Because they were moving across country, I convinced my parents to allow me to live off campus for my final two years, figuring I would need a place to stay at times when the dorms were closed.  In June, we took a trip up to Albany to set up my new room with much of my furniture from my room at home.  In early August, we began the 10-day drive across country.  We went thru Wilkes-Barre, Toledo, Chicago, St. Louis, Tulsa, Amarillo, Albuquerque, Flagstaff and Kingman before arriving in Las Vegas. 

            Once we arrived, I spent an additional two to three weeks in Las Vegas before flying back to New York to get ready for school.  For the next two years, Las Vegas was essentially my home.  For the following ten years or so, I would visit 2-3 times a year.  My parents had an incredible ‘retirement’ in Las Vegas.  Well, maybe retirement isn’t the right word.  My father would go on to become the ‘godfather’ of video poker and change the casino floor forever with his work on games like Three Card Poker, Let It Ride, Caribbean Stud and Spanish 21.

            It is now the summer of 2011, 26 years later.  To quote Yogi Berra – it’s déjà vu all over again.  My wife and I have spent the last 6 months staging our house and packing up our stuff in anticipation of our move to Las Vegas.  We promised that once my eldest son was in college that we would head out of the New York area.  After researching countless cities, we decided that Las Vegas had the most to offer us.  Most of our friends think we’re going because of my profession.  There are benefits there as well.  The ability to see games in person will certainly help me write about games and develop new games.  But, the primary reasons dealt with the quality of life that Las Vegas affords us.

            As I write this column, we are 2-3 days away from the ‘hurricane of the century’ hitting us almost directly.  Of course, it is expected to come in as a Category 1 hurricane, so what we will endure will be seem like a light rain compared to what those in New Orleans dealt with a few years ago.  I’m likely to see more rain this weekend than I will the next 2-3 years in the Las Vegas valley.  If this wasn’t bad enough, we actually had an earthquake here too this past week.  I personally didn’t feel a thing, but about an hour before it hit, we were at the top of the Empire State Building, where I am told it WAS felt.  I can’t really say that I won’t deal with the same in Las Vegas.  I was there in 1992 when a significant earthquake hit between Los Angeles and Las Vegas and felt my parent’s apartment get shaken up quite a bit.

            Several months ago, I announced that I was changing the name of Compu-Flyers to Gambatria.  I knew then, that that was the beginning of a good deal of change in our lives.  In about 2-3 weeks when we arrive in Las Vegas, the end phase of that change will begin.  Compu-Flyers, now known as Gambatria will return to Las Vegas after a 13-year hiatus.  From a base of operations in Las Vegas, I hope to be able to  write about more up and coming games and to write in more detail about what I see going on in the casinos.

            I hope that Las Vegas will be as good to my family as it was to my parents.  I hope that I can be as good for Las Vegas as my father was. 

Taking the Mystery Out of the Machine!

            I get a daily e-newsletter from the American Gaming Association.  This past week, while leafing through it, a column about debunking the myths of the slot machine caught my attention.  I clicked on the full story and wound up at this PDF:

http://www.americangaming.org/files/aga/uploads/docs/taking_the_mystery_out_of_the_machine_brochure_final.pdf

            My father and I have desperately tried to get people to break the slot habit for more than 2 decades, so I was quite interested to see what myths they were referring to.  Obviously, you don’t put together a flyer like this unless you are hoping to attract people to playing slots.

           

            Ironically, while I doubt it was what was intended, I could not have put together a better flyer myself.  I agree with virtually everything on it, and I think it does a wonderful job of telling people why you should NEVER PLAY SLOTS!

Here are some points on the flyer:

Players can determine a machine’s odds by counting the symbols on each reel.

False.  Because multiple numbers generated by the RNG can correspond to the same symbol on

a reel, there are many more number combinations possible than are visible to the eye. Even though there may be only 15 symbols on a reel, there can be thousands of virtual stops.

            I couldn’t possibly add to the above statement.  What you see is NOT what you get with slots.  With Video Poker, what you see is EXACTLY what you get.

