Pokerstrategy.us Pai Gow Tile Guide, by Jacob Gluck 1/3/2008

Legend and Explanation for the Pai Gow Combination Table

The following Pai Gow Tile Table enumerates the 960 possible ways one can be dealt a 4-tile Pai Gow hand in which the tile numbers of each selection differ from all other selections. In addition any selection that contains a pair is enumerated separately; e.g. 8854 where the two eights are paired is considered a different selection from 8854 where the two eights are not paired. There are a total of 960 possible "number selections" of 4 tiles out of the 32-tile deck using such criteria.

On this website each of the 16 pairs is represented by the letter "H" (=High) or "L" (=Low) followed by the tile number as follows:

Moy: H0

Ping: L0

Foo: 1

Teen: H2

Day: L2

GeeJoon: 3

Gor: H4

Bon: L4

ChopNg: 5

Chong: H6

Look: L6

Tit: H7

ChopChit: L7

Yon: H8

ChopBot: L8

ChopGow: 9

However in this table we don't distinguish between a high tile and a low tile of the same face value. Therefore, we will omit the H or L and list each tile selection in the form of a string of four digits, each digit representing the tile which has its face value. Thus, the first number selection in this table, 7664, refers to a selection that contains either one of the 7 tiles plus two sixes and either one of the 4 tiles (the High 4 or the Low 4).

NOTE: If the selection contains a pair then the pair will always be listed before the remaining two tiles. Thus a number selection of 7664 does NOT contain the paired sixes since paired sixes would be listed as 6674. In addition all pairs are underlined, which is the primary distinguishing mark of a pair on this table.

NOTE: The digit "3" in a number selection merely represents the gee joon tile. This does not mean that it is being played as a three in that particular selection; it could very well be played as a six since the jee goon tile is a wildcard and plays as a 3 or 6 depending on which forms a higher number. The digit "3" is just used to represent the tile.

Combinations. The second column is the combination column which contains the number of different ways each selection in column one can be mathematically combined. The number ranges from 1 to 256 and is always a factor of 2. This column is important in calculating the mathematical probability of being dealt that particular PGT hand. The more combinations a selection has the more often you will get such a Number Selection. To find out the exact percentage chance of getting dealt any particular selection, simply divide the number of its combinations by 35,960 (which is the total number of different 32-tile combinations).

Point Total. The "point total" of a PGT hand is usually determined by adding the number formed by the high hand with the number formed by the low hand. A gong is counted as a 10, Wong is counted as 11 and all pairs are counted as 12.

Typically, it does not matter which "division" one uses to set the hand; the point total will still add up to the same value. For example a hand of 8764 can be played as 0-5, 1-4 or 2-3. Those are three different "divisions" but they all add up to 5 and so we say that this hand has a point total of 5. "Unacceptable divisions" are obviously ignored. For example, we wouldn't count 8744 as a 3-point hand based on the 1-2 division since such a division is NEVER considered when setting the hand, as it is inferior in the front and back to the other division of 5-8.

Sometimes, however, a hand will add up to a different point total depending on how one sets the hand, and the lower point total will NOT be deemed an Unacceptable Division. For example, 2264 could be played as "nothing-bo" or 6-8. The House Way is 6-8 which results in a 14-point total but 0-12 is NOT an unacceptable division (since the back hand is much stronger relative to the other division). Conversely 7710 is played as a 13-point hand, 1-12, according to House Way but if we choose to play 7-8 instead we wind up with a 15-point hand. In such cases we always follow the House Way in determining the point total of the hand, which brings us to the next question: what is the House Way?

House Way. We have chosen the House Way as practiced by the Atlantic City Hilton (which is where the author of this article works). For the most part the ACH House way is identical to what is commonly called the "traditional way". However, I have noticed that some casino's in Atlantic City have different House Way rules from the ACH and so following are several of ACH rules to keep in mind.

High 3 rule. In the absence of a High Nine or better in the back hand, the House Way strategy is to "balance the hand" AS LONG AS a high-three (a three that contains the chong tile or better) can be played in the front hand. If a high three cannot be played in the front hand AND a seven or better can be played in the back hand, then the House plays the division which yields the best possible back hand. I have noticed that the Taj Mahal does not follow this rule; they will play any three in the front hand.

NOTE: Selections that contain tiles which are subject to the high-3 rule are divided according to the assumption that a high three is present, and the House Way setting will therefore be 3-x. However, in order to alert you to the necessity of setting the hand differently if a high-3 is not present, I have chosen a light green background for the House Way cells in those selections.

Exception hands: 9544 is an exception hand. The normal "balance the hand" rules call for a 4-8 division but experience has shown that with this particular hand it is preferable to play 3-H9 instead (this is because the 4 is so bad that the House is not interested in sacrificing the H9 for it) and that is the House Way.

Many other exception rules pertain to hands which contain two tiles of the same number and the high tile is being played in the back hand instead of the front hand. However, since these "switches" do not change the actual number of the subhands it is irrelevant to us.

