Advantage: Dealer

            I don't think this will shock any of you.  Every table game has a house advantage.  Numerous mechanisms are used to build this house advantage.  By now, most Players are probably used to most of these methods, that they barely notice them.  If the game of Three Card Poker were played such that the Player made a wager, got three cards and then simply went head-to-head against the Dealer's 3 cards, the game would be a 100% payback.  Any game in which the Player and Dealer get the same number of cards and no decisions after the initial wager is made is simply one big push.

            In the game of blackjack, the Player must act first.  If he busts, he loses.  It won't matter if the Dealer busts also.  This is an advantage for the house.  The Player's ability to double down, split and decide when to hit/stick are advantages for the Player.  I've often be quite amazed that the game of blackjack was developed centuries ago without the use of computers (obviously) and somehow managed to deliver a payback right where you would want it! 

            In the game of Three Card Poker, the Player and Dealer receive the same number of cards, so that's an even game.  The Player, however, gets to decide when to Play/Fold so this is an advantage to him.  He can take his really weak hands and walk away from them without making another wager.  He can wait for his stronger hands and Play.  In the background to this process is the fact that because the Dealer always gets 3 cards, the Player knows what the 'average' hand for the Dealer is.  In fact, he can know the frequency of every possible hand.  This is what allows him to create the proper strategy for Playing vs. Folding.  If the game ended here, the Player would have a significant advantage.  To offset this and get back to a house advantage, the Dealer must qualify with a Queen High Hand.  As a result of this, the Dealer essentially surrenders 30% of his weakest hands and cuts the payout to the Player in half.  For a small portion of these hands, a bad Player might actually benefit - by Playing a hand below Q-6-4 and going against the right strategy.  Despite these occasional wins, the casinos will more than gladly make up for this with all the Jack High hands that the Player will lose.

            Ultimate Texas Hold'em adds a twist to the idea of Dealer qualifying.  In UTH, if the Dealer doesn't qualify, the Ante wager pushes, but the Play wager stays in Play.  If we were to use this rule in Three Card Poker, it wouldn't make a difference to the overall payback because a Player should fold every hand that would result in loss where the Dealer does not qualify.  However, in UTH, Players sometimes make a 4x wager or a 2x wager with something less than a Pair.  If the hand doesn't develop (usually you're shooting for a Straight or a Flush), the Player may be left with a very poor hand.  If we used the TCP qualifying rule, the Play wager might push and the Ante wager would pay even money.  In UTH qualifying, the Ante pushes and the Play wager is in play.  The Player could be left with a Queen High hand.  If the Dealer has an Ace High hand, the Ante will push and the Play wager will lose.  This subtle difference in how qualifying is handled gives the casino just a smidge more edge.  In the case of UTH, this is the difference between the game having no house edge and having just the right amount of house edge.

            Moving on, we find ourselves at Four Card Poker.  Four Card Poker has no Dealer qualifying.  Every hand is in play.  All wagers are in play (assuming the Player doesn't fold).   So, where does the house advantage come from?  The Dealer gets an extra card.  Despite the name of the game, the Player gets five cards to make his best 4-card hand.  The Dealer gets six cards to make his best 4-card hand.  This little 'advantage' is enough to get rid of qualifying and to allow the Player to make a 3x Play wager if he so chooses.  If the Dealer were to get the same number of cards as the Player, then each would win the same percent of hands.  Even to allow an optional 1x Player wager would require the adding of some sort of qualifying.  To allow a 3x Play wager, the qualifying might not even be enough.  Instead the Dealer gets an extra card, meaning that he will win a larger percentage of the hands. 

            I'm sure that if I were to look at all the games on the casino floor, I'd see a variety of other different methods for creating a house advantage.  While each has a math component and provide different amounts of house advantage, the real impact of the methods is more psychological than mathematical.  How do you feel about the Dealer having a stronger hand, on average, by being dealt more cards?  If you beat the Dealer, you might win more than you would if you play him in a game where you are each dealt the same number of cards.  There is no real correct answer.  There is simply a variety of proven methods for doing this - and probably even more that haven't been thought of yet.

