Pai Gow Tiles hand library: every hand the house way plays wrong

The dealer follows a fixed procedure. On 524 hands that procedure is not the best available play. These are the 250 that cost the most, each with the exact expected value of all three splits.

Short answer

Copying the house way costs 0.79% of every bet against optimal play. That loss is not spread evenly. It is concentrated in 524 specific hands, and the 250 listed here account for 81.4% of it. Learn these and you capture most of the gap without learning the whole game.

Each page enumerates every one of the 20,475 hands the dealer can hold and reports the exact expected value of all three ways you can set your tiles. The numbers are computed, not estimated, and they are not published anywhere else.

HandCorrect settingCost of the house way
Day + Yun + Chop Gow + Chop Ng7 points with 7 points21.79%
Teen + Yun + Chop Gow + Chop Ng7 points with 7 points16.48%
Gor + Mooy + Chop Gow + Chop Chit9 points with 1 point14.08%
Gor + Mooy + Tit + Chop Gow9 points with 1 point13.85%
Day + Yun + Look + Chop Gow8 points with 7 points12.97%
Gor + Foo + Chop Gow + Chop Ng9 points with 0 points12.80%
Mooy + Bon + Chop Gow + Chop Chit9 points with 1 point11.53%
Mooy + Bon + Tit + Chop Gow9 points with 1 point11.31%
Bon + Foo + Look + Chop Chit8 points with 0 points10.62%
Yun + Gor + Chop Bot + Chop Chit6 points with 1 point10.09%
Day + Yun + Ping + Chop Ng8 points with 7 points10.06%
Bon + Foo + Tit + Look8 points with 0 points9.94%
Bon + Foo + Chop Gow + Chop Ng9 points with 0 points9.92%
Day + Mooy + Bon + Tit7 points with 6 points9.82%
Day + Mooy + Bon + Chop Chit7 points with 6 points9.82%
Mooy + Bon + Look + Chop Gow9 points with 0 points9.76%
Day + Yun + Foo + Chop Ng9 points with 7 points9.72%
Day + Gor + Tit + Chop GowWong with 1 point9.70%
Day + Gor + Chop Gow + Chop ChitWong with 1 point9.70%
Bon + Foo + Look + Chop Bot9 points with 0 points9.42%
Gor + Mooy + Look + Chop Gow9 points with 0 points9.39%
Mooy + Bon + Look + Chop Chit7 points with 0 points9.29%
Yun + Gor + Tit + Chop Bot6 points with 1 point9.22%
Gor + Mooy + Look + Chop Chit7 points with 0 points9.14%
Day + Chop Gow + Chop Bot + Chop Ng7 points with 7 points9.06%
Day + Yun + Bon + Foo9 points with 6 points9.00%
Day + Yun + Chop Bot + Chop Ng7 points with 6 points8.87%
Foo + Look + Chop Bot + Chop Ng9 points with 1 point8.82%
Day + Yun + Bon + Chop Gow7 points with 6 points8.74%
Teen + Yun + Look + Chop Gow8 points with 7 points8.74%
Day + Gor + Mooy + Tit7 points with 6 points8.69%
Day + Gor + Mooy + Chop Chit7 points with 6 points8.69%
Bon + Ping + Chop Gow + Chop Chit9 points with 1 point8.65%
Mooy + Bon + Tit + Look7 points with 0 points8.60%
Gor + Mooy + Tit + Look7 points with 0 points8.45%
Bon + Ping + Tit + Chop Gow9 points with 1 point8.42%
Yun + Chong + Chop Gow + Chop Ng7 points with 1 point8.41%
Foo + Look + Chop Chit + Chop Ng8 points with 1 point8.37%
Day + Yun + Bon + Ping8 points with 6 points8.32%