88-98: The overall percentage that a machine will return to players in the long run. For every $100 wagered, players might lose approximately $2 to $12 over time.

            88%???  That’s about 7 points below what ANY video poker pays.  But, that’s not really the main point.  The real point here is that if you had every slot machine in the world available to you, you would have NO WAY of knowing which is 88% and which is 98%.  Put a video poker machine in front of me, show me the paytable and I’ll tell you the payback with absolute certainty.

            And here is the scariest fact on the flyer:

59: The percentage of Americans who consider slot machines their favorite casino game

            Really? 59%???  No wonder they keep putting up billion dollar casinos!  Please folks, it is time to break the slot habit and keep more of your own money.  Play video poker.  Play table games.  Don’t play slots!

            

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.

Royal Alterations

            Last week’s column discussed how by altering your strategy, you can make Royals appear more often.  Let’s face it, by altering your strategy, you can make any hand you want to appear more often.  Just because Royal Flushes are the highest paying hand does NOT mean that by getting more of them you will automatically win.  If your goal is the bragging rights as the King or Queen of Royal Flushes, it might be worth it to you.  In reality, however, you’ll also be ‘flushing’ your bankroll by doing this.

            That isn’t to say that there isn’t a right time to alter your strategy in order to make a Royal appear sooner.  The obvious case of this is when you are playing a Progressive, where the meter is considerably above the normal 800 for 1 payout.  The intriguing part about playing Progressives is that the strategy keeps changing as the meter increases.  Even under normal circumstances it would be unusual for the meter to get to double the normal payout, but nowadays with some professionals monitoring progressive payouts, the likelihood is even less.  As soon as the meter gets to the point where the game is positive, a team of Players can hit a bank of machines and just keep playing until the jackpot is hit. 

            The Expert Player realizes that as the jackpot goes up, the strategy changes and the frequency of a Royal Flush can increase, which can push the payback up even more.  Using Expert Strategy for a full-pay jacks or better machine will result in a Royal (on average) every 40,400 hands.   If the Royal is paying 1600 for 1, we alter our strategy to make a Royal appear (on average) every 32,700 hands.  This increase in frequency allows us to extract an additional 0.9% of payback out of the Royal Flush hand.  Of course, this change in strategy costs us about 0.7% of payback on all the other hands.  The net increase is 0.2%, however.  So, you can play the Progressive using the altered strategy at 99.5% or you can use standard (8-5) strategy and play it at 99.3%.  It doesn’t seem like much of a choice to me.

            So, what are some of the changes we use when playing a Progressive paying 1600 for 1 on a Royal?  One of the biggest is that the 3-Card Royal now outranks a High Pair.  Yep, this one is going to hurt.  You going to throw away a sure winner (High Pair) and go for the Royal Flush.  Your odds of hitting that Royal is a bit more than 1000 to 1.  But, it’s paying 1600 for 1!  Throw in the fact that you still have many chances to hit a Straight Flush, a Flush, a Straight, Trips, Two Pair and a High Pair and quite frankly, the math isn’t even close.  The 3-Card Royal has an expected value of more than 2, while the High Pair is down at 1.5.

            Another significant change in our strategy is that the A-10 Royal is now playable.  Normally, when playing jacks or better, we do NOT hold a 2-Card Royal consisting of A-10.  We only have 1 way to fill it for Straights and/or the Royal Flush (with the JQK), which greatly reduces its expected value.  However, with the Royal Flush’s payout pumped up to 1600, we’re still better off holding the 2-Card Royal vs. holding just the Ace.  Keep in mind, however, that this hand is just barely playable.  This means that many other combinations of cards might be held instead (such as a 3-Card Straight Flush), so don’t forget to look at your WHOLE hand before getting overly excited about a suited A-10.