What to Play

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

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

·         Know which game to play

·         Know how to play that game

·         Know what to expect

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

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

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

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

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

Four Play

           

            Four Card Poker has a special place in my heart because it sort of launched my career as a gaming analyst.  Ironically, I didn't analyze it as it was being developed.  Rather, I wrote about it right here in Gaming Today way back in February 2004.  The column got noticed by the then President of Shuffle Master, who put me in touch with Roger Snow, the inventor of the game and at the time, the Manager of Table Games for Shuffle Master.  That introduction was the beginning of what has been a very successful collaboration which has included blockbuster games such as Ultimate Texas Hold'em and Mississippi Stud, along with countless sidebets for virtually every game in the casino.

            Four Card Poker was also an important game for the evolution of proprietary table games.  By the time Four Card Poker hit stride, there had been a bit of a lull in table game creation.  The casino floor had already changed a good deal with Let It Ride, Caribbean Stud Poker, Three Card Poker and Spanish 21, but those games were all already several years old.  Perhaps there were some other games in between that I am unaware of.  Admittedly, this lull I speak of, occurred after my father passed away and before I entered the field.

            The game itself didn't really break any new ground in terms of betting structure or rules.   The new ground was broken by Four Card Poker's 'crazy' cousin - Crazy 4 Poker, which introduced the Super Bonus wager - which is more commonly known as the Blind wager on more recent Shuffle Master games.  This wager will push if the Player wins with a poor or so-so hand and will win odds if the Player wins with a strong hand.  I'll cover more about Crazy 4 Poker in a few weeks.  Crazy 4 Poker has about 100 tables in the marketplace as compared to Four Card Poker which has about 250.

            Four Card Poker utilizes the same betting structure as Three Card Poker.  There are two separate wagers - Aces Up and Ante/Play.   The Aces Up pays on a pair of Aces or better and is not concerned with the Dealer's hand at all.   The Ante/Play is the wager where you are playing head to head against the Dealer's hand.  You make an Ante wager to begin play and you are dealt your hand which you can review.  Now you can either make a Play wager of 1x - 3x your Ante or Fold, forfeiting your Ante wager.  If you beat the Dealer's hand, you are paid even money.  If you don't you lose both wagers.   Also, similar to Three Card Poker are the Ante Bonuses.  These pay the Player whether he wins or loses against the Dealer - if the Player can achieve a Four of a Kind, Straight Flush or Three of a Kind.  They pay 25, 20 and 2, respectively.

            So, by this point, if you are not familiar with Four Card Poker already, you're probably guessing that the Player and Dealer each get 4 cards and you might be wondering what hand the Dealer needs to qualify.  WRONG!  The name comes from the size of the hand the Player makes.  He is dealt FIVE cards to make a FOUR card hand.  The Dealer is dealt SIX Cards to make a FOUR card hand.  Thanks to this little benefit, the Dealer does NOT need to qualify in Four Card Poker.  Every hand plays. 

            In Three Card Poker, many people follow a strategy to just do what the Dealer does - and play any hand that is Queen or better.  This is a little below perfect, but will not hurt your bankroll significantly.  If you want to play like an Expert, you go with Queen-6-4 as the lowest hand you Play.  So, with the Dealer qualifying on every hand in Four Card Poker, you have nothing to guide you at all.  Adding to the dilemma is when to Play 1x vs. Play 3x.  As is normally, the case, we NEVER bet 2x.  We either cut our losses (FOLD), hedge (Play 1x) or slam on the gas (Play 3x).

            When Four Card Poker was introduced, Shuffle Master supplied information cards that included a basic strategy on them.  This strategy produced a 98.41% payback and includes only 3 rules.  In my analysis of the game, I took that strategy a bit further and produced one with about 7 rules (admittedly, more complex rules too) that takes the payback up to 98.60%.  Even this strategy is not absolutely perfect as it does not take into account specific suit make up of the Player's hand nor go any further than the first 'kicker' in the Player's hand.  It is my expert opinion that to do so would only get the Player an additional 0.01 - 0.02% in payback, but it would also greatly increase the probability of errors by making the strategy that much more complex.

            Without further ado, I present the basic strategy which Shuffle Master initially developed and I have verified.