Gor + Foo + Look + Chop Chit8 points with 0 points8.32%
Gor + Mooy + Chop Gow + Chop Bot9 points with 2 points8.26%
Yun + Bon + Look + Chop Gow7 points with 0 points8.16%
Day + Mooy + Tit + Chop Ng7 points with 7 points8.15%
Day + Mooy + Chop Chit + Chop Ng7 points with 7 points8.15%
Day + Yun + Gor + Chop Gow7 points with 6 points8.02%
Teen + Yun + Bon + Chop Gow7 points with 6 points7.84%
Foo + Tit + Look + Chop Ng8 points with 1 point7.71%
Gor + Foo + Tit + Look8 points with 0 points7.65%
Chong + Bon + Foo + Tit8 points with 0 points7.63%
Chong + Bon + Foo + Chop Chit8 points with 0 points7.63%
Gor + Ping + Chop Gow + Chop Chit9 points with 1 point7.50%
Gor + Foo + Look + Chop Bot9 points with 0 points7.43%
Chong + Foo + Chop Bot + Chop Ng9 points with 1 point7.40%
Yun + Gor + Tit + Chop Gow7 points with 1 point7.39%
Yun + Gor + Chop Gow + Chop Chit7 points with 1 point7.39%
Mooy + Look + Chop Chit + Chop Ng7 points with 1 point7.37%
Bon + Ping + Look + Chop Gow9 points with 0 points7.36%
Yun + Bon + Tit + Chop Gow7 points with 1 point7.35%
Yun + Bon + Chop Gow + Chop Chit7 points with 1 point7.35%
Gor + Ping + Tit + Chop Gow9 points with 1 point7.28%
Mooy + Chong + Bon + Chop Gow9 points with 0 points7.22%
Day + Tit + Chop Gow + Chop NgWong with 2 points7.21%
Chong + Foo + Tit + Chop Ng8 points with 1 point7.18%
Chong + Foo + Chop Chit + Chop Ng8 points with 1 point7.18%
Yun + Bon + Chop Bot + Chop Chit6 points with 1 point7.18%
Mooy + Chong + Tit + Chop Ng7 points with 1 point7.06%
Mooy + Chong + Chop Chit + Chop Ng7 points with 1 point7.06%
Yun + Mooy + Foo + Chop Bot9 points with 8 points7.04%
Day + Chop Gow + Chop Chit + Chop NgWong with 2 points6.99%
Day + Bon + Ping + Tit7 points with 6 points6.96%
Day + Bon + Ping + Chop Chit7 points with 6 points6.96%
Teen + Day + Yun + Foo9 points with 4 points6.87%
Yun + Chong + Bon + Chop Gow7 points with 0 points6.77%
Mooy + Tit + Look + Chop Ng7 points with 1 point6.71%
Day + Gor + Mooy + Chop Gow9 points with 6 points6.66%
Mooy + Chong + Bon + Tit7 points with 0 points6.62%
Mooy + Chong + Bon + Chop Chit7 points with 0 points6.62%
Day + Mooy + Bon + Chop Gow9 points with 6 points6.60%
Yun + Bon + Foo + Look9 points with 0 points6.54%
Day + Yun + Chong + Chop Gow8 points with 7 points6.52%
Mooy + Bon + Chop Gow + Chop Bot9 points with 2 points6.43%
Chong + Bon + Foo + Chop Bot9 points with 0 points6.41%
Day + Ping + Chop Bot + Chop Ng8 points with 7 points6.41%
Gor + Mooy + Chop Bot + Chop Chit8 points with 1 point6.37%
Gor + Mooy + Chong + Chop Gow9 points with 0 points6.37%
Day + Yun + Tit + Chop Ng7 points with 5 points6.35%
Day + Yun + Chop Chit + Chop Ng7 points with 5 points6.35%
Yun + Bon + Tit + Chop Bot6 points with 1 point6.31%
Mooy + Bon + Look + Chop Bot8 points with 0 points6.30%
Yun + Chong + Bon + Foo9 points with 0 points6.27%
Day + Mooy + Chop Gow + Chop Ng9 points with 7 points6.21%
Teen + Foo + Ping + Look8 points with 1 point6.21%
Gor + Mooy + Tit + Chop Chit7 points with 1 point6.14%
