Pai Gow probabilities
February 18th, 2012 at 2:21:59 PM
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Background
Thanks for some excellent threads in the forum. So when I stumbled across Pai Gow in two London casinos last weekend, thought I must learn the game and, like Blackjack Switch, try to perform my own calculations to get a better insight into a strategy that I can remember. www.paigow.com has an excellent description for beginners like me.
What I found easiest was after realizing the tiles are essentially a 6-6 domino set (without blanks) where some tiles are duplicated. All the doubles, plus a few others, are in the top row (of 8) and the second row has four pairs in order and then the remaining four couples in value order.
Methodology
When working out Pai Gow (cards) for a given seven cards you hold it's fairly easy to work out all the possible Hi and Lo hands the dealer can get with the remaining ones, and hence their associated probabilities. Then maximize your chances given the options for the various ways of playing the hand.
I was naively assuming as a first approximation for Tiles (yes I know it wouldn't be totally correct, for instance the dealer can't actually get a pair when you have the tile) to work out the initial distributions of the dealer's hands and using this compare house way with the best way to set every combination - concentrating on obvious differences.
Then a penny dropped.
With Pai Gow tiles for a given set of four tiles it's a matter of working out how your various two hand options compare against each of the 3620 possible dealer's two hands AND you can adjust the weightings if there are overlaps.
Question
Does it sound reasonable to use an approximation to see which are the obvious cases where house way is wrong (i.e. by most percentage error) and then work them out in details?
Using a spreadsheet was this a fair way to calculate house for four odds tiles (hands with One or Two pairs seems easy)
(i) Best Lo is same combo as Best Hi then One Way
(ii) If Value(Best Hi) < 7 play BestLo
(iii) Gong/Wong/exceptions (which I ignored at this stage)
(iv) If Best Lo < C3 play BestHi
(v) Choice of Wong/Gong/Hi9 : best LoHand keeping >=Hi9 in Hi
(vi) Strengthen high hand if value of Hi hand is same under BestHi and BestLo options and Lo>=8 (i.e. shuffle tiles)
(vii) Similarly if value of hands are (6-7) (6-8) (6-9) or with (7-9):(8-8) play BestLo except if two highest rank tiles in one hand then play BestHi
(viii) minor other exceptions (which I ignored at this stage)
(ix) Make best Lo
Many thanks
Charlie P
Thanks for some excellent threads in the forum. So when I stumbled across Pai Gow in two London casinos last weekend, thought I must learn the game and, like Blackjack Switch, try to perform my own calculations to get a better insight into a strategy that I can remember. www.paigow.com has an excellent description for beginners like me.
What I found easiest was after realizing the tiles are essentially a 6-6 domino set (without blanks) where some tiles are duplicated. All the doubles, plus a few others, are in the top row (of 8) and the second row has four pairs in order and then the remaining four couples in value order.
Methodology
When working out Pai Gow (cards) for a given seven cards you hold it's fairly easy to work out all the possible Hi and Lo hands the dealer can get with the remaining ones, and hence their associated probabilities. Then maximize your chances given the options for the various ways of playing the hand.
I was naively assuming as a first approximation for Tiles (yes I know it wouldn't be totally correct, for instance the dealer can't actually get a pair when you have the tile) to work out the initial distributions of the dealer's hands and using this compare house way with the best way to set every combination - concentrating on obvious differences.
Then a penny dropped.
With Pai Gow tiles for a given set of four tiles it's a matter of working out how your various two hand options compare against each of the 3620 possible dealer's two hands AND you can adjust the weightings if there are overlaps.
Question
Does it sound reasonable to use an approximation to see which are the obvious cases where house way is wrong (i.e. by most percentage error) and then work them out in details?
Using a spreadsheet was this a fair way to calculate house for four odds tiles (hands with One or Two pairs seems easy)
(i) Best Lo is same combo as Best Hi then One Way
(ii) If Value(Best Hi) < 7 play BestLo
(iii) Gong/Wong/exceptions (which I ignored at this stage)
(iv) If Best Lo < C3 play BestHi
(v) Choice of Wong/Gong/Hi9 : best LoHand keeping >=Hi9 in Hi
(vi) Strengthen high hand if value of Hi hand is same under BestHi and BestLo options and Lo>=8 (i.e. shuffle tiles)
(vii) Similarly if value of hands are (6-7) (6-8) (6-9) or with (7-9):(8-8) play BestLo except if two highest rank tiles in one hand then play BestHi
(viii) minor other exceptions (which I ignored at this stage)
(ix) Make best Lo
Many thanks
Charlie P