·         Fold with a Pair of 2's or Less

·         Bet 1X with a Pair of 3's thru 9's

·         Bet 3X with a Pair of 10's or Better

           

            It's that simple if you want to earn the 98.41% payback which is respectable.   Expect to Fold a good amount of the time - just under half.  Four Card Poker was designed to be quite a bit more volatile than Three Card Poker.   As Roger told me way back in 2004, "one of three things typically happens.  One, you double up.  Two, you get crushed.  Three, both one and two, and not necessarily in that order." 

            If you'd like to learn more about Four Card Poker, including the Expert Strategy, I highly recommend my Expert Strategy for Four Card Poker.  You can order it by sending $5.95 to Gambatria, P.O. Box 36474, Las Vegas, NV 89133.  This price includes free shipping and handling.

For the Love of the Game

            Perseverance can be a positive trait when you are trying to invent a new table game.  Unfortunately, it can also be a negative one which can all but kill your chances of ever having a game reach the casino floor.  This translates to one simple thought - Don't fall in love with your game.

            Getting a game into a casino is not an easy thing.  Getting it stay in the casino if you manage to get it placed is even harder.  Perhaps 5% of all games that are conceived of make it to the floor.  Of those that do, maybe 5% that make it there stay for any length of time and continue to grow.  When you add it all up, about 1% of all games invented are some type of financial success for the inventor. 

            This past week I had a conversation with a newcomer to the industry and reminded him that only 1 out of a hundred games becomes a success.  His response was that he'll just have to make sure he comes up with 100 games so that one of them can be successful.  That type of perseverance is the type you want to have. 

            A few years ago, I got a call from an inventor who wanted me to tweak a game that my father had originally worked on for him.  I found the file.  My father had worked on the game 10 years earlier.  In the 10 years, the game had been given a trial or two in a casino and been pulled out relatively quickly.  This is not a time for tweaks.  It is a time to move on to the next idea.  This type of perseverance could be a killer. 

            Roger Snow, Executive VP of Shuffle Master, may very well be the most prolific table game inventor of them all, with games like UltimateTexas Hold'em, Four Card Poker and Crazy 4 Poker to his credit.  He likes to remind people that he has probably invented more flops than anyone in the industry as well.  This doesn't mean that you should take any idea you have and quickly try to get it into a casino, with the goal being to try as any games as you can and hope something sticks.  Unless you have a track record of success, casinos are going to give you only so many chances, so you do want to put your best foot forward.

            If you do manage to get your game into the casino for a trial, it is time to take off the rose-colored glasses.  Listen to the feedback the table games manager gives you.  If the game isn't fairing well, don't start blaming it all on the casino that was kind enough to give you the trial.  They are NOT setting you up for failure.  Even in a free trial, it costs the casino money to try out your game.  They need to train the dealers.  They need to make room for your game by removing some other game that might have been doing okay - in hopes that yours will do great.

            No one can predict the success or failure of a game with a high degree of certainty.  In the end, it must perform which means its success is at the whim of the Players.  I have been working directly with inventors for a decade and indirectly for three decades and there is no clear rhyme or reason as to what succeeds and what doesn't.   The only thing is certain is that if you bring it to the Players and the Players don't like it - it is NOT a success.  It does not matter that your brother, sister, mother and Aunt Tilly all love the game and think it is the greatest thing they've ever seen.  I don't know how to tell you this - but they are BIASED!  This is the same bunch that told you how much they love that new pair of glasses - you know, the ones that make you look like a 1970's version of Elton John.

            If you spend 10 or 15 years trying to get a single game into the casino, you will likely have overlooked many other good ideas that you might have had.  There is a 99% chance that any single game idea you have will fail.  Every game that is invented is, as they say, a slave to the math.  That same math should be telling you that after a certain number of setbacks, your chances of success are greater by moving on than by insisting that the reason your game failed was some flaw of anything but the game itself.  Putting it another way, the expected value of working on the next game is greater than continuing to beat the dead horse.  And by now, you all know that the right play is the one with the higher expected value.

Who Isn't Crazy 4 Poker?