            Besides learning some of the changes to the strategy for a Progressive, another key point is learned.  Every change to the paytable can impact the strategy.  Now, if you sit down and play a full-pay bonus poker game using jacks or better strategy, I’m not saying you’ll get wiped out in 10 minutes.  But, what is the point of learning strategy if you’re just going to wing it when you change which type of game you’re playing.  0.1% or 0.2% might not seem like a lot to give up – but in reality, this may increase your loss rate by 20-50%!

            One of the best ways to learn how to play all the different games out there is to learn the strategy tables from a book like Winning Strategies for Video Poker and then practice what you’ve learned on your PC using Masque’s Video Poker Strategy Pro.  For a limited time, we’re offering a package of both the book and the software for only $14.95.  For an additional $5 ($19.95 in total) we’ll also include Video Poker: America’s National Game of Chance which is 200 pages of Lenny Frome’s best articles, quizzes and stories.  If you’d like to order, please send a check or money order to Compu-Flyers, P.O. Box 132, Bogota, NJ 07603. 

Royal Appearance

            Last week’s column was prompted by a reader who raised some concerns that Players who use their frequent player cards are somehow cheated by casinos.  The ‘proof’ of this is that some locals (i.e. frequent Players) don’t seem to get as many Royals as the tourists.  Previously, I had cited at least two reason for this. 

            The first is selective memory.  We tend to remember things we want to remember.  When we go through an extended cold streak, every other scream of “Royal” is burned into our brains.  I’m guessing that in the week you hit your last Royal, someone else did too that week, but it didn’t bother you one bit.  If you’ve gone a year without one, everytime someone gets one, it hits you like a ton of bricks.

            Secondly, even if you’re trying to be relatively objective about it, you also have to remember that ‘you’ are greatly outnumbered by ‘them’.  Even if there are a couple of you playing together, there are dozens if not hundreds of other people playing around you.  It is no surprise that they WILL actually get more Royals than your group will.

            There is, of course, another possibility – other people ARE actually get more Royals than you are!  So, am I buying into the whole ‘rigged’ video poker machine theory?  ABSOLUTELY NOT! 

            But, the number of Royals you get over an extended period of time is greatly influenced by the strategy you use.  So, there are two possibilities.  YOU may be using the wrong strategy which is reducing the probability of a Royal OR the other guy is using the wrong strategy which might INCREASE the probability of a Royal.

            Let’s look at these two scenarios.  The proper strategy for any particular video poker machine is one that maximizes the overall payback, not one that maximizes the probability of hitting a Royal.  What do you do when you’re dealt the following?

A♥       Q♥       10♥      5♥        5♠

            Do you hold the Low-Pair?  The 4-Card Flush?  The 3-Card Royal?

            The correct answer is the 3-Card Royal.  If you’re playing one of the other two, not only are you hurting yourself from a payback perspective, you’re lowering your chances of hitting a Royal.  By the way, the decision is not even close.  The expected value (EV) of the 3-Card Royal is 1.41.  The 4-Card Flush has an EV of 1.22 and the Low Pair a meager 0.82.

            So, if you’re not playing this hand correctly, don’t be surprised if some others around you are hitting more Royals.  Of course, they may have their own issues.  What do you do when you’re dealt the following?

A♥       Q♥       10♥      5♥        Q♠

            The correct answer is hold the High Pair with an expected value of 1.54.  Now, you may be doing this, but that ‘tourist’ behind you may not.  What is the impact of holding the 3-Card Royal.  Well, he’ll lower his overall expected payback, BUT he will increase his probability of hitting a Royal.

            The examples I used here are not the most common occurrences, so these will not make a big difference to the frequency of a Royal happening.  Far more common are the hands that include a 2-Card Royal that also include 3-Card and 4-Card Flushes and Straights.  I have little doubt that there are many novice Players who get Royal fever and just play every 2-Card Royal instead of 4-Card Straights and Flushes or 3-Card Straight Flushes.  Doing so, will make them hit more Royals than you will, but they won’t be any richer for it. 

