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Mini Pai Gow
Gaming Entertainment, the owners of Mini Pai Gow, claim that my analysis is incorrect. The only specific error given was that my probability of a tie is too high. Let me make it perfectly clear that with anything on this site, I could be wrong. Casino game analysis is not easy. Computer code can be thousands of lines long, and if you blow it on just one line, it can cause the entire analysis to be wrong. My program for Mini Pai Gow is 1050 lines long. I do my best to compare my game analysis with other sources, but in the case of Mini Pai Gow, there is nothing else in the public domain about it. My request to see Gaming Entertainment's own math report was rebuffed. So, please take this analysis with a grain of salt.
Mini Pai Gow is a pai gow poker variant, using six cards instead of seven. In Las Vegas, it is most likely to be found at Harrah's-owned properties. There is no 5% commission on wins, but most ties go to the banker, which are common in the one-card low hand. Every hand is fairly obvious how to play, there are lots of pushes, and it has a slow speed of play. For the player looking for an easy game with a low level of risk, Mini Pai Gow may make an enjoyable experience. A house edge of 2.64%, according to my analysis, is lower than most new games.
- The game is played with a single 53-card deck, consisting of the usual 52 cards plus one joker.
- The joker can be used to compete a straight, flush, straight flush, or royal flush; otherwise it is treated as an ace.
- After making a wager, the player and dealer each receive six cards.
- The player should arrange his six cards into a five-card hand high and a one-card low hand. The high hand must be higher in poker value than the low hand.
- After the player sets his hand, the dealer will set his, according to the house way below.
- The player's high hand shall be compared to the dealer's high hand; and the higher poker-valued hand wins. Likewise, the player's low hand shall be compared to the dealer's low hand; and the higher card wins.
- If both player hands win, the player's bet shall pay even money. If both player hands lose, the player's bet shall lose. If one player hand wins, and one hand loses, then the bet shall push.
- If the player and dealer have identical hands, then the tie shall go to the dealer, with two exceptions as follows.
- If the player uses the joker as an ace in the low hand, it shall beat an ace in the dealer's low hand.
- Any other ace/ace tie, including player ace vs. dealer joker, shall be a push, and the outcome of the bet will be decided entirely on the five-card hands.
- The A2345 straight is the second highest.
The dealer must play the highest class (royal flush, straight flush, four of a kind, etc.) of poker hand possible in the high hand. If a class of hand can be played two or more ways, then the dealer will play the way resulting in the highest low hand. For example, with JJJQQQ, the dealer can play two different full houses, QQQJJ and JJJQQ, in the high hand. The dealer will play JJJQQ, maximizing the low hand with a Q. If the dealer’s best high hand is ace high or less, then he will play the second highest singleton in the low hand.
It took me months of pestering dealers to arrive at this understanding of the house way. Still, I could be mistaken. If the above is not correct, I welcome correction.
The dealer house way is going to be correct the vast majority of the time. A likely exception would be that if the player can play two different types of hands, both straight or higher, he should play the way resulting in the higher low hand. For example, with 4h, 5h, 6s, 7h, 8h, Ah the house would play flush/6, but I believe that straight/ace would be better.
The following table shows the various outcomes of a random simulation, in which both player and dealer followed the house way.
Mini Pai Gow Simulation
|Player wins both||1||272756408||0.148512|
|Player wins high, ace-ace tie for low||1||90505910||0.049279|
|Player wins high, joker-ace tie for low||1||21593791||0.011757|
|Dealer wins high, player wins low||0||466444175||0.253972|
|Player wins high, dealer wins low||0||466470915||0.253986|
|Player wins high, tie for low||0||66872795||0.036411|
|Dealer wins high, joker-ace tie for low||0||18478232||0.010061|
|Tie for high, player wins low||0||97365||0.000053|
|Tie for high, joker-ace tie for low||0||4749||0.000003|
|Dealer wins both||-1||272751553||0.148509|
|Dealer wins high, ace-ace tie for low||-1||93608360||0.050968|
|Dealer wins high, tie for low||-1||66864090||0.036406|
|Tie for high, dealer wins low||-1||97316||0.000053|
|Tie for both||-1||29165||0.000016|
|Tie for high, ace-ace tie for low||-1||23576||0.000013|
The next table summarizes the results of this same computer simulation. The lower right cell shows a house edge of 2.64%. Again, this assumes the player follows the house way. I have not analyzed optimal strategy, but my educated opinion is that it would be only a marginal improvement.
Mini Pai Gow Simulation
The following table shows the side bet pay table at O'Sheas casino, when I played there in November 2007. It pays based on the best possible player five-card hand, whether or not the player sets his high hand that way.
Mini Pai Gow Side Bet
|Five of a kind||1000||48||0.000002||0.002091|
|Four of a kind||50||19752||0.00086||0.043019|
|Three of a kind||3||853264||0.037167||0.111501|
The lower right cell shows a house edge of 7.38% on the side bet.