             Shortly after  Four Card Poker was being launched, another similar, yet different, game hit the marketplace.  It was called Crazy 4 Poker.  In a recent conversation with Roger Snow, Executive Vice President at Shuffle Master, he revealed that Crazy 4 Poker was invented on January 28, 2002.  How does he remember the specific day?  It was the same day that Four Card Poker went live at Jackson Rancheria in California.  Fearful that Four Card Poker was going to flop, he immediately went to work on its successor game.  As it turns out, he got them both right.

            For reasons not fully known, the game was a big hit in Nevada.  There are currently about 100 Crazy 4 Poker tables, of which 40 are in Nevada.  Virtually every major casino in Las Vegas has one.  Crazy 4 Poker is an important piece in the history of table games.  It introduced the concept of a ‘Super Bonus’ (now more commonly referred to as the “Blind” wager) in Shuffle Master games.  This has become a staple of their more recent games.

            Crazy 4 Poker is broken down into two separate wagers.  The first is called Queens Up is like Pair Plus.  If the Player is dealt a Pair of Queens or better he wins according to the paytable in use.  The second portion of the game is like Ante/Play.  It requires that the Player make both an Ante wager and a Super Bonus wager.  The Player and the Dealer are each dealt FIVE cards to make their best FOUR card hand.

            Once the Player has reviewed his hand, he can either Fold, forfeiting his Ante and Super Bonus wagers, or he can Play.  If the Player has a Pair of Aces or better, he may Play 3 times his Ante wager.  If he has less than a Pair of Aces, he can only wager 1 times his Ante.  Thus, when the Player has a strong hand, he can really sock it to the casino. 

            After all Players have decided what they want to do, the Dealer reveals his hand.  If the Dealer does not have at least a King High, his hand does not qualify.  In this case, the Ante wager is pushed and the Play wager is paid even money.  This means that if you have a strong hand and Play 3x you will still win even money on this when the Dealer does not qualify.  If the Dealer’s hand IS a King High or better, his hand qualifies.  In this case, if the Player’s hand outranks the Dealer’s hand, he will be paid even money on both his Ante and Play wagers.  If the Dealer’s hand outranks the Player’s hand, the Player will lose his Ante and Play wagers.

            The payouts on the Super Bonus wager are a bit more complex.  If the Player has a Straight or better (keep in mind with a 4-card hand, Trips outrank Straights and Flushes), he is paid according to the paytable regardless of the Dealer’s hand.  If the Player beats the Dealer, but with a hand less than a Straight, the wager pushes.  If the Player loses to the Dealer with a hand less than a Straight, the wager loses.

            The strategy for Crazy 4 Poker is rather similar to that of Three Card Poker.  The Player must remember only a single strategy to master the game – K-Q-8.  If the Player’s hand is K-Q-8 or higher, he should Play.  Technically, he must also remember to Play 3x if he has a Pair of Aces or better, but I consider this part of the strategy to be more than a little obvious.  The Player will win 90% of these hands.  It should be noted that K-Q-8 is not actually ‘perfect strategy’.  There are a handful of hands which should be Folded above K-Q-8 and a few that should be Played below.  However, these require taking into account the specific suit makeup of the hand and are more likely to cause errors by the Players than they are worth.  The difference between ‘perfect’ and ‘expert’ strategy is a mere 0.01% of payback.

            Speaking of payback, if you follow the simple strategy provided here, you’ll find Crazy 4 Poker affords a 98.91% payback on the Ante/Play portion of the game.  Given the relatively easy strategy, this is a very strong payback to offer.   As a side note to those that like to play games like this and never Fold.  Never folding in Crazy 4 Poker will take the payback down to 96.5%.  Considering an average wager of more than 3 units per hand, a $5 Player will be throwing away about $15 per hour more by following this wayward strategy.

            Stick to the K-Q-8 and before you know it, you’ll be Crazy 4 Poker too!  You can read more about Crazy 4 Poker and many other games at my website – www.gambatria.com.

The Storm After the Calm

            After Three Card Poker takes the casinos by storm, there is a bit of a lull in activity of new games.  That’s not to say that there weren’t many attempts, some with some success.  Up until Three Card Poker, casinos were not exactly chomping at the bit to put in new games.  Of course, as Three Card Poker grew in popularity and casinos started making that much more money even AFTER paying for the table, they probably began to realize that there was more money to be made with yet newer games.

