FWIW, Pai-Gow is Probably Beatable

I was in Vegas with friends this weekend, and while playing Pai-Gow, it occurred to me a pretty simple count method could take advantage of the dragon hand (extra hand) option. The idea is simple: 5 confederate players, 4 always making minimum bets, and the 5th player always making the maximum bet. (Note there's no varying of wager here.) All 5 players communicate the number of Aces seen, as well as if the Joker is seen. For simplicity, treat aces and Joker equallly, so the count spans 0 thru 5. On average, the count is either 2 or 3. Fairly often, the count is 4 or 5. I propose that the dragon hand has a +EV for a high count (rationale: strip out the joker and aces from the deck, and the player probably has a significant advantage). So, when the count is bad, one of the minimum players takes the dragon. But, when the count is good, the minimum players pass the dragon, and the max bettor takes the option. (The dragon bet must equal the initial wager.)

I haven't run through the analysis yet, because I figure the net won't be too fantastic. Since the commission is 5% on a winning hand, the per hand house edge is probably about 1.25%. Let's say the max bet is 100x the min bet (e.g., $10 min bet, $1000 max bet). So, the 4 min bets together are only 1/25 of the single max bet, and we can ignore the negative EV of the min bets for now. We need to run the analysis for the various counts, and perhaps use specific pair-splitting tables per count. I'm guessing that the edge from the optimized pair-splitting tables is only .25%. However, in the best case (all aces and jokers out), the dragon hand may be +5% EV. But, the total EV is the optimized EV per count weighted by the count frequency, and the net might not be very much. I'm guessing the overall EV is positive, but even if it's +1%, is it worth it? You'll have 5 guys trying to take $10/hand out of a game?

Any comments? Can you convince me to do the analysis? (I have some C++ code for California Pai-Gow, with the wild joker. I'd have to do so updating of the code, etc.)

Stephen

Pai-Gow is a pretty slow game. People squeezing out hands, asking advise on how to set it, then the dragon is offered, taken, and set.

It's pretty dumb of the casino to allow people to take additional action after seeing all the cards. I'm sure if this works, you'll hit it, and they'll take away the dragon. However, it's hard to change tradition. The current ettiquitte (inferred from Asian players) is that you don't take the dragon if you have a good hand; you allow the next person the chance, in case he has a bad hand. (They use it as a hedge.) Of course, in reality, the dragon should be taken if the count is good, and passed altogether if it is bad.

Don't forget, you're splitting the profit amongst 5 confederates. Also, it's pretty hard to get 5 friends together at any time (most everyone has families). I'm not sure if the dragon is offered in Southern California. I think I've only seen it in Vegas. So, you pretty much have to live there.

Lets say there is a huge EV or whatever. How do you know if those cards are in the dealers hand or the dragon hand. Still sounds 50/50 to me. Its not like BlackJack where the dealer can bust. You may have some information maybe on how to set your hand, but those 14 cards that are left, even if you know exactly what cards they are, they are just as likely still to be anywhere.

I figured I might know the count, but I don't know which hand is better (bank or dragon). But then it occurred to me that the real question is, "is a stripped (loaded) deck better for the player?" I'm guessing that it is, but I haven't run the analysis yet, mostly because I don't think the edge is so great. Also, I only go to Vegas once a year, and I probably wouldn't do this either.

The advantage is very analogous to blackjack -- you have deep deck penetration every hand, the known ace & joker count, and the option to make a huge bet on the dragon. I should just run the analysis.

I'm guessing that it is, but I haven't run the analysis yet, mostly because I don't think the edge is so great.

Hi Stephen, it is interesting to hear from a guy with an eye for unusual angles.

I agree with most of what you've said. The effects of removal are obviously going to be fairly symmetrical. I once tried dealing hundreds of hands when I knew the dealer's cards, and it is surprsing how infrequently it is possible to change strategy to exploit this (I know this isn't exactly what you are getting at). That said, if you crunch the numbers and can get a small edge, 1% would probably cut it even in a slow game.
The reason is that pai gow poker has the lowest variance of all casino games. You can bet much more aggressively than you would at the blackjack table with the same risk of ruin.

