Poker Odds and Statistics

There are many sites out there listing simple odds and statistics for poker. I couldn't find one that told me all of the stuff I wanted to know, so I wrote a program to calculate stuff for me. All calculations on this page relate to Texas Hold'em.

Miscellaneous hand totals

In Hold'em, there are:

A bit more on the 7,462 truly unique 5-card hands (taking the best 5 out of your 7 cards). How does that break down?

So, if you take the 7,462 unique hands, each can be assigned a point value from 1 through 7,462. That means that 5-4-3-2-A unsuited (the lowest straight) is only 1 point better than A-A-A-K-Q (the highest Three of a Kind). I bring that up because that's one of the keys to my calculations below.

Chances of winning the hand given specific hole cards (heads up)

Let's say it's down to you and one other player. You have the big stack. You are first in the betting and have absolutely no clue what your opponent holds. Should you go all-in?

In order to calculate this, I iterated over all possible flops. For each of those possible flops, I iterated over each possible hand your opponent could have from the remaining cards. I compared each of those to the hand you'd have and figured whether you won, lost, or tied. In all, that's just over two billion different possibilities for each of the hole card combinations you can have.  (With a Pentium4, each of these takes about 3.5 hours to run).

Rank Hole Cards Combos Hands You Win Hands You Lose Hands You Tie Hands You Don't Lose (Win + Tie)
1 A-A 6 1,718,508,418 84.93% 304,661,670 14.52% 11,402,312 0.54% 1,792,910,730 85.48%
2 K-K 6 1,722,470,558 82.12% 363,424,882 17.33% 11,676,960 0.56% 1,734,147,518 82.67%
3 Q-Q 6 1,670,338,644 79.63% 414,934,680 19.78% 12,299,076 0.59% 1,682,637,720 80.22%
4 J-J 6 1,618,339,604 77.15% 465,955,440 22.21% 13,277,356 0.63% 1,631,616,960 77.79%
5 10-10 6 1,566,053,110 74.66% 516,772,724 24.64% 14,746,566 0.70% 1,580,799,676 75.36%
6 9-9 6 1,503,238,936 71.67% 577,905,278 27.55% 16,428,186 0.78% 1,519,667,122 72.45%
7 8-8 6 1,441,396,848 68.72% 637,479,762 30.39% 18,695,790 0.89% 1,460,092,638 69.61%
8 A-K suited 4 1,389,004,215 66.22% 673,957,209 32.13% 34.620,976 1.65% 1,423,625,191 67.87%
9 A-Q suited 4 1,370,002,117 65.31% 690,016,869 32.90% 37,553,414 1.79% 1,407,555,531 67.10%
