Quote:
Originally Posted by tringlomane
Wow, I'm a tard. When he has a king high back, the highest front he can have is QJ. But I'm not sure where you got the player beating a K high from the dealer 99.75% of the time. If the dealer gets a K high in the back 6.71% of the time, so do we. And when we do get K-high or less, we win half of them, barring a nearly impossible front copy with a high card. So our overall equity is closer to 100 - 6.71%/2 = 96.645% in the front.
Now for the back, like you pointed out, the dealer must play QJ or less. Here the best way to determine the dealer's average front is to start counting out all the K-high hands or lower. But since I want to watch overtime hockey, I have to come back to this. From rough inspection though, I don't think the house edge changes a lot.
http://wizardofodds.com/games/pai-gow-poker/appendix/1/
For 5-card hands 9-5 through K-10, I multiplied their probabilities by the Banker PR stat, then summed the products. That came to 0.25%, which represents the probability of the dealer getting K-high or lower AND beating you in the 5-card hand. The top of that page explains what those figures mean.
Yes we get it 6.71% of the time too, but given what we're comparing, it's only relevant if the dealer also has it (6.71% of time). The chances of both of us having K-high or worse is 6.71% * 6.71%, or 0.45%. Cut THAT in half, and you get 0.23%, which matches my figure above when you account for rounding and banker winning ties.
edit: these are not hyper-accurate numbers, since I'm not accounting for the effect of card removal... but they're ballpark figures.
Last edited by Lattimer; 05-30-2012 at 11:33 PM.