Why is it 5 percent to the house? The house sets the hand determined by the best case scenario. Its almost a 50/50 game. The house still has a slight edge on this game because of the "Banker wins copy hands rule". In some casinos you can gain the upper hand here by "Banking" yourself, but that rule is disappearing fast (not sure why it would either considering the house asseses absolutely no risk during this time). However, the evenness of this game is eaten away because of the commission. Unlike Baccarat, where the bank is the 53/47 favorite, the commission here in Pai Gow is taken from a close underdog as it is, making your take in this game even harder if not impossible to overcome the odds.

There is a concept Baccarat though that will net you a fortune, which is interesting, but a severe longshot. In the game of Baccarat, the cut off is all but 14 cards, this will allow a person to keep track of EVERY single card and know for certain what 14 cards are left by the end of the shoe. Normally you get a 2nd to last hand when the cut card comes out so you could possibly get down to the final 9 cards. Here's the longshot. Keep track of every single card on your "scorecard" (which you are allowed to do) and when you get down to the final hand of the shoe it is possible to be left with all of one value of card (for example, all face cards). That is when you bet your ENTIRE bankroll on TIE. You will know for sure that if the last 10 cards are any one value, then it will become a tie bet and it pays 8 to 1.

Sorry to get off the Pai Gow issue.

Why is it 5 percent to the house? The house sets the hand determined by the best case scenario. Its almost a 50/50 game. The house still has a slight edge on this game because of the "Banker wins copy hands rule". In some casinos you can gain the upper hand here by "Banking" yourself, but that rule is disappearing fast (not sure why it would either considering the house asseses absolutely no risk during this time). However, the evenness of this game is eaten away because of the commission. Unlike Baccarat, where the bank is the 53/47 favorite, the commission here in Pai Gow is taken from a close underdog as it is, making your take in this game even harder if not impossible to overcome the odds.

The house edge for the player is just over 2.5% depending on what house way is used.

There is a concept Baccarat though that will net you a fortune, which is interesting, but a severe longshot. In the game of Baccarat, the cut off is all but 14 cards, this will allow a person to keep track of EVERY single card and know for certain what 14 cards are left by the end of the shoe. Normally you get a 2nd to last hand when the cut card comes out so you could possibly get down to the final 9 cards. Here's the longshot. Keep track of every single card on your "scorecard" (which you are allowed to do) and when you get down to the final hand of the shoe it is possible to be left with all of one value of card (for example, all face cards). That is when you bet your ENTIRE bankroll on TIE. You will know for sure that if the last 10 cards are any one value, then it will become a tie bet and it pays 8 to 1.

Unfortunately this will occur every few ice ages.
You can do better by betting extreme densities of ranks which are not quite so infrequent, though still very infrequent. For example, a last hand composed of fives and tens yields an edge of 400%, a subset I once managed to actually get a large bet down on. I wrote about this in my Baccarat for the clueless.

But, this is not a strategy for the faint-hearted. It is probably the hardest form of advantage play to master. It requires sitting around for months, possibly years, betting as little as possible and frequently leaving the table, to make one bet, that might be worth hundreds of thousands of dollars in EV, but still has a <50% chance of winning. Make one error in counting a card during the shoe which yields a big bet and you could cost yourself a year's wages in EV.

There are only half-a-dozen players on the planet mad enough to have attempted this.

How can the player have an advantage in Pai Gow when the best way to set your hand is the house way. First, is this way the "best" way to play? Second, if the house wins copies, shouldn't that take away from the player advantage making it a house game before commission? Just wondering why it is a 2.5% and not more.

As for Baccarat, of course it only happens once in a million years. As for tracking densities of values, its easy, just keep track with the scorecard the casino offers, or make your own and bring them with you. It IS allowed, that is until books are widely published on the matter.