Teen + Mooy + Foo + Look8 points with 1 point6.14%
Gor + Mooy + Chong + Tit7 points with 0 points6.06%
Gor + Mooy + Chong + Chop Chit7 points with 0 points6.06%
Day + Yun + Bon + Chop Bot6 points with 6 points5.99%
Gor + Foo + Tit + Chop Chit8 points with 1 point5.98%
Teen + Mooy + Chong + Foo8 points with 1 point5.98%
Day + Yun + Gor + Chop Bot6 points with 6 points5.96%
Day + Yun + Mooy + Bon8 points with 6 points5.95%
Yun + Foo + Ping + Chop Bot9 points with 8 points5.94%
Day + Yun + Chop Gow + Gee Joon (2-4)8 points with 7 points11.76%
Day + Yun + Chop Gow + Gee Joon (1-2)8 points with 7 points11.74%
Teen + Mooy + Bon + Chop Gow9 points with 6 points5.82%
Teen + Gor + Mooy + Chop Gow9 points with 6 points5.80%
Gor + Chong + Foo + Tit7 points with 1 point5.80%
Gor + Chong + Foo + Chop Chit7 points with 1 point5.80%
Yun + Look + Chop Gow + Chop Ng7 points with 1 point5.79%
Day + Yun + Mooy + Chop Ng8 points with 7 points5.75%
Yun + Tit + Chop Gow + Chop Ng7 points with 2 points5.68%
Gor + Mooy + Look + Chop Bot8 points with 0 points5.67%
Bon + Foo + Tit + Chop Chit8 points with 1 point5.66%
Bon + Ping + Chop Bot + Chop Chit8 points with 1 point5.58%
Mooy + Bon + Chop Bot + Chop Chit8 points with 1 point5.57%
Gor + Mooy + Tit + Chop Bot8 points with 1 point5.51%
Yun + Chop Gow + Chop Chit + Chop Ng7 points with 2 points5.43%
Yun + Gor + Tit + Chop Chit5 points with 1 point5.43%
Chong + Bon + Ping + Chop Gow9 points with 0 points5.43%
Yun + Bon + Look + Chop Bot6 points with 0 points5.42%
Teen + Yun + Chop Bot + Chop Ng7 points with 6 points5.32%
Day + Foo + Ping + Look8 points with 1 point5.26%
Bon + Ping + Look + Chop Chit7 points with 0 points5.23%
Yun + Gor + Look + Chop Bot6 points with 0 points5.23%
Bon + Ping + Look + Chop Bot8 points with 0 points5.20%
Day + Mooy + Foo + Look8 points with 1 point5.19%
Gor + Ping + Chop Bot + Chop Chit8 points with 1 point5.09%
Yun + Chong + Foo + Chop Ng9 points with 1 point5.06%
Day + Bon + Ping + Chop Bot8 points with 6 points5.03%
Day + Mooy + Chong + Foo8 points with 1 point5.03%
Day + Mooy + Bon + Chop Bot8 points with 6 points4.95%
Day + Yun + Ping + Look8 points with 8 points4.81%
Teen + Mooy + Chop Gow + Chop Ng9 points with 7 points4.80%
Teen + Yun + Ping + Chop Ng8 points with 7 points4.78%
Teen + Chong + Foo + Ping8 points with 1 point4.73%
Day + Ping + Chop Gow + Chop Ng9 points with 7 points4.72%
Bon + Ping + Tit + Chop Bot8 points with 1 point4.71%
Mooy + Bon + Tit + Chop Bot8 points with 1 point4.71%
Teen + Gor + Tit + Chop GowWong with 1 point4.63%
Teen + Gor + Chop Gow + Chop ChitWong with 1 point4.63%
Yun + Gor + Look + Chop Gow7 points with 0 points4.63%
Day + Yun + Gor + Foo9 points with 6 points4.62%
Ping + Look + Chop Bot + Chop Ng8 points with 1 point4.62%
Gor + Bon + Foo + Chop Gow8 points with 0 points4.60%
Bon + Ping + Tit + Look7 points with 0 points4.55%
Yun + Gor + Bon + Chop Ng9 points with 2 points4.52%
Yun + Gor + Chong + Chop Gow7 points with 0 points4.52%
