Three-Player Power Ratings in Texas Hold ’Em

Introduction

The following table ranks the top hands in a 3-player game. This table assumes that all players stay in until the end.

Explanation of column headings:

Cards: Initial two-card hand.
Probability of win: Probability that this hand will win, or tie for the win.
Average win: This is how much the player will win on average, including his own bets, if the player does win. This is less than 3 because sometimes the player will have to split the pot.
Expected value: This is how many units the player can expected to win (positive) or lose (negative) with this hand. For example if the player had a pair of aces and contributed $1 to the pot then the player could expect to have a net win of $1.20.
Probability: Probability of getting this hand to begin with.
Additive probability: Probability of getting this hand or any stronger hand to begin with.

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Initial Hold'em Hands in Rank Order for 3-Player Game

Cards	Probability of Win	Average Win	Expected Value	Probability	Additive Probability
Pair of A's	73.78%	2.99	1.2034	0.45%	0.45%
Pair of K's	69.21%	2.99	1.066	0.45%	0.9%
Pair of Q's	65.29%	2.98	0.9475	0.45%	1.36%
Pair of J's	61.57%	2.98	0.835	0.45%	1.81%
Pair of T's	58.02%	2.98	0.7272	0.45%	2.26%
Pair of 9's	54.08%	2.97	0.6084	0.45%	2.71%
A/K suited	51.77%	2.94	0.5221	0.3%	3.02%
Pair of 8's	50.46%	2.97	0.4986	0.45%	3.47%
A/Q suited	50.56%	2.93	0.4824	0.3%	3.77%
A/K unsuited	49.28%	2.93	0.4462	0.9%	4.68%
A/J suited	49.49%	2.92	0.4461	0.3%	4.98%
K/Q suited	48.28%	2.93	0.4128	0.3%	5.28%
A/T suited	48.5%	2.91	0.4121	0.3%	5.58%
A/Q unsuited	48.01%	2.93	0.4045	0.9%	6.49%
Pair of 7's	47.02%	2.97	0.3945	0.45%	6.94%
K/J suited	47.22%	2.92	0.3772	0.3%	7.24%
A/J unsuited	46.84%	2.91	0.3652	0.9%	8.14%
K/T suited	46.24%	2.91	0.3436	0.3%	8.45%
A/9 suited	46.16%	2.9	0.3366	0.3%	8.75%
K/Q unsuited	45.61%	2.92	0.3318	0.9%	9.65%
A/T unsuited	45.79%	2.9	0.3289	0.9%	10.56%
Q/J suited	45.55%	2.91	0.3256	0.3%	10.86%
A/8 suited	45.31%	2.88	0.3058	0.3%	11.16%
Pair of 6's	43.77%	2.96	0.2958	0.45%	11.61%
Q/T suited	44.59%	2.9	0.2932	0.3%	11.92%
K/J unsuited	44.46%	2.91	0.293	0.9%	12.82%
A/7 suited	44.32%	2.87	0.2719	0.3%	13.12%
K/9 suited	43.88%	2.89	0.2689	0.3%	13.42%
J/T suited	43.44%	2.9	0.2582	0.3%	13.73%
K/T unsuited	43.42%	2.9	0.2576	0.9%	14.63%
A/9 unsuited	43.25%	2.88	0.2473	0.9%	15.54%
A/5 suited	43.59%	2.85	0.2431	0.3%	15.84%
Q/J unsuited	42.76%	2.9	0.2406	0.9%	16.74%
A/6 suited	43.19%	2.86	0.2348	0.3%	17.04%
Q/9 suited	42.25%	2.89	0.2193	0.3%	17.35%
A/4 suited	42.7%	2.85	0.2161	0.3%	17.65%
A/8 unsuited	42.31%	2.87	0.2136	0.9%	18.55%
Q/T unsuited	41.73%	2.89	0.206	0.9%	19.46%
K/8 suited	41.91%	2.88	0.2048	0.3%	19.76%
Pair of 5's	40.7%	2.95	0.2017	0.45%	20.21%
A/3 suited	41.8%	2.85	0.1901	0.3%	20.51%
J/9 suited	41.11%	2.88	0.1844	0.3%	20.81%
K/7 suited	41.19%	2.86	0.1786	0.3%	21.12%
A/7 unsuited	41.25%	2.85	0.177	0.9%	22.02%