0.	4-tile number selection	Combinations	Point Total	House Way Front	House Way Back
1.	7664	64	3	1	2
2.	2100	32	3	1	2
3.	7764	64	4	1	3
4.	8664	64	4	2	2
5.	7665	32	4	2	2
6.	2200	16	4	2	2
7.	4100	32	5	1	4
8.	9664	32	5	2	3
9.	8764	256	5	2	3
10.	8665	32	5	2	3
11.	7765	32	5	2	3
12.	2210	32	5	2	3
13.	5100	16	6	1	5
14.	9665	16	6	2	4
15.	8864	64	6	2	4
16.	8774	64	6	2	4
17.	6640	64	6	2	4
18.	4200	64	6	2	4
19.	9764	128	6	3	3
20.	8765	128	6	3	3
21.	7766	16	6	3	3
22.	6641	32	7	0	7
23.	6100	32	7	0	7
24.	5200	32	7	0	7
25.	3100	16	7	0	7
26.	8874	64	7	2	5
27.	6650	32	7	2	5
28.	9864	128	7	3	4
29.	9774	32	7	3	4
30.	9765	64	7	3	4
31.	8865	32	7	3	4
32.	8775	32	7	3	4
33.	8766	64	7	3	4
34.	7640	256	7	3	4
35.	4210	128	7	3	4
36.	7100	32	8	0	8
37.	6642	64	8	0	8
38.	6200	64	8	0	8
39.	3200	32	8	0	8
40.	6651	16	8	1	7
41.	9874	128	8	3	5
42.	9766	32	8	3	5
43.	9441	16	8	3	5
44.	8875	32	8	3	5
45.	7650	128	8	3	5
46.	7641	128	8	3	5
47.	5210	64	8	3	5
48.	9865	64	8	4	4
49.	9775	16	8	4	4
50.	8866	16	8	4	4
51.	8776	64	8	4	4
52.	8773	32	8	4	4
53.	8640	256	8	4	4
54.	7740	64	8	4	4
55.	4400	16	8	4	4
56.	4220	64	8	4	4
57.	8100	32	9	0	9
58.	7642	256	9	0	9
59.	7200	64	9	0	9
60.	6643	32	9	0	9
61.	6544	32	9	0	9
62.	6652	32	9	1	8
63.	9884	32	9	3	6
64.	7660	64	9	3	6
65.	7651	64	9	3	6
66.	6210	128	9	3	6
67.	3210	64	9	3	6
68.	9875	64	9	4	5
69.	9866	32	9	4	5
70.	9776	32	9	4	5
71.	9773	16	9	4	5
72.	9640	128	9	4	5
73.	9541	32	9	4	5
74.	8876	64	9	4	5
75.	8873	32	9	4	5
76.	8740	256	9	4	5
77.	8650	128	9	4	5
78.	8641	128	9	4	5
79.	7750	32	9	4	5
80.	7741	32	9	4	5
81.	5400	32	9	4	5
82.	5220	32	9	4	5
83.	4410	32	9	4	5
84.	4221	32	9	4	5
85.	8200	64	10	0	10
86.	8642	256	10	0	10
87.	9100	16	10	1	9
88.	7544	32	10	1	9
89.	6653	16	10	1	9
90.	7652	128	10	1	9
91.	7210	128	10	1	9
92.	7742	64	10	1	9
93.	6644	16	10	2	8
94.	7661	32	10	3	7
95.	7643	128	10	3	7
96.	9885	16	10	4	6
97.	9740	128	10	4	6
98.	8840	64	10	4	6
99.	8660	64	10	4	6
100.	8651	64	10	4	6
101.	7760	64	10	4	6
102.	7751	16	10	4	6
103.	7730	32	10	4	6
104.	6400	64	10	4	6
105.	6220	64	10	4	6
106.	5221	16	10	4	6
107.	4420	64	10	4	6
108.	4300	32	10	4	6
109.	3220	32	10	4	6
110.	9876	128	10	5	5
111.	9873	64	10	5	5
112.	9650	64	10	5	5
113.	9641	64	10	5	5
114.	9431	32	10	5	5
115.	8877	16	10	5	5
116.	8750	128	10	5	5
117.	8741	128	10	5	5
118.	5410	64	10	5	5
119.	9642	128	11	0	11
120.	9200	32	11	0	11
121.	8742	256	11	1	10
122.	8652	128	11	1	10
123.	8210	128	11	1	10
124.	7752	32	11	2	9
125.	7662	64	11	2	9
126.	7220	64	11	2	9
127.	6654	32	11	2	9
128.	8544	32	11	3	8
129.	7653	64	11	3	8
130.	7644	64	11	3	8
131.	7443	32	11	3	8
132.	9840	128	11	4	7
133.	8661	32	11	4	7
134.	8643	128	11	4	7
135.	7761	32	11	4	7
136.	7743	32	11	4	7
137.	7731	16	11	4	7
138.	7400	64	11	4	7
139.	6221	32	11	4	7
140.	3221	16	11	4	7
141.	9886	32	11	5	6
142.	9883	16	11	5	6
143.	9877	32	11	5	6
144.	9750	64	11	5	6
145.	9741	64	11	5	6
146.	9660	32