Bon + Chop Gow + Chop Bot + Chop Chit7 points with 1 point4.48%
Teen + Yun + Foo + Chop Ng9 points with 7 points4.44%
Mooy + Chong + Chop Gow + Chop Chit7 points with 5 points4.43%
Gor + Chop Gow + Chop Bot + Chop Chit7 points with 1 point4.43%
Yun + Gor + Chong + Foo9 points with 0 points4.36%
Yun + Gor + Foo + Look9 points with 0 points4.36%
Yun + Mooy + Foo + Chop Ng9 points with 5 points4.30%
Day + Ping + Tit + Chop Ng7 points with 7 points4.29%
Day + Ping + Chop Chit + Chop Ng7 points with 7 points4.29%
Day + Yun + Gor + Ping8 points with 6 points4.29%
Mooy + Chong + Ping + Chop Gow9 points with 6 points4.28%
Yun + Chong + Bon + Chop Bot6 points with 0 points4.27%
Day + Yun + Gor + Mooy8 points with 6 points4.24%
Gor + Ping + Tit + Chop Bot8 points with 1 point4.23%
Mooy + Look + Chop Bot + Chop Ng8 points with 1 point4.21%
Day + Foo + Tit + Chop Ng8 points with 7 points4.19%
Day + Foo + Chop Chit + Chop Ng8 points with 7 points4.19%
Yun + Bon + Ping + Look8 points with 0 points4.17%
Yun + Bon + Chop Gow + Chop Bot7 points with 2 points4.09%
Teen + Day + Mooy + Chop Gow9 points with 4 points4.07%
Day + Yun + Ping + Chop GowWong with 8 points4.07%
Teen + Yun + Bon + Foo9 points with 6 points4.07%
Teen + Day + Look + Look8 points with 8 points16.22%
Gor + Ping + Look + Chop Bot8 points with 0 points4.04%
Mooy + Chong + Bon + Look6 points with 0 points4.04%
Mooy + Chong + Ping + Tit7 points with 6 points4.02%
Mooy + Chong + Ping + Chop Chit7 points with 6 points4.02%
Gor + Mooy + Ping + Chop Ng9 points with 0 points4.01%
Gor + Chong + Tit + Gee Joon (2-4)9 points with 1 point7.99%
Gor + Chong + Chop Chit + Gee Joon (2-4)9 points with 1 point7.99%
Day + Bon + Foo + Tit8 points with 6 points3.98%
Day + Bon + Foo + Chop Chit8 points with 6 points3.98%
Gor + Chong + Tit + Gee Joon (1-2)9 points with 1 point7.95%
Gor + Chong + Chop Chit + Gee Joon (1-2)9 points with 1 point7.95%
Day + Bon + Ping + Chop Gow9 points with 6 points3.93%
Teen + Mooy + Bon + Tit7 points with 6 points3.90%
Teen + Mooy + Bon + Chop Chit7 points with 6 points3.90%
Gor + Foo + Chop Bot + Chop Chit9 points with 1 point3.87%
Mooy + Chong + Tit + Look7 points with 2 points3.87%
Mooy + Chong + Look + Chop Chit7 points with 2 points3.87%
Bon + Tit + Chop Gow + Chop Bot7 points with 1 point3.83%
Teen + Yun + Chop Gow + Gee Joon (2-4)8 points with 7 points7.61%
Teen + Yun + Chop Gow + Gee Joon (1-2)8 points with 7 points7.59%
Gor + Chong + Foo + Chop Bot9 points with 0 points3.80%
Teen + Chop Gow + Chop Bot + Chop Ng7 points with 7 points3.79%
Gor + Tit + Chop Gow + Chop Bot7 points with 1 point3.78%
Teen + Day + Ping + Look8 points with 2 points3.78%
Day + Chong + Foo + Ping8 points with 1 point3.78%
Mooy + Chong + Tit + Chop Gow7 points with 5 points3.78%
Ping + Look + Chop Chit + Chop Ng7 points with 1 point3.77%
Yun + Gor + Chong + Chop Bot6 points with 0 points3.76%
Day + Mooy + Tit + Chop GowWong with 7 points3.68%
Day + Mooy + Chop Gow + Chop ChitWong with 7 points3.68%