K/9 unsuited	40.88%	2.88	0.1769	0.9%	22.93%
J/T unsuited	40.58%	2.89	0.171	0.9%	23.83%
A/2 suited	40.86%	2.85	0.163	0.3%	24.13%
T/9 suited	40.38%	2.88	0.1617	0.3%	24.43%
Q/8 suited	40.28%	2.87	0.1564	0.3%	24.74%
K/6 suited	40.29%	2.85	0.1483	0.3%	25.04%
A/5 unsuited	40.46%	2.83	0.1458	0.9%	25.94%
A/6 unsuited	40.04%	2.84	0.1374	0.9%	26.85%
Q/9 unsuited	39.2%	2.87	0.1262	0.9%	27.75%
K/5 suited	39.51%	2.84	0.122	0.3%	28.05%
J/8 suited	39.14%	2.87	0.1219	0.3%	28.36%
A/4 unsuited	39.45%	2.83	0.1155	0.9%	29.26%
K/8 unsuited	38.75%	2.86	0.1079	0.9%	30.17%
Pair of 4's	37.42%	2.95	0.1026	0.45%	30.62%
T/8 suited	38.46%	2.86	0.1004	0.3%	30.92%
K/4 suited	38.63%	2.84	0.0956	0.3%	31.22%
Q/7 suited	38.33%	2.85	0.0937	0.3%	31.52%
J/9 unsuited	38.05%	2.87	0.0908	0.9%	32.43%
A/3 unsuited	38.5%	2.83	0.0879	0.9%	33.33%
K/7 unsuited	37.96%	2.84	0.0792	0.9%	34.24%
9/8 suited	37.74%	2.86	0.079	0.3%	34.54%
Q/6 suited	37.7%	2.84	0.0712	0.3%	34.84%
K/3 suited	37.78%	2.84	0.0712	0.3%	35.14%
T/9 unsuited	37.36%	2.86	0.0692	0.9%	36.05%
J/7 suited	37.21%	2.85	0.0605	0.3%	36.35%
Q/8 unsuited	37.09%	2.85	0.0585	0.9%	37.25%
A/2 unsuited	37.47%	2.82	0.0579	0.9%	38.16%
K/6 unsuited	37%	2.83	0.0469	0.9%	39.06%
K/2 suited	36.91%	2.83	0.0464	0.3%	39.37%
Q/5 suited	36.93%	2.83	0.0455	0.3%	39.67%
T/7 suited	36.51%	2.85	0.0394	0.3%	39.97%
J/8 unsuited	35.94%	2.85	0.0237	0.9%	40.87%
9/7 suited	35.95%	2.84	0.0223	0.3%	41.18%
Q/4 suited	36.08%	2.83	0.0203	0.3%	41.48%
K/5 unsuited	36.15%	2.82	0.0183	0.9%	42.38%
8/7 suited	35.65%	2.84	0.0134	0.3%	42.68%
Pair of 3's	34.33%	2.94	0.0087	0.45%	43.14%
T/8 unsuited	35.26%	2.84	0.0026	0.9%	44.04%
J/6 suited	35.33%	2.83	0.0009	0.3%	44.34%
Q/3 suited	35.22%	2.83	-0.0042	0.3%	44.65%
Q/7 unsuited	35.01%	2.83	-0.0082	0.9%	45.55%
K/4 unsuited	35.19%	2.81	-0.0104	0.9%	46.46%
J/5 suited	34.79%	2.82	-0.0182	0.3%	46.76%
9/8 unsuited	34.55%	2.84	-0.0185	0.9%	47.66%
T/6 suited	34.64%	2.83	-0.0194	0.3%	47.96%
Q/2 suited	34.4%	2.83	-0.0279	0.3%	48.27%
Q/6 unsuited	34.33%	2.82	-0.0326	0.9%	49.17%
9/6 suited	34.08%	2.83	-0.0357	0.3%	49.47%
K/3 unsuited	34.26%	2.81	-0.0374	0.9%	50.38%
8/6 suited	33.88%	2.83	-0.0416	0.3%	50.68%
J/7 unsuited	33.86%	2.83	-0.0422	0.9%	51.58%
7/6 suited	33.85%	2.83	-0.0424	0.3%	51.89%
J/4 suited	33.95%	2.82	-0.043	0.3%	52.19%
Q/5 unsuited	33.48%	2.81	-0.0607	0.9%	53.09%
T/7 unsuited	33.19%	2.82	-0.0626	0.9%	54%
K/2 unsuited	33.34%	2.81	-0.0642	0.9%	54.9%
J/3 suited	33.14%	2.82	-0.0659	0.3%	55.2%
T/5 suited	32.81%	2.81	-0.0768	0.3%	55.51%
9/7 unsuited	32.6%	2.82	-0.0799	0.9%	56.41%
Pair of 2's	31.4%	2.93	-0.0804	0.45%	56.86%
8/7 unsuited	32.33%	2.82	-0.0881	0.9%	57.77%
Q/4 unsuited	32.55%	2.8	-0.0886	0.9%	58.67%
J/2 suited	32.33%	2.82	-0.0891	0.3%	58.97%
6/5 suited	32.21%	2.82	-0.0923	0.3%	59.28%
9/5 suited	32.24%	2.81	-0.0927	0.3%	59.58%
T/4 suited	32.22%	2.81	-0.0945	0.3%	59.88%
7/5 suited	32.1%	2.82	-0.0962	0.3%	60.18%
8/5 suited	32.06%	2.81	-0.0979	0.3%	60.48%
J/6 unsuited	31.85%	2.81	-0.106	0.9%	61.39%
