"Behind the Bank" is a winning bet in Pai Gow

[septimus]

@Dead_Cat

I’ve only barely heard of Pai Gow, but I can answer this question for you: if there is a simple strategy that creates a positive expectation for the player, it won’t be allowed by the casino (I say simple to exclude card counting in Blackjack).

The behind-bank bet combined with the ordinary banker bet (also made by a player) have exactly the same combined disadvantage as a larger banker bet would have.

And casinos aren’t always as smart as one thinks! As just one example, when Caesar’s Palace sets its Pai Gow tiles it always keeps Jee Joon together though that is often wrong. Googling to see if I could point to this fact, I found a SDMB post by myself. :smack:

@septimus

…
Here’s another example where casinos don’t always follow odds: For a while I was interested in Pai Gow (the tile game, not the poker variant). Caesar’s Palace had a rule always to keep Je Joon when available “because it can’t lose.” But even without doing computer study, it’s easy to see that if the other tiles are, say, 5 and 6, splitting the Je Joon is much more profitable. (Splitting is also very unlikely to lose, but is also much less likely to tie.)

(The details of Pai Gow are complicated and uninteresting and unnecessary for solving, in a summary or abstract way, the “puzzle” I posed. If you want me to describe a gambling game with fascinating procedures, ask me about the Hi-Lo dice game played in Thailand!)