10 7-7 6 1,378,636,878 65.73% 697,512,212 33.25% 21,423,310 1.02% 1,400,060,188 66.75%
11 A-J suited 4 1,350,786,717 64.40% 705,041,543 33.61% 41,744,140 1.99% 1,392,530,857 66.39%
12 A-K off-suit 12 1,352,291,878 64.47% 709,592,683 33.83% 35,687,839 1.70% 1,387,979,717 66.17%
13 A-10 suited 4 1,331,725,962 63.49% 719,134,692 34.28% 46,711,746 2.23% 1,378,437,708 65.72%
14 A-Q off-suit 12 1,332,142,795 63.51% 726,706,236 34.65% 38,723,369 1.85% 1,370,866,164 65.35%
15 A-J off-suit 12 1,309,720,573 62.54% 742,722,264 35.41% 43,129,563 2.06% 1,354,850,136 64.59%
16 K-Q suited 4 1,309,061,790 62.41% 746,895,468 35.61% 41,615,142 1.98% 1,350,676,932 64.39%
17 A-9 suited 4 1,290,209,940 61.51% 754,019,509 35.95% 53,342,951 2.54% 1,343,552,891 64.05%
18 A-10 off-suit 12 1,291,435,142 61.57% 757,743,309 36.12% 48,393,949 2.31% 1,339,829,091 63.88%
19 6-6 6 1,315,178,390 62.70% 757,863,966 36.13% 24,530,044 1.17% 1,339,708,434 63.87%
20 K-J suited 4 1,289,515,286 61.48% 762,297,170 36.34% 45,759,944 2.18% 1,335,275,230 63.66%
21 K-10 suited 4 1,270,857,555 60.59% 776,310,470 37.01% 50,404,375 2.40% 1,321,261,930 62.99%
22 A-7 suited 4 1,245,678,450 59.39% 784,885,484 37.42% 67,008,466 3.19% 1,312,686,916 62.58%
23 A-5 suited 4 1,217,936,943 58.06% 801,655,845 38.22% 77,979,612 3.72% 1,295,916,555 61.78%
24 A-6 suited 4 1,220,344,506 58.18% 804,780,676 38.37% 72,447,218 3.45% 1,292,791,724 61.63%
25 Q-J suited 4 1,239,054,394 59.07% 808,665,883 38.55% 49.852,123 2.38% 1,288,906,517 61.45%
26 A-8 off-suit 12 1,224,440,175 58.37% 810,270,096 38.63% 62,862,129 3.00% 1,287,302,304 61.37%
27 5-5 6 1,250,992,922 59.64% 817,847,556 38.99% 28,731,922 1.37% 1,279,724,844 61.01%
28 A-4 suited 4 1,198,506,708 57.14% 819,532,598 39.07% 79,533,094 3.79% 1,278,039,802 60.93%
29 A-3 suited 4 1,181,668,536 56.34% 836,814,184 39.89% 79,089,680 3.77% 1,260,758,216 60.11%
30 A-2 suited 4 1,164,284,001 55.51% 854,728,551 40.75% 78,559,848 3.75% 1,242,843,849 59.25%
31 J-10 suited 4 1,177,887,186 56.15% 862,082,680 41.10% 57,602,534 2.75% 1,235,489,720 58.90%
32 4-4 6 1,180,021,110 56.26% 885,403,592 42.21% 32,147,698 1.53% 1,212,168,808 57.79%
33 10-9 suited 4 1,098,642,842 52.38% 929,682,183 44.32% 69,247,375 3.30% 1,167,890,217 55.68%
