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

(Two or three decades ago I discovered a trivial fact about a gambling game which AFAIK has hardly been published. It popped into my head just now and I decided to publish it in SDMB, a journal of record!
Mods: feel free too move this to the “Too mundane and pointless even for MPSIMS” forum if you wish.)

The game is Pai Gow (the tile game, not the “poker” version). The trivial fact applies to a special bet called “behind the bank.” Googling for “behind the bank” I see this website which acknowledges the concept, though without explaining it:

Briefly, when the banker’s bet is exhausted during pay-out, remaining player’s bets are ignored – they neither lose nor win. But if someone has bet “behind the bank,” his (otherwise ignored) bet takes over and settles with those remaining players.

The (slightly) interesting factoid is that, ignoring any house commission, the behind bet is much more favorable than the ordinary banker bet. I’ll summarize why if there’s interest. Or, better yet, another Doper may be able to deduce what property Pai Gow might have that leads to the factoid.

Is the “banker” ordinarily the same as the “house”? And what happens if you bet “behind the bank” and the bank isn’t exhausted-- Is it just a push?

It’s easiest to describe how the croupier actually manipulates the chips when settling a round. Here’s an example:

Suppose Banker bets $40. Suppose Players 1-7 each bet $10; suppose their results are Win-Win-Lose-Draw-Draw-Lose-Lose.

Going in order, croupier will take $10 from banker’s bet (a pile of chips) and give it to Player 1, take $10 more and give it to Player 2; then take Player 3’s bet and $10 from Banker’s bet and put it into a pile for banker’s winnings. The drawn bets of Players 4 and 5 are ignored. Player 4’s bet is paired with the last $10 in banker’s bet and added to Banker’s winnings.

At this point, Banker’s $40 bet has been reduced to zero, but there is a pile of banker’s winnings which happens to have $40. Banker has broken even. Player’s 6 and 7 have not been matched with banker money and (in the absence of a “behind the bank” bet) would have their bets ignored – indeed the croupier might not even expose their hands to see if they would have won or lost.

But if there were a “behind the bank” bet of $10, it would be matched with Player 6’s bet. (A bet of $15 would also get half of the Player 7 action; $20 or more would cover both Players completely.)

(ETA: The right to bank rotates among the players. In Nevada, the house will act as a “Player” and take its turn to bank just as the other players. When the game was played decades ago in Northern California, the house was not legally allowed to Bank and took its profit as commission or table fee.)

So behind the bank bet wins if player losses exceed the banker’s bet?

In your hypothetical, if all 7 players lost, banker would win $40, behind the bank $10 and 6-7 are ignored?

The behind the bank bet comes into play (to either win or lose) when combined players’ wins and losses exceed the bank. Stated differently, in the example with $40 bank and total player bets of $70, the behind bet will come into play whenever player draws sum to less than $30.

Yes, assuming behind-bank bet is $10. If all 7 players won, banker would lose $40, behind lose $10, and two of the players would not get paid off.

(BTW, I don’t know if these “behind-bank” bets are even allowed in Nevada casinos. I saw them at NoCal (Emeryville) card rooms in the 1980’s.
… In Nevada I think the casino will effectively be betting “behind the bank” whenever banker’s bet is insufficient.)

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:

(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!)

I’d like to ask you about the Hi-Lo dice game played in Thailand.

(I’d start a new thread if I though interest would warrant.)

The Hi-Lo game played in rural Thailand has important differences from the Hi-Lo game played in Asian casinos. (I don’t know which variant is played in the illegal Bangkok casinos that cater to upper class.) The differences start with the printed playing layout itself. As you can see, it seems to have fewer options – but this is somewhat misleading. A banknote placed between two places on the layout might be a bet on both or either; in some cases the distinction is made by whether the banknote is flat or folded.

To start a game you must get permission from the local police (or keep the game very quiet). An exception is made for funeral wakes: neighbors are needed to protect from ghosts and police allow gambling as a means to stay awake.

The same person operates as banker throughout, normally the owner of the dice and other equipment. (I banked once when my brother-in-law needed to rest. That led to great excitement as the game transmuted to “Fool the Foreigner.”) Three dice are placed on a plate, covered with an opaque bowl, and shaken once (surprisingly lightly). Anyone may now place bets; bets are settled when the bowl is lifted to reveal the dice.

I won’t detail the bets and payoffs except to note an important difference from the standard casino game. The most common bets are Hi (three dice total 11 or more) and Lo (three dice total 10 or less). To give the House a vigorish, triplets (three Aces, or Three Deuces, or three Sixes, etc.) do not payoff as either Hi or Lo.

However, in the rural game the vigorish for the Hi and Lo bets is done differently. Triplets do payoff but Eleven total does not. (This may seeem very odd, since it seems to make the Lo bet an even-money proposition with no vigorish. I guess, however, that it is an implicit acknowledgement that rural dice are often loaded and high numbers more likely!)

I haven’t yet mentioned the most amazing aspect of the betting procedure. When you first observe the game you may see a player place a 100-baht note on Hi and someone else (his wife?) then move the banknote to Lo. The first player (husband?) now moves the note back to Hi. At first I assumed that the husband and wife were debating what their wisest bet was and had eventually settled on Hi. Boy was I wrong!

When the woman moved the banknote she performed a ‘Yak’ bet (from ยักย้าย, to divert). The man Yak’ed her back! There is still just the single banknote on the playing surface but 300 baht of bets exist!

When the dice are exposed the banker pays only the bets represented on the layout. Assuming Lo, he would take the man’s 100 baht. But the man is obligated for another 100 baht payable to the woman, whose Lo bet he Yakked! (Had the dice been Hi, banker and woman would each pay the man 100 baht.)

Had the woman moved the banknote to Lo a second time, and the man then moved it back to Hi again, there would be 500 baht of bets represented by that single banknote! Man or woman would have to pay the other 200 baht. Memory becomes important! Banker is only responsible for the bets still visible after all Yakking is complete, but will try to remember Yakking history – he wants the game to remain amicable.

I’ve been personally acquainted with four people who operated Hi-Lo games (though I’ve not even witnessed a game for a few years: my life is increasingly tame; the community increasingly civilized and sober). Another surprise was to learn that some dice, when sixes were on top, would cause a flashdrive-sized device to vibrate. I didn’t even Google to find out where such were for sale or what the price was; I was just amazed to see it in the very low-tech backwater place I live. :smiley:

ETA: ‘Yakked’ and ‘Yakking’ are words I invented for the post. Thai verbs aren’t conjugated at all, let alone with English conjugation endings.

(Yet once agan, a 6-minute edit window would have worked much much better for me than the 5-minute window.)

I hate Pai Gow. Can’t we just play Quang Jong?