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.	6420	256	12	6	6
2.	7420	256	13	4	9
3.	7620	256	15	6	9
4.	7640	256	7	3	4
5.	7642	256	9	0	9
6.	8420	256	14	4	10
7.	8620	256	16	6	10
8.	8640	256	8	4	4
9.	8642	256	10	0	10
10.	8720	256	17	8	9
11.	8740	256	9	4	5
12.	8742	256	11	1	10
13.	8760	256	11	5	6
14.	8762	256	13	4	9
15.	8764	256	5	2	3
16.	4210	128	7	3	4
17.	4320	128	12	6	6
18.	5420	128	11	5	6
19.	6210	128	9	3	6
20.	6320	128	14	6	8
21.	6410	128	11	5	6
22.	6421	128	13	6	7
23.	6430	128	13	6	7
24.	6432	128	15	7	8
25.	6520	128	13	6	7
26.	6540	128	15	6	9
27.	6542	128	17	8	9
28.	7210	128	10	1	9
29.	7320	128	15	6	9
30.	7410	128	12	5	7
31.	7421	128	14	5	9
32.	7430	128	14	7	7
33.	7432	128	16	7	9
34.	7520	128	14	5	9
35.	7540	128	16	7	9
36.	7542	128	18	9	9
37.	7610	128	14	7	7
38.	7621	128	16	7	9
39.	7630	128	16	7	9
40.	7632	128	18	9	9
41.	7641	128	8	3	5
42.	7643	128	10	3	7
43.	7650	128	8	3	5
44.	7652	128	10	1	9
45.	7654	128	12	3	9
46.	8210	128	11	1	10
47.	8320	128	16	6	10
48.	8410	128	13	5	8
49.	8421	128	15	5	10
50.	8430	128	15	7	8
51.	8432	128	17	7	10
52.	8520	128	15	5	10
53.	8540	128	17	8	9
54.	8542	128	19	9	10
55.	8610	128	15	7	8
56.	8621	128	17	7	10
57.	8630	128	17	8	9
58.	8632	128	19	9	10
59.	8641	128	9	4	5
60.	8643	128	11	4	7
61.	8650	128	9	4	5
62.	8652	128	11	1	10
63.	8654	128	13	4	9
64.	8710	128	16	7	9
65.	8721	128	18	9	9
66.	8730	128	11	5	6
67.	8732	128	13	4	9
68.	8741	128	10	5	5
69.	8743	128	12	5	7
70.	8750	128	10	5	5
71.	8752	128	12	3	9
72.	8754	128	14	5	9
73.	8761	128	12	5	7
74.	8763	128	14	5	9
75.	8765	128	6	3	3
76.	9420	128	15	4	11
77.	9620	128	17	6	11
78.	9640	128	9	4	5
79.	9642	128	11	0	11
80.	9720	128	18	9	9
81.	9740	128	10	4	6
82.	9742	128	12	3	9
83.	9760	128	12	6	6
84.	9762	128	14	5	9
85.	9764	128	6	3	3
86.	9820	128	19	9	10
87.	9840	128	11	4	7
88.	9842	128	13	3	10
89.	9860	128	13	6	7
90.	9862	128	15	5	10
91.	9864	128	7	3	4
92.	9870	128	14	7	7
93.	9872	128	16	7	9
94.	9874	128	8	3	5
95.	9876	128	10	5	5
96.	3210	64	9	3	6
97.	4200	64	6	2	4
98.	4220	64	8	4	4
99.	4310	64	11	5	6
100.	4321	64	13	6	7
101.	4420	64	10	4	6
102.	5210	64	8	3	5
103.	5320	64	13	6	7
104.	5410	64	10	5	5
105.	5421	64	12	6	6
106.	5430	64	15	6	9
107.	5432	64	17	8	9
108.	6200	64	8	0	8
109.	6220	64	10	4	6
110.	6310	64	13	6	7
111.	6321	64	15	7	8
112.	6400	64	10	4	6
113.	6422	64	14	6	8
114.	6431	64	14	7	7
115.	6440	64	14	6	8
116.	6442	64	16	8	8
117.	6510	64	12	6	6
118.	6521	64	14	7	7
119.	6530	64	14	6	8
120.	6532	64	16	7	9
121.	6541	64	16	7	9
122.	6543	64	18	9	9
123.	6620	64	14	6	8
124.	6640	64	6	2	4
125.	6642	64	8	0	8
126.	7200	64	9	0	9
127.	7220	64	11	2	9
128.	7310	64	14	7	7
129.	7321	64	16	7	9
130.	7400	64	11	4	7
131.	7422	64	15	6	9
132.	7431	64	15	7	8
133.	7440	64	15	7	8
134.	7442	64	17	8	9
135.	7510	64	13	6	7
136.	7521	64	15	6	9
137.	7530	64	15	7	8
138.	7532	64	17	8	9
139.	7541	64	17	8	9
140.	7543	64	12	3	9
141.	7600	64	13	6	7
142.	7622	64	17	8	9
143.	7631	64	17	8	9
144.	7644	64	11	3	8
145.	7651	64	9	3	6
146.	7653	64	11