34 3-3 6 1,108,341,244 52.84% 953,411,342 45.45% 35,819,814 1.71% 1,114,161,058 54.55%
35 9-8 suited 4 1,024,795,719 48.86% 991,202,871 47.25% 81,573,810 3.89% 1,106,369,529 52.75%
36 2-2 6 1,035,889,822 49.39% 1,021,877,238 48.72% 39,805,340 1.90% 1,075,695,162 51.28%
? A-8 suited 4 ? ? ? ? ? ? ? ?
? K-9 suited 4 ? ? ? ? ? ? ? ?
? K-8 suited 4 ? ? ? ? ? ? ? ?
? K-7 suited 4 ? ? ? ? ? ? ? ?
? K-6 suited 4 ? ? ? ? ? ? ? ?
? K-5 suited 4 ? ? ? ? ? ? ? ?
? K-4 suited 4 ? ? ? ? ? ? ? ?
? K-3 suited 4 ? ? ? ? ? ? ? ?
? K-2 suited 4 ? ? ? ? ? ? ? ?
? Q-10 suited 4 ? ? ? ? ? ? ? ?
? Q-9 suited 4 ? ? ? ? ? ? ? ?
? Q-8 suited 4 ? ? ? ? ? ? ? ?
? Q-7 suited 4 ? ? ? ? ? ? ? ?
? Q-6 suited 4 ? ? ? ? ? ? ? ?
? Q-5 suited 4 ? ? ? ? ? ? ? ?
? Q-4 suited 4 ? ? ? ? ? ? ? ?
? Q-3 suited 4 ? ? ? ? ? ? ? ?
? Q-2 suited 4 ? ? ? ? ? ? ? ?
? J-9 suited 4 ? ? ? ? ? ? ? ?
? J-8 suited 4 ? ? ? ? ? ? ? ?
? J-7 suited 4 ? ? ? ? ? ? ? ?
? J-6 suited 4 ? ? ? ? ? ? ? ?
? J-5 suited 4 ? ? ? ? ? ? ? ?
? J-4 suited 4 ? ? ? ? ? ? ? ?
? J-3 suited 4 ? ? ? ? ? ? ? ?
? J-2 suited 4 ? ? ? ? ? ? ? ?
? 10-8 suited 4 ? ? ? ? ? ? ? ?
? 10-7 suited 4 ? ? ? ? ? ? ? ?
? 10-6 suited 4 ? ? ? ? ? ? ? ?
? 10-5 suited 4 ? ? ? ? ? ? ? ?
? 10-4 suited 4 ? ? ? ? ? ? ? ?
? 10-3 suited 4 ? ? ? ? ? ? ? ?
? 10-2 suited 4 ? ? ? ? ? ? ? ?
? 9-7 suited 4 ? ? ? ? ? ? ? ?
? 9-6 suited 4 ? ? ? ? ? ? ? ?
? 9-5 suited 4 ? ? ? ? ? ? ? ?
? 9-4 suited 4 ? ? ? ? ? ? ? ?
? 9-3 suited 4 ? ? ? ? ? ? ? ?
? 9-2 suited 4 ? ? ? ? ? ? ? ?
? 8-7 suited 4 ? ? ? ? ? ? ? ?
? 8-6 suited 4 ? ? ? ? ? ? ? ?
? 8-5 suited 4 ? ? ? ? ? ? ? ?
? 8-4 suited 4 ? ? ? ? ? ? ? ?
? 8-3 suited 4 ? ? ? ? ? ? ? ?
? 8-2 suited 4 ? ? ? ? ? ? ? ?
? 7-6 suited 4 ? ? ? ? ? ? ? ?
? 7-5 suited 4 ? ? ? ? ? ? ? ?
? 7-4 suited 4 ? ? ? ? ? ? ? ?
? 7-3 suited 4 ? ? ? ? ? ? ? ?
? 7-2 suited 4 ? ? ? ? ? ? ? ?
? 6-5 suited 4 ? ? ? ? ? ? ? ?
? 6-4 suited 4 ? ? ? ? ? ? ? ?
? 6-3 suited 4 ? ? ? ? ? ? ? ?
? 6-2 suited 4 ? ? ? ? ? ? ? ?
? 5-4 suited 4 ? ? ? ? ? ? ? ?
? 5-3 suited 4 ? ? ? ? ? ? ? ?
? 5-2 suited 4 ? ? ? ? ? ? ? ?
? 4-3 suited 4 ? ? ? ? ? ? ? ?
? 4-2 suited 4 ? ? ? ? ? ? ? ?
? 3-2 suited 4 ? ? ? ? ? ? ? ?
? A-9 off-suit 12 ? ? ? ? ? ? ? ?
? A-7 off-suit 12 ? ? ? ? ? ? ? ?
? A-6 off-suit 12 ? ? ? ? ? ? ? ?
? A-5 off-suit 12 ? ? ? ? ? ? ? ?
? A-4 off-suit 12 ? ? ? ? ? ? ? ?
? A-3 off-suit 12 ? ? ? ? ? ? ? ?