Mooy + Bon + Tit + Chop Chit7 points with 1 point3.65%
Gor + Ping + Look + Chop Chit7 points with 0 points3.64%
Day + Mooy + Foo + Chop Ng7 points with 1 point3.57%
Teen + Yun + Bon + Ping8 points with 6 points3.55%
Day + Mooy + Chop Bot + Chop Ng8 points with 7 points3.49%
Mooy + Ping + Chop Gow + Chop Bot9 points with 8 points3.48%
Teen + Mooy + Foo + Chop Ng7 points with 1 point3.47%
Bon + Ping + Chop Gow + Chop Bot9 points with 2 points3.45%
Teen + Day + Tit + Chop NgHigh Nine with 7 points3.36%
Teen + Day + Chop Chit + Chop NgHigh Nine with 7 points3.36%
Yun + Chong + Bon + Ping8 points with 0 points3.34%
Mooy + Bon + Ping + Chop Ng9 points with 0 points3.33%
Chong + Bon + Tit + Gee Joon (2-4)9 points with 1 point6.66%
Chong + Bon + Chop Chit + Gee Joon (2-4)9 points with 1 point6.66%
Mooy + Foo + Tit + Chop Bot9 points with 7 points3.33%
Mooy + Foo + Chop Bot + Chop Chit9 points with 7 points3.33%
Teen + Ping + Chop Gow + Chop Ng9 points with 7 points3.31%
Mooy + Foo + Chop Chit + Chop Chit8 points with 7 points13.25%
Chong + Bon + Tit + Gee Joon (1-2)9 points with 1 point6.62%
Chong + Bon + Chop Chit + Gee Joon (1-2)9 points with 1 point6.62%
Mooy + Chong + Look + Chop Ng6 points with 1 point3.30%
Teen + Day + Foo + TitHigh Nine with 3 points3.30%
Teen + Day + Foo + Chop ChitHigh Nine with 3 points3.30%
Foo + Tit + Chop Chit + Chop Ng8 points with 2 points3.30%
Chong + Ping + Chop Bot + Chop Ng8 points with 1 point3.29%
Chong + Bon + Ping + Look6 points with 0 points3.22%
Yun + Chop Gow + Chop Bot + Chop Ng7 points with 3 points3.22%
Teen + Day + Bon + TitHigh Nine with 6 points3.21%
Teen + Day + Bon + Chop ChitHigh Nine with 6 points3.21%
Teen + Day + Gor + TitHigh Nine with 6 points3.18%
Teen + Day + Gor + Chop ChitHigh Nine with 6 points3.18%
Day + Gor + Mooy + Chop Bot8 points with 6 points3.18%
Teen + Mooy + Bon + Ping6 points with 0 points3.16%
Teen + Yun + Gor + Chop Gow7 points with 6 points3.15%
Teen + Bon + Ping + Chop Gow9 points with 6 points3.15%
Bon + Foo + Chop Bot + Chop Chit9 points with 1 point3.14%
Teen + Yun + Gor + Chop Bot6 points with 6 points3.14%
Teen + Yun + Bon + Chop Bot6 points with 6 points3.13%
Teen + Bon + Chop Gow + Chop BotGong with 3 points3.12%
Ping + Tit + Look + Chop Ng7 points with 1 point3.11%
Gor + Mooy + Chong + Look6 points with 0 points3.07%
Bon + Look + Chop Gow + Chop Bot7 points with 0 points3.06%
Yun + Bon + Ping + Tit8 points with 1 point3.00%
Yun + Bon + Ping + Chop Chit8 points with 1 point3.00%
Gor + Ping + Look + Chop Gow9 points with 0 points3.00%
Mooy + Bon + Ping + Tit7 points with 4 points2.97%
Mooy + Bon + Ping + Chop Chit7 points with 4 points2.97%
Gor + Ping + Tit + Look7 points with 0 points2.95%
Teen + Day + Chong + TitHigh Nine with 8 points2.91%
Teen + Day + Chong + Chop ChitHigh Nine with 8 points2.91%

EXACT Cost per unit bet, five percent commission on winning hands, dealer banking. Sorted by total expected value recoverable, which weights the size of the error by how often the hand occurs.