Q/3 unsuited	31.63%	2.8	-0.115	0.9%	62.29%
T/3 suited	31.42%	2.81	-0.1172	0.3%	62.59%
T/6 unsuited	31.16%	2.8	-0.1262	0.9%	63.5%
J/5 unsuited	31.26%	2.79	-0.1268	0.9%	64.4%
5/4 suited	30.98%	2.81	-0.1295	0.3%	64.71%
T/2 suited	30.6%	2.81	-0.1405	0.3%	65.01%
Q/2 unsuited	30.72%	2.8	-0.1413	0.9%	65.91%
9/6 unsuited	30.61%	2.8	-0.1421	0.9%	66.82%
6/4 suited	30.42%	2.81	-0.1453	0.3%	67.12%
8/6 unsuited	30.43%	2.8	-0.1473	0.9%	68.02%
7/6 unsuited	30.41%	2.8	-0.1477	0.9%	68.93%
9/4 suited	30.35%	2.8	-0.1492	0.3%	69.23%
7/4 suited	30.21%	2.81	-0.1522	0.3%	69.53%
J/4 unsuited	30.35%	2.79	-0.1538	0.9%	70.44%
8/4 suited	30.16%	2.8	-0.1542	0.3%	70.74%
9/3 suited	29.78%	2.8	-0.1654	0.3%	71.04%
J/3 unsuited	29.44%	2.79	-0.1798	0.9%	71.95%
5/3 suited	29.18%	2.8	-0.1821	0.3%	72.25%
T/5 unsuited	29.21%	2.78	-0.1872	0.9%	73.15%
9/2 suited	28.98%	2.8	-0.1883	0.3%	73.45%
6/5 unsuited	28.7%	2.79	-0.1998	0.9%	74.36%
6/3 suited	28.55%	2.8	-0.2002	0.3%	74.66%
9/5 unsuited	28.63%	2.78	-0.2035	0.9%	75.57%
J/2 unsuited	28.56%	2.78	-0.2052	0.9%	76.47%
7/5 unsuited	28.54%	2.78	-0.2053	0.9%	77.38%
T/4 unsuited	28.55%	2.78	-0.2072	0.9%	78.28%
4/3 suited	28.28%	2.8	-0.2074	0.3%	78.58%
8/5 unsuited	28.47%	2.78	-0.2078	0.9%	79.49%
7/3 suited	28.3%	2.8	-0.2082	0.3%	79.79%
8/3 suited	28.28%	2.8	-0.2093	0.3%	80.09%
8/2 suited	27.73%	2.79	-0.2253	0.3%	80.39%
T/3 unsuited	27.68%	2.77	-0.2324	0.9%	81.3%
5/2 suited	27.3%	2.79	-0.2371	0.3%	81.6%
5/4 unsuited	27.37%	2.78	-0.2401	0.9%	82.5%
6/2 suited	26.65%	2.79	-0.2559	0.3%	82.81%
6/4 unsuited	26.76%	2.77	-0.2576	0.9%	83.71%
T/2 unsuited	26.79%	2.77	-0.2578	0.9%	84.62%
4/2 suited	26.49%	2.79	-0.2599	0.3%	84.92%
7/2 suited	26.44%	2.79	-0.2628	0.3%	85.22%
9/4 unsuited	26.59%	2.77	-0.2644	0.9%	86.12%
7/4 unsuited	26.51%	2.77	-0.2657	0.9%	87.03%
8/4 unsuited	26.42%	2.77	-0.2687	0.9%	87.93%
9/3 unsuited	25.97%	2.76	-0.2825	0.9%	88.84%
3/2 suited	25.61%	2.79	-0.285	0.3%	89.14%
5/3 unsuited	25.46%	2.76	-0.2961	0.9%	90.05%
9/2 unsuited	25.1%	2.76	-0.3073	0.9%	90.95%
6/3 unsuited	24.74%	2.76	-0.3168	0.9%	91.86%
4/3 unsuited	24.49%	2.76	-0.3238	0.9%	92.76%
7/3 unsuited	24.47%	2.76	-0.3256	0.9%	93.67%
8/3 unsuited	24.4%	2.75	-0.3285	0.9%	94.57%
8/2 unsuited	23.79%	2.75	-0.3462	0.9%	95.48%
5/2 unsuited	23.43%	2.75	-0.3558	0.9%	96.38%
6/2 unsuited	22.69%	2.75	-0.3769	0.9%	97.29%
4/2 unsuited	22.56%	2.75	-0.3801	0.9%	98.19%
7/2 unsuited	22.44%	2.74	-0.3854	0.9%	99.1%
3/2 unsuited	21.61%	2.74	-0.4072	0.9%	100%
Total		2.84		100%

Methodology:

This table is the result of a random simulation of 68,612,544,000 games and assumes all players stay in until the end of the hand.

The following table shows my power rating for each initial 2-card hand in a 3-player game. The numbers are on a 0 to 40 scale. Use the top table if you have a pair, the middle table if your cards are suited, and the bottom table if your cards are unsuited. Except for a pair,look up your high card along the left and your low card along the top.