AA
82.22%
Wins 81.95%, ties 0.54%
22
17.78%
Wins 17.51%, ties 0.54%
AA against 22: the numbers
| Hand | Wins | Ties | Loses | Equity |
|---|---|---|---|---|
| AA | 81.948 | 0.537 | 17.515 | 82.217 |
| 22 | 17.515 | 0.537 | 81.948 | 17.783 |
Both hands are pocket pairs: AA and 22. A pair against a smaller pair is the classic crush: the smaller pair needs one of its two remaining cards to make a set.
AA is a big favorite here before anyone sees a flop. A split pot comes up on 0.54% of boards, so the wins and the equity differ by half of that.
AA ranks number 1 of 169 starting hands, and 22 ranks number 87, by equity against a random hand.
| Hand | Boards won, about | Boards tied, about | Boards lost, about |
|---|---|---|---|
| AA | 50,515,000 | 331,000 | 10,797,000 |
| 22 | 10,797,000 | 331,000 | 50,515,000 |
36 specific deals times 1,712,304 boards gives the exact total. The won, tied and lost counts are approximations from the five-decimal percentages, rounded to the nearest thousand.
| Hand | Equity as odds (to 1) | Wins one deal in | Loses one deal in | Pot odds needed to call (to 1) |
|---|---|---|---|---|
| AA | 4.623 | 1.220 | 5.709 | 0.216 |
| 22 | 0.216 | 5.709 | 1.220 | 4.623 |
The last column is the break-even price: the pot odds a call needs to offer, as a ratio of pot to call.
Who is ahead on which flops
If you know the kind of flop that came, the numbers shift: AA holds 87.39% on paired flops and 70.86% on low rainbow flops (nine high or lower). AA stays ahead on all five textures, but the swing between them is large, so how the flop looks matters a great deal.
| Flop | Share of flops | AA wins | Ties | 22 wins | AA equity |
|---|---|---|---|---|---|
| Rainbow, ten or higher | 24.595 | 84.434 | 0.287 | 15.279 | 84.578 |
| Rainbow, nine or lower | 6.314 | 70.127 | 1.456 | 28.417 | 70.855 |
| Two-tone | 46.363 | 80.904 | 0.503 | 18.593 | 81.156 |
| Monotone | 5.152 | 75.405 | 2.709 | 21.886 | 76.759 |
| Paired | 17.576 | 87.389 | 0.007 | 12.604 | 87.392 |
Flop types: rainbow means three different suits, two-tone means one suit twice, monotone means one suit three times, paired means a repeated rank.
Compared with a random hand
Start from the random-hand figures, 85.20% for AA and 50.33% for 22. This opponent changes them by -2.98 and -32.55 points.
| Case | Equity here | Against a random hand | Change in points | Times the random-hand equity |
|---|---|---|---|---|
| AA, all flops | 82.217 | 85.204 | -2.987 | 0.96494 |
| AA, rainbow, ten or higher | 84.578 | 85.204 | -0.626 | 0.99265 |
| AA, rainbow, nine or lower | 70.855 | 85.204 | -14.349 | 0.83159 |
| AA, two-tone | 81.156 | 85.204 | -4.048 | 0.95249 |
| AA, monotone | 76.759 | 85.204 | -8.445 | 0.90088 |
| AA, paired | 87.392 | 85.204 | +2.188 | 1.02568 |
| 22, all flops | 17.783 | 50.334 | -32.551 | 0.35330 |
| 22, rainbow, ten or higher | 15.422 | 50.334 | -34.912 | 0.30639 |
| 22, rainbow, nine or lower | 29.145 | 50.334 | -21.189 | 0.57903 |
| 22, two-tone | 18.844 | 50.334 | -31.490 | 0.37438 |
| 22, monotone | 23.241 | 50.334 | -27.093 | 0.46174 |
| 22, paired | 12.608 | 50.334 | -37.726 | 0.25049 |
Does a shared suit matter?
Does suit overlap move the numbers? AA has 82.35% when the hands share a suit and 81.55% when they do not. AA does better with a shared suit, by 0.80 points.
| Deals | Specific deals | Share of deals | AA wins | Ties | 22 wins | AA equity |
|---|---|---|---|---|---|---|
| Share a suit | 30 | 83.33 | 82.078 | 0.544 | 17.378 | 82.350 |
| No shared suit | 6 | 16.67 | 81.298 | 0.500 | 18.202 | 81.548 |
How often this matchup comes up
The class pair covers 36 combinations of specific cards in a fixed seat order, 0.0022% of 1,624,350, and 72 (0.0044%) in either order.
A worked example
Put $100 each into a $200 pot and deal every board once: AA averages $164.44 back, ahead of its $100 by $64.44, while 22 averages $35.56, short of its $100 by $64.44.
Think in thousands: about 820 of 1,000 go to AA, about 175 go to 22, and about 5 are chopped.
The same matchup from the other side
Read it from the other side: 22 against AA is the same matchup with the numbers swapped, so 22 holds 17.78% and AA holds 82.22%. That address sends you back to this page.
Keep exploring
Open the calculator with AsAh against 2d2c already entered, a deal with no shared suit, and change any card to try your own hand. The matchups after it each swap one hand for a nearby one in the ranking.
How this was computed
Method: exact enumeration. The 36 specific deals are grouped by suit pattern, each is run against all 1,712,304 boards, and both seven-card hands are scored. Equity adds half of every tie, and flop textures are tallied over the ten flops inside each board.
Source: our own exact count from the GeorgeLiPoker poker math library. No outside data is used.
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