? A-2 off-suit 12 ? ? ? ? ? ? ? ?
? K-Q off-suit 12 ? ? ? ? ? ? ? ?
? K-J off-suit 12 ? ? ? ? ? ? ? ?
? K-10 off-suit 12 ? ? ? ? ? ? ? ?
? K-9 off-suit 12 ? ? ? ? ? ? ? ?
? K-8 off-suit 12 ? ? ? ? ? ? ? ?
? K-7 off-suit 12 ? ? ? ? ? ? ? ?
? K-6 off-suit 12 ? ? ? ? ? ? ? ?
? K-5 off-suit 12 ? ? ? ? ? ? ? ?
? K-4 off-suit 12 ? ? ? ? ? ? ? ?
? K-3 off-suit 12 ? ? ? ? ? ? ? ?
? K-2 off-suit 12 ? ? ? ? ? ? ? ?
? Q-J off-suit 12 ? ? ? ? ? ? ? ?
? Q-10 off-suit 12 ? ? ? ? ? ? ? ?
? Q-9 off-suit 12 ? ? ? ? ? ? ? ?
? Q-8 off-suit 12 ? ? ? ? ? ? ? ?
? Q-7 off-suit 12 ? ? ? ? ? ? ? ?
? Q-6 off-suit 12 ? ? ? ? ? ? ? ?
? Q-5 off-suit 12 ? ? ? ? ? ? ? ?
? Q-4 off-suit 12 ? ? ? ? ? ? ? ?
? Q-3 off-suit 12 ? ? ? ? ? ? ? ?
? Q-2 off-suit 12 ? ? ? ? ? ? ? ?
? J-10 off-suit 12 ? ? ? ? ? ? ? ?
? J-9 off-suit 12 ? ? ? ? ? ? ? ?
? J-8 off-suit 12 ? ? ? ? ? ? ? ?
? J-7 off-suit 12 ? ? ? ? ? ? ? ?
? J-6 off-suit 12 ? ? ? ? ? ? ? ?
? J-5 off-suit 12 ? ? ? ? ? ? ? ?
? J-4 off-suit 12 ? ? ? ? ? ? ? ?
? J-3 off-suit 12 ? ? ? ? ? ? ? ?
? J-2 off-suit 12 ? ? ? ? ? ? ? ?
? 10-9 off-suit 12 ? ? ? ? ? ? ? ?
? 10-8 off-suit 12 ? ? ? ? ? ? ? ?
? 10-7 off-suit 12 ? ? ? ? ? ? ? ?
? 10-6 off-suit 12 ? ? ? ? ? ? ? ?
? 10-5 off-suit 12 ? ? ? ? ? ? ? ?
? 10-4 off-suit 12 ? ? ? ? ? ? ? ?
? 10-3 off-suit 12 ? ? ? ? ? ? ? ?
? 10-2 off-suit 12 ? ? ? ? ? ? ? ?
? 9-8 off-suit 12 ? ? ? ? ? ? ? ?
? 9-7 off-suit 12 ? ? ? ? ? ? ? ?
? 9-6 off-suit 12 ? ? ? ? ? ? ? ?
? 9-5 off-suit 12 ? ? ? ? ? ? ? ?
? 9-4 off-suit 12 ? ? ? ? ? ? ? ?
? 9-3 off-suit 12 ? ? ? ? ? ? ? ?
? 9-2 off-suit 12 ? ? ? ? ? ? ? ?
? 8-7 off-suit 12 ? ? ? ? ? ? ? ?
? 8-6 off-suit 12 ? ? ? ? ? ? ? ?
? 8-5 off-suit 12 ? ? ? ? ? ? ? ?
? 8-4 off-suit 12 ? ? ? ? ? ? ? ?
? 8-3 off-suit 12 ? ? ? ? ? ? ? ?
? 8-2 off-suit 12 ? ? ? ? ? ? ? ?
? 7-6 off-suit 12 ? ? ? ? ? ? ? ?
? 7-5 off-suit 12 ? ? ? ? ? ? ? ?
? 7-4 off-suit 12 ? ? ? ? ? ? ? ?
? 7-3 off-suit 12 ? ? ? ? ? ? ? ?
? 7-2 off-suit 12 ? ? ? ? ? ? ? ?
? 6-5 off-suit 12 ? ? ? ? ? ? ? ?
? 6-4 off-suit 12 ? ? ? ? ? ? ? ?
? 6-3 off-suit 12 ? ? ? ? ? ? ? ?
? 6-2 off-suit 12 ? ? ? ? ? ? ? ?
? 5-4 off-suit 12 ? ? ? ? ? ? ? ?
? 5-3 off-suit 12 ? ? ? ? ? ? ? ?
? 5-2 off-suit 12 ? ? ? ? ? ? ? ?
? 4-3 off-suit 12 ? ? ? ? ? ? ? ?
? 4-2 off-suit 12 ? ? ? ? ? ? ? ?
? 3-2 off-suit 12 ? ? ? ? ? ? ? ?