            Enter Four Card Poker.  My initial reaction to hearing the name of the game was that I hoped it was NOT just Three Card Poker with four cards.  Fortunately, it is not.  Four Card Poker holds an interesting place in my heart.  On one hand, it is one of the few successful table games that was NOT analyzed by my father or myself.  It was developed after my dad passed away and before I jumped into the profession.  Nonetheless, it helped speed my entry into the profession. 

            Shortly after starting to write for Gaming Today in 2003, I received an e-mail from a reader about my Three Card Poker article.  He asked me if I had ever heard of Four Card Poker.  I had just read about the game earlier that day and the gentleman and I had an exchange of a few e-mails.  I finally asked him if he had a financial interest in the game (based on his questions) and he told me that he had just become the President of Shuffle Master (Paul Meyer).  Obviously, he had not been using his company e-mail address.  A few months later, after completing an analysis of Four Card Poker, I wrote an article about it in Gaming Today.  Again, I received an e-mail from Paul, this time commending me on nailing the math for the game.  I had accurately repeated the original analysis of the game.  Paul wound up putting me in touch with Roger Snow, then Manager of Table Games for Shuffle Master.  Roger gave me a few small projects to ‘test’ me and the rest is as they say ‘history.’  Roger and I have been working together ever since.

            Four Card Poker does have some similarities to Three Card Poker.  It is broken down into two games – the Ante/Play and the Aces Up wagers.  The latter is like Pair Plus.  The Player is paid if dealt a Pair of Aces or better.  Despite the name of the game, neither Player NOR Dealer get dealt four cards.  The Player is dealt five cards to make his best four card hand.  The Dealer, in the meantime, is dealt SIX cards to make his best four card hand.  One of his cards is dealt face up, but this makes only a minor amount of difference to our strategy.  To help compensate the Player for the Dealer’s ‘extra’ card, the Player has the opportunity to bet up to 3 times his base wager as part of Ante/Play.  So, he can Fold (forfeiting his Ante), Play 1 times his Ante or Play 3 times his Ante.  Also, there is no qualifying in Four Card Poker.  Once you decide to Play it is your hand vs. the Dealer hand.  There is one additional benefit to the Player in Four Card Poker.  The Player wins all ties.  Ties mean identical four card hands.  The cards not used to make the four card hands are NEVER taken into consideration.  If the Player’s hand beats or ties the Dealer’s hand, he is paid even money on his Ante and Play Wagers.  Additionally, the Player is paid an Ante Bonus if he has a Three of a Kind or better.

            With 5 Player cards and 6 Dealer cards, there are 28 TRILLION possible hands that can be dealt.  This makes creating a program to run all of them impractical.  Instead, we go in search of the beacon hands.  These are the hands that are at the strategy points.  In the case of Four Card Poker, we need to find two of them.  We need to know when to Fold vs. Play 1x and we need to know when to Play 3x instead of 1x.  Much to my surprise, Shuffle Master provided a basic strategy for the game on their information card.  When I simulated this strategy, I found a payback of 98.41%.  When I performed a more complete analysis, I found that I could push this up to 98.60%, but it requires memorizing a strategy that is a bit more complex.

            The basic strategy is as follows:

• Play 3x if you have a Pair of 10’s or Better
• Play 1x if you have a Pair of 3’s through 9’s
• Fold if you have a Pair of 2’s or less

            The Expert Strategy I developed has 6 rules for when to Bet 3x which more fully takes into account the Dealer upcard.  While the additional 0.19% might not sound like a lot, it cuts the house edge by about 12%, which is significant.  If you’re interested in learning more about Four Card Poker, you can order Expert Strategy for Four Card Poker for $5.95.  Send a check or money order to Compu-Flyers, P.O. Box 132, Bogota NJ 07603.

            Four Card Poker was an important milestone in table game development as it showed that Three Card Poker wasn’t just a fluke success.  The Players were looking for more games with more excitement than the casino standards of Blackjack, Craps and Roulette.  Four Card Poker would soon lead to Crazy 4 Poker and then the Texas Hold’em craze started to build.  You can read about some of these other games on my website at www.gambatria.com or you can just stay tuned here and I’ll be covering them in the coming weeks.