Pai Gow Poker Odds

Published: 12/05/2012

In Pai Gow Poker, it is not enough to beat the Banker on the 5-card High Hand. To collect on a wager at even money, the 2-card Low Hand must be successful, too. This makes calculating Pai Gow Poker odds more complex than it is for 7-Card Stud, Texas Hold’em or Omaha, where only one hand is in play and needed to win.

In considering the odds of winning, the first number a Pai Gow Poker player needs to be aware of is the percentage that represents the House Edge. Because there are several variations of the game with different House Rules, the overall advantage to the House on every hand can be as high as 2.3% or as low as 1.3%. A player who is skillful in using a hand-setting strategy that is very close to the House Way can reduce the margin. In fact, this is central to developing a Pai Gow Poker strategy.

To get a handle on Pai Gow Poker odds, it is useful to think of the game as having only four possible outcomes for each deal. The most desirable of these is for the player to win both hands and collect even money, less the House commission. Two outcomes result in a “push” with no winner or loser: the player win either the 5-card High Hand or the 2-card Low Hand, but loses the other. Lastly, the Banker may win both of the hands and collect the player’s entire wager.

Because half of the outcomes result in a push, with no money changing hands, wins and losses occur much less frequently in Pai Gow Poker than in most casino table games. Mathematically, the Banker and Player have the same probability of winning. The House is ensured of its profitability only by charging a commission, the so-called “vigorish,” which is usually 5% on all winnings.

The vigorish can be reduced somewhat, however, by playing at tables where the commission can be “pre-paid.” For example, instead of wagering 100 units to claim 95 after paying a commission of 5 units, such tables allow a wager of 105 units to win 100 units, deducting a commission of 5 units, which actually lowers the vigorish to 4.76%.

Another factor that must be taken into account is the effect of the “copy” rule, which gives the Banker hand an additional advantage. When two hands are identical, a “copy,” the Banker’s hand wins. The probability of the two 5-card High Hands being identical is 2.55%. For the two 2-card Low Hands, the probability of a copy occurring is 0.10%. At tables where the casino’s dealer plays the Banker hand, these “copy” percentages translate into a slight boost to the House Edge.

Of the four possible Pai Gow Poker outcomes, the Player can be expected to win both hands 28.61% of the time, while the Banker should win them both on 29.91% of all occasions. The remaining deals, or 41.48%, can be expected to end in a push. The numbers therefore indicate that at tables where participants are permitted to hold the Banker hand, they should accept the opportunity and the slight advantage it conveys.

Another approach to analysing Pai Gow Poker odds is to considering the frequency of various hand combinations. The 5-card High Hand can be expected to contain Five Aces about once in every 138,000 hands. By contrast, the probability of being dealt a pair is 41.66% and the likelihood of being able to form a 5-card High Hand with better than a pair is 42.26%. An unsuited, unconnected 5-card High Hand with no pair, straight or flush can be expected with a frequency of 16.08%, or about once in every 6.25 deals.

One other useful calculation relates to the “power” of a hand—how likely it is to beat the corresponding hand held by the Banker. On average, the 5-card High Hand will contain a pair of Jacks, which should be successful in 49.8% of all showdowns. The average 2-card Low Hand Behind is the A-7, and it can be expected to win 49.7% of the time. Whenever a hand contains combinations ranking higher than such “median” hands, it is strong. Hands containing lower ranking combinations are seen as weak.

Published on: 12/05/2012

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Comment on this article
don white  at 31/03/2014 19:17:16

look like your odds on the 5 card copy hand and two card copy have are reversed.

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