Pai Gow Poker Calculation

Recently, I’ve been studying Pai Gow Poker and analyzing some data from the wizard website. I have a question: on the wizard website /games/pai-gow-poker/appendix/1/, in the Five Card Power Ratings table, the number of AAA combinations is listed as 635,504, but my calculations show only 634,656. According to the Trump Plaza house way rules, only 5 Aces (AAAAA+XY: 1,056 combinations) and full house (AAA+BB+XY: 633,600 combinations) should appear. I wrote a program to implement the house way, and my results match my calculations. Is there anyone who can discuss this with me?
Additionally, I am very impressed with how quickly Pai Gow calculator on wizard website can compute the number of win, push, and loss combinations for a hand. Does anyone have any ideas on how it works? I want to develop my own strategy based on specific casino rules .

Okay, I've verified that the Wizard's tables are stated to be based on the Trump Plaza House Way rules and he does show 635504 combinations for 3 aces + 2 singletons in the 5 card hand

I agree that 5 Aces (AAAAA+XY) has 1,056 combinations.

I looked at (AAA+BB+XY: 633,600 combinations) and I am also calculating 633,600 combinations.

I'll continue looking at this tomorrow.

I have been asked to take a look at this thread. First, here are a couple links.

PGP power ratings

Trump Plaza house way

As to the five aces, isn't the only way to play that with WAAAAKK (where W = wild), which has 6 combinations? With any other five aces, wouldn't the house split the five aces into AAA in the high and AA in the low?

Well I've spent a lot of time on this and I still agree with your calculation of 634,656 combinations for AAA-xy in the 5-card hand.

So, I think the number that appears in Appendix 1 in WOO is incorrect by 848 combinations, as you have indicated. I have been unable to identify any possibilities for what the Wizard's miscalculation of 848 combinations might have originated from. His total number of combinations for all 5-card hands does sum to the correct number (which is combin(53,7)) when he uses 635,504 combinations for AAA-xy so the implication is that one of the other numbers in this App1. table must also be too low by 848 combinations. But I just can't figure out what the source of the error is.

Wizard is away from the forum for a few days; I'll call this to his attention when he returns.

Thank you for your response. When there are five As with pair, high hands are full house not AAA.So it must be WAAAAXY.

Thanks. In my results, the number of low hand pairs A is exactly 848 more than the website. I speculate that it may be because when straight or flush with WAA , my result is AA+straight or flush, and the website is XY+3A. Besides, in my split results, there are more straight or flush hand hands than the website.

Should I calculate all C(53,7) * C(46,7) combinations in order to get the RTP? Are there any tricks that can help me simplify the calculation?

Quote: Allen

Thank you for your response. When there are five As with pair, high hands are full house not AAA.So it must be WAAAAXY.
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Yes, when dealer has WAAAAXY, the rules for the Trump Casino House Way say that the hand is split AAAXY | AA; whereas WAAAABB is set as AAABB|AA. I have considered many other hands and cannot find any hands other than AAAAAXY and AAABBXY that are set with AAAXY in the back 5-card hand.

Quote: Wizard

I have been asked to take a look at this thread. First, here are a couple links.

PGP power ratings

Trump Plaza house way

As to the five aces, isn't the only way to play that with WAAAAKK (where W = wild), which has 6 combinations? With any other five aces, wouldn't the house split the five aces into AAA in the high and AA in the low?
link to original post

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