Think Loss Rate

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

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

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

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

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

4♥        5♥        6♥        7♥        8♦

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

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

An Error of Commission?

            A couple of weeks ago I discussed methods used by game developers to create a house advantage.  I realized that I left off two common one.  They are somewhat related as the second one was created in attempt to get rid of the first.  The first method is called taking a commission, which I've generally thought of as a misnomer, because it only applies to winning bets.  In the games of Pai Gow Poker and Baccarat, certain wagers pay a 5% commission when they win.  Another way of looking at this is that the Player is paid 19 to 20 for a winning wager, which I think is more accurate.  Commissions, to me, are paid on a wager, not on a winning wager.  If you pay a commission to a real estate agent, you don't pay it if you get a good deal or only on your profit, you pay it when your house sells - on the gross sales price.

            If you wager $20 and you lose, you lose $20.  If the wager pushes, you get your full $20 back.  If you win, you get $39 - your $20 plus the $19 you win.  So, in reality, you're simply making a wager that pays a little less than even money.  In Pai Gow Poker, this applies to the base wager.  A mechanism such as this must be used because the only other advantage that the House has is that it wins hands that are copies.  But, with a 2-card hand and a 5-card hand, ties are not that common.  While this provides some advantage to the house, it simply isn't enough.  So, they pay 19 to 20 for winning hands.  At first glance, this might seem to create a 2.5% house advantage because the Player and Dealer win nearly the same number of hands.   However, since it is paid only only wins and about 42% of all hands finish as pushes, we find that it really only generates a little under a 1.5% house edge.  When combined with the house edge generated by the house winning copies and the overall house edge is about 2.73%.  This is offset somewhat if the Player chooses to act as the banker which provide an edge for the Player.  But, I'll save that for another day.

            In Baccarat, the Player has the option to wager on either the Player or the Banker hand.  In reality, it is more like Hand 1 and Hand 2 because no hand really belongs to the Player if you can wager on the other hand.  Based on the drawing rules used in Baccarat, the Banker hand has a small advantage.  Because the Player can wager on this hand, this translates to an advantage to the Player.  To offset this, the House again takes a commission on winning wagers on the Banker Hand.   Again, winning wagers on the Banker Hand pay 19 to 20.  The net impact is that the Banker Hand wager has a 1.06% house edge, which is actually LOWER than the Player Hand Wager without a commission.

            The problem with paying commissions is not that it costs the Player money.  Every casino game costs the Player money.  The real question is not what mechanism is used to generate the house edge, but how much of a house edge it generates.  In the case of these two games, it generates a relatively normal sized edge.  Pai Gow's edge is a little on the high side and Baccarat's is on the lower side.  But, nothing incredibly unusual about either.  The issue is that the commission is slow and messy.  Players don't always wager in multiples of $20.  In these cases, the casino might use some method to accrue the commission and then take it when the amount adds up to a round amount.  Calculating a 19 to 20 payback is also not a simple thing for the Dealer.  Sure, a $100 wager pays $95 which is easy enough, but still messier than paying $100.  But, what about when the Player wagers $75?

            These issues led to a desire to do away with the commissions in these games.  In both cases, a similar mechanism was used.   In the case of Pai Gow, a hand that is normally a sure loser for the House is turned into a Push.  In one common version of 'commission free' Pai Gow, if the Dealer has a Queen High Pai Gow hand, then the hand is automatically a Push.  This creates a house advantage nearly identical to the commission.   Now all wins can pay even money and the game is cleaner and simpler.   Only in the occasional situation where the Dealer has this hand is the normal flow interrupted at all, and the impact is relatively minimal to game speed.

            In Baccarat, one of the common mechanisms is to take a sure winner for the Banker hand and turn it into a Push.  The most common hand is a Banker 3-card 7 which wins.  The impact, like in Pai Gow is a virtually identical payback but with the messy commission removed.  Now all wagers can pay even money and the only impact is that special Banker Hand and even when that happens it simply becomes a push.

            In order to be an Expert Player, a Player needs to understand that all casino games are built with a House edge.  The edge comes from a variety of mechanisms.  The specific mechanism is not important to the end financial result.  It can impact the feel of the game and a Player may prefer one mechanism vs. another.  However, that House edge will be there no matter what.  If you play a no-commission version of Baccarat or Pai Gow, mathematically you're playing a nearly identical version of the game.  If you like the simplicity of the no-commission version, play that.  If you get annoyed and pushing hands you should win, then maybe these versions aren't for you.  At the end of the night, you'll probably be a nearly similar financial situation.

            

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.