dinkus
Joined: Jan 6, 2013
• Posts: 1
January 6th, 2013 at 9:30:44 PM permalink
What is the probability of one or more players receiving a 9 high pai gow as well as the dealer having a 9 high pai gow? As most are aware there are two ways of making a 9 high pai gow. For the purposes of this question it is irrelevant which of the two 9 high pai gows it is.
Paigowdan
Joined: Apr 28, 2010
• Posts: 5692
January 6th, 2013 at 9:37:35 PM permalink
Here are the probabilities of Pai Gow/High Card hands occuring in Pai Gow Poker;
Actually, there are 31,080 ways of making a 9-high pai gow hand with no straight, flush or pair when you consider the suit combinations that cannot form a four-card or better flush. It just seems that rare because there are 154M ways of getting a Pai Gow hand. Still, the 9-high is one in 5,000 hands, a very rare hand.

Hand_______Combinations_____P(Hand)_______Payout_______Value
Loses_______129,358,340______0.839209519____-1___________-0.839209519
A High PG___14,430,780________0.093619383____3___________0.280858148
K High PG___6,386,940_________0.041435139____5___________0.207175697
Q High PG___2,719,500_________0.017642699____7___________0.123498895
J High PG____963,480__________0.006250556____15__________0.093758345
T High PG____248,640__________0.001613047___25___________0.04032617
9 High PG___31,080________0.000201631__100_______0.020163085
Total:________154,143,080_______1_________________________-7.34%

The propabilities of a 9-hign facing another 9-high are about one in 24.6 Million; actually, a little higher because low off-suit cards were used up in the facing 9-high hand. But this is approximately correct.

NO one would design a bet for this.
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