Texas Holdem


I'm presently analysing Holdem using a small supercomputer.

Instead of evaluating a sample of games (e.g. the several 1000 a particular player may have come across), I'm trying to play "all" possible games to create a "perfect" strategy.

It's early days yet. I have a number of programs that look at various aspects of the basic game. The major components of the strategy are evaluating the hole cards and betting strategies for different tables. I'm more interested in tournament play than winning single games.

As a taste of what I'm doing, the following is a table of approximate "values" current algorithms recommend for each pair of hole cards.

Positive values indicate a better-than-even prospect of a win, assuming the showdown will be a head to head against one other player. Negative values indicate folding is probably in order if we're playing an early tournament round. Higher values indicate more aggressive betting is likely worthwhile.

Note some of the non-obvious recommendations.

As my software improves and/or accumulated cpu time increases, results are likely to change.

If you have questions or random constructive comments, feel free to drop me a line.

Cards Value
AA 0.873491
KK 0.793639
QQ 0.721740
JJ 0.657795
TT 0.607334
99 0.553529
88 0.506819
77 0.467009
KA suited 0.466016
KA 0.458913
QA suited 0.452015
QA 0.444783
JA suited 0.438037
66 0.433830
JA 0.430676
TA suited 0.427108
TA 0.419623
9A suited 0.403828
9A 0.396175
55 0.393455
8A suited 0.390566
8A 0.382777
7A suited 0.377304
7A 0.369379
44 0.364184
6A suited 0.364042
6A 0.355981
5A suited 0.351669
5A 0.343463
33 0.341749
4A suited 0.338875
4A 0.330525
22 0.326149
3A suited 0.326081
QK suited 0.318756
3A 0.317586
2A suited 0.313287
QK 0.310331
JK suited 0.304648
2A 0.304647
JK 0.296092
TK suited 0.293594
TK 0.284915
9K suited 0.275925
9K 0.267077
8K suited 0.249775
8K 0.240752
7K suited 0.236513
7K 0.227354
6K suited 0.223251
6K 0.213956
5K suited 0.210878
5K 0.201439
4K suited 0.198084
4K 0.188500
JQ suited 0.185951
3K suited 0.185290
JQ 0.176323
TQ suited 0.175586
3K 0.175562
2K suited 0.172496
TQ 0.165832
2K 0.162623
9Q suited 0.157030
9Q 0.147109
8Q suited 0.138083
8Q 0.127987
7Q suited 0.108600
7Q 0.098320
6Q suited 0.095338
6Q 0.084922
5Q suited 0.082966
5Q 0.072405
TJ suited 0.072004
4Q suited 0.070171
TJ 0.061296
4Q 0.059466
3Q suited 0.057377
9J suited 0.052971
3Q 0.046527
2Q suited 0.044583
9J 0.042096
2Q 0.033589
8J suited 0.033185
8J 0.022137
7J suited 0.013115
7J 0.001882
6J suited -0.019767
6J -0.031194
5J suited -0.032140
9T suited -0.036902
5J -0.043712
4J suited -0.044934
9T -0.048608
4J -0.056650
8T suited -0.057187
3J suited -0.057728
8T -0.069071
3J -0.069589
2J suited -0.070522
7T suited -0.078201
2J -0.082528
7T -0.090269
6T suited -0.099560
6T -0.111821
89 suited -0.133442
5T suited -0.134664
89 -0.146045
5T -0.147136
4T suited -0.147459
79 suited -0.154692
4T -0.160074
3T suited -0.160253
79 -0.167478
3T -0.173013
2T suited -0.173047
69 suited -0.176767
2T -0.185952
69 -0.189746
59 suited -0.198382
59 -0.211570
78 suited -0.217926
78 -0.231315
49 suited -0.236707
68 suited -0.240165
39 suited -0.249501
49 -0.250111
68 -0.253746
29 suited -0.262295
58 suited -0.262404
39 -0.263050
29 -0.275989
58 -0.276193
48 suited -0.285417
67 suited -0.290568
48 -0.299423
67 -0.304639
57 suited -0.313029
38 suited -0.326150
57 -0.327307
47 suited -0.336664
28 suited -0.338944
38 -0.340377
56 suited -0.350970
47 -0.351156
28 -0.353316
37 suited -0.360565
56 -0.365626
46 suited -0.374601
37 -0.375279
46 -0.389469
36 suited -0.399021
27 suited -0.402996
36 -0.414109
27 -0.417934
45 suited -0.423313
26 suited -0.424042
45 -0.438546
26 -0.439355
35 suited -0.447454
35 -0.462904
25 suited -0.472288
34 suited -0.475583
25 -0.487960
34 -0.491283
24 suited -0.500161
23 suited -0.515766
24 -0.516081
23 -0.531824