Pai Gow Tiles house edge
Computed by exact enumeration of every one of the 736,281,000 player and dealer matchups. No simulation.
Short answer
Setting your hands by the house way while the dealer banks costs 2.3939% per hand with the standard five percent commission. Playing optimally cuts it to 1.6035%. Taking your turn to bank cuts it to 0.6067%. Roughly two hands in five push, so the game is also one of the lowest-variance bets on the floor.
The three scenarios
| Scenario | You win | You lose | Push | House edge |
|---|---|---|---|---|
| Dealer banks, you use the house way | 29.5478% | 30.4643% | 39.9879% | 2.3939% |
| Dealer banks, you play optimally | 29.5537% | 29.6795% | 40.7667% | 1.6035% |
| You bank, both use the house way | 30.4643% | 29.5478% | 39.9879% | 0.6067% |
EXACT All figures enumerated over every one of the 35,960 player hands against every one of the 20,475 dealer hands drawable from the remaining 28 tiles. Five percent commission on winning hands. The dealer always sets by the house way.
Three things these numbers say
1. Skill is worth more here than almost anywhere
The gap between house-way play and optimal play is 0.79% of every bet. For comparison, the gap between correct and sloppy blackjack basic strategy is smaller. Very few casino games reward study this heavily, and almost nobody at the table is collecting it.
2. The commission is the entire house edge
Look at the third row with the commission switched off. A player who banks, with both sides on the house way and no commission charged, holds an edge of 0.9165%. The banker wins every copy and every zero-versus-zero tie, and that is worth close to a full percent by itself.
So the commission is not a surcharge on a game the house already wins. It is the mechanism that makes the house win. This also explains why no-commission Pai Gow, offered in a few jurisdictions, always comes with the condition that the dealer banks every hand.
3. Take the bank
Banking moves you from the wrong side of every copy to the right side of it. That is worth 2.3939% down to 0.6067%, a saving of nearly 1.8% per hand, which is a bigger effect than playing optimally. If you can cover the bets, bank whenever it is your turn.
Why so many pushes
You must win both comparisons to be paid, and lose both to lose your bet. Every other result returns your money. That happens on 39.9879% of hands. Your bankroll erodes slowly, which is a real part of the game's appeal and worth understanding before you mistake a long flat session for being due.
Method and honesty notes
The engine enumerates rather than simulates. It reproduces every published checkpoint we could test it against: 35,960 four-tile hands, 3,620 distinct sets, 120 two-pair hands, 6,720 one-pair hands, 29,120 no-pair hands and 2,704 Wong hands without a pair. The dealer strategy reproduces all fifteen worked examples published with the Generic House Way.
Two disclosures. First, these figures are computed against the Generic House Way, not against any one named casino's house way, for the reasons set out on the house way page. A specific casino's rules will move the third and fourth decimal places, not the headline. Second, published sources differ slightly on the single-tile tie-break rank of the two Gee Joon tiles. We rank the 2-4 just below the Chop Chit tiles and the 1-2 last of all, which is the finer of the two published orderings. It affects a small number of tie resolutions.
TODO: per-hour expected loss and session-length figures require a hands-per-hour rate we have not measured. Not published rather than invented.
TODO: the Fortune and Bonanza style side bets sometimes offered on Pai Gow Tiles are not yet analyzed. Not published rather than invented.