            Under normal circumstances, for a jacks or better machine, a Royal should appear about once every 40,000 hands or so.  By altering one’s strategy it is very easy to reduce this to once every 30,000 hands or so, which is considerably more frequent.  But, it will come at a cost of lowering the payback by a significant amount too.  So, the next time you’re upset that someone else got a Royal, start worrying about how you’re playing and not what’s happening around the corner.  They may pay dearly for their Royal appearance.

           

To Card or Not to Card

            This past week I received an e-mail from a reader who wanted to know whether the casinos could essentially reward “non-frequent” players with better hands in video poker.  As we all know, the craze of the past decade or so is to have a frequent shopper card for each store.  My keyring is lined with them.  I’ve got one from grocery stores, drugstores, bookstores and countelss others.  Casinos are no different.  When you play, you put your frequent player card into the machine and it keeps track of how much you wager and in turn rewards you with points for comps, etc…

           

            So the question being asked is – can/do the casinos make the machines pay more for people who do NOT put a card in the machine.  The reader who sent this e-mail was echoing sentiments he has heard from other local and/or frequent Players.  He also stated that it ‘seems’ like more Royal Flushes go to non-regular Players.

           

            I could probably write several pages about this topic, looking at it from a variety of different angles.  I’ll try to hit the highlights of some of these today.  As I have stated many times in this column, it is the law in most casino jurisdictions (Las Vegas certainly included) that any video game that uses what appears to be an ordinary object (i.e. a deck of cards) MUST be completely random.  This means that at any point in time, the probability of any card not already dealt showing up is the same as any other card not already dealt showing up.  Given this, it is absolutely NOT possible to favor one set of Players over another.

            This is NOT to say that you can’t make a computer do this.   As an IT professional with over 20 years of experience, I know that it would be very easy to favor Players based on such criteria.  Even if it were legal to do so, I’m not so sure that I would necessarily favor the infrequent Player over the frequent Player at casino games.  As we all well know, many tourists will joyfully lose money at a posh casino as long as they can enjoy the marble columns while they are doing it.  Locals, on the other hand, tend to look for better paytables and care less about the physical surroundings.

            It is in this very topic that the three key components of Expert Strategy collide – knowing which games to play, knowing the right strategy and knowing what to expect.  My reader did not present any true evidence that one group of people are getting Royals at a higher rate than another.  He only stated that it ‘seemed’ that way.  Nothing makes the casinos happier than a Player doing something less than optimal because it feels right.  There is only ONE way for things to swing when a Player does this.  In the long run, the casinos will win more and the Player will win less.

            While the casinos have certainly cut back over the past few years on points, comps and cashback, there is still one simple math fact.  If we go with the notion that the casinos DO NOT play favorites based on whether or not the card is in the machine, then removing your card from the machine only serves one purposes.  You get an overall lower payback by not getting your comps and cashback.

            The decision to pull one’s card from the machine would appear to be based on the notion that it ‘seems’ as if others are getting more Royals and thus it MUST be because the house is favoring someone else.  All of us who have played for hours have gone through dry periods in which we’re sure that everytime we discard a King, it is replaced by a King – especially when drawing on a 4-Card Straight or 4-Card Flush.  Or we seem to be dealt an overabundance of a certain Low Pair which never seem to turn into trips.  A significant portion of this is simply our minds playing tricks on us.

            There is only one of you.  Even if you’re playing with a spouse or a friend or two, there is still only two or three of you.  Then there is the rest of the casino, which you ‘assume’ are not regulars – especially if you don’t remember seeing them all the time.  Even if they truly are NOT regulars and they are NOT playing with a card in the machine, there are still far more of them than there of you.  When you hit a Royal, you probably don’t notice all the people around you who haven’t hit them.  When you go through a rough patch, all of a sudden you notice every time someone else hits one. 

            Of course, there IS the possibility that other Players are getting Royals more frequently than you are – but it doesn’t mean the casinos are out to get you.  Nor does it mean that the other guy is doing himself any favors.  But, I’ll save that for next week!  In the meantime, leave your frequent Player card in the machine.  Don’t make a cold streak even worse by leaving your comps and cashback on the table.