Friday, June 14, 2013

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.

Wednesday, June 5, 2013

The Nature of the Game

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

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

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

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

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

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

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

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