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Pai Gow Tiles odds

Every number on this page comes from counting all 35,960 ways to deal four tiles from a 32-tile set. Nothing is simulated or estimated.

Quick answer

You hold at least one pair in 19.02% of deals, the Gee Joon pair in 1.21% (about 1 in 83), and two pairs in 0.334% (about 1 in 300). In 53.62% of deals your best high hand is an ordinary point hand.

35,960possible four-tile deals
0.334%two pairs
19.02%at least one pair
1.21%Gee Joon pair

Two tiles

Every two-tile hand

A 32-tile set can make 496 different two-tile hands (32 tiles choose 2). This is how they split by class.

All 496 two-tile hands a 32-tile set can make, from strongest class to weakest. Example tiles are one way to make each hand.
HandExampleHandsShare of 496
Pair163.23%
Wong81.61%
Gong163.23%
High Nine163.23%
9 points326.45%
8 points5611.29%
7 points5210.48%
6 points5611.29%
5 points448.87%
4 points5210.48%
3 points489.68%
2 points448.87%
1 point326.45%
0 points244.84%

Four tiles

Your best high hand from four tiles

For each of the 35,960 deals we tried all three splits and kept the strongest high hand available. The share of deals in each class:

The strongest high hand you can make from your four tiles, counted over all 35,960 possible deals.
Best high hand availableDealsShare
A pair6,84019.02%
Wong2,7047.52%
Gong4,24011.79%
High Nine2,8968.05%
Points only19,28053.62%

Pairs

Pairs, Gee Joon and two pairs

Counts over all possible four-tile deals.
EventDealsShareAbout 1 in
At least one pair6,84019.02%5.3
Gee Joon pair4351.21%83
Two pairs1200.334%300

Two pairs need four tiles that form two of the 16 permitted pairs at once, which is why they are so rare. Most pairs you see will be a single pair with two loose tiles.

Setting

Equal splits and the obvious best play

In 2,872 deals (7.99%), two different splits give exactly the same low hand and the same high hand, tie-break included. Our practice trainer accepts either split in those deals.

In 12,000 deals (33.37%), one split is at least as strong as every other split in both hands. That is the “obvious best play” that our house-way guide takes first, and the hand calculator flags it.

Method

How we counted

  • The set is the standard 32 tiles: 11 designs twice and 10 designs once, as listed on the tile chart.
  • Hands are scored in the order on the hand rankings page: 16 pairs, then Wongs, Gongs, High Nines, then points from nine to zero, with single-tile rank breaking equal totals.
  • Each Gee Joon tile counts as three or six, whichever is better, when it is not part of the pair.
  • The figures describe your own four tiles only. They are not chances of beating a banker, and they do not include commissions or fees.
  • The counting code is the same code that runs the hand calculator and trainer in your browser.

Data

Download the data

Pai Gow Tiles odds (CSV)
32-tile ranking (CSV)

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