A3s
49.45%
Wins 49.11%, ties 0.70%
22
50.55%
Wins 50.19%, ties 0.70%
A3s against 22: the numbers
| Hand | Wins | Ties | Loses | Equity |
|---|---|---|---|---|
| A3s | 49.106 | 0.697 | 50.197 | 49.454 |
| 22 | 50.197 | 0.697 | 49.106 | 50.546 |
A3s is a suited hand and 22 is a pocket pair. A pair against two higher cards is the classic race: the pair is usually a small favorite or close to even, and each overcard that pairs is a way to take the lead.
With only 1.10 points between them, the board decides this matchup far more than the cards in hand. 0.70% of boards are ties, so the equity of each hand is its win rate plus half of that.
A3s ranks number 38 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 |
|---|---|---|---|
| A3s | 20,180,000 | 286,000 | 20,629,000 |
| 22 | 20,629,000 | 286,000 | 20,180,000 |
The board total is exact, 24 deals at 1,712,304 boards each. Won, tied and lost counts are rounded to the nearest thousand from the five-decimal percentages.
| Hand | Equity as odds (to 1) | Wins one deal in | Loses one deal in | Pot odds needed to call (to 1) |
|---|---|---|---|---|
| A3s | 0.978 | 2.036 | 1.992 | 1.022 |
| 22 | 1.022 | 1.992 | 2.036 | 0.978 |
In the last column, a pot-to-call ratio at or above the figure makes a call break even or better at this equity.
Who is ahead on which flops
If you know the kind of flop that came, the numbers shift: 22 holds 56.43% on low rainbow flops (nine high or lower) and 49.66% on paired flops. 22 is the favorite overall but falls behind on two-tone flops and paired flops.
| Flop | Share of flops | A3s wins | Ties | 22 wins | A3s equity |
|---|---|---|---|---|---|
| Rainbow, ten or higher | 25.220 | 48.685 | 0.291 | 51.024 | 48.830 |
| Rainbow, nine or lower | 5.689 | 42.861 | 1.416 | 55.723 | 43.569 |
| Two-tone | 46.545 | 49.919 | 0.451 | 49.630 | 50.145 |
| Monotone | 5.212 | 47.897 | 3.789 | 48.314 | 49.791 |
| Paired | 17.334 | 49.951 | 0.778 | 49.271 | 50.340 |
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
How much does the opponent matter? Compared with its random-hand 58.22%, A3s changes by -8.77 points, and 22, from 50.33%, by +0.22.
| Case | Equity here | Against a random hand | Change in points | Times the random-hand equity |
|---|---|---|---|---|
| A3s, all flops | 49.454 | 58.220 | -8.766 | 0.84943 |
| A3s, rainbow, ten or higher | 48.830 | 58.220 | -9.390 | 0.83872 |
| A3s, rainbow, nine or lower | 43.569 | 58.220 | -14.651 | 0.74835 |
| A3s, two-tone | 50.145 | 58.220 | -8.075 | 0.86130 |
| A3s, monotone | 49.791 | 58.220 | -8.429 | 0.85522 |
| A3s, paired | 50.340 | 58.220 | -7.880 | 0.86465 |
| 22, all flops | 50.546 | 50.334 | +0.212 | 1.00421 |
| 22, rainbow, ten or higher | 51.170 | 50.334 | +0.836 | 1.01661 |
| 22, rainbow, nine or lower | 56.431 | 50.334 | +6.097 | 1.12113 |
| 22, two-tone | 49.855 | 50.334 | -0.479 | 0.99048 |
| 22, monotone | 50.209 | 50.334 | -0.125 | 0.99752 |
| 22, paired | 49.660 | 50.334 | -0.674 | 0.98661 |
Does a shared suit matter?
Two kinds of deal exist here. In 12 of them the hands share a suit and 22 holds 50.72%. In 12 they do not, and it holds 50.37%. 22 does better with a shared suit, by 0.35 points.
| Deals | Specific deals | Share of deals | A3s wins | Ties | 22 wins | A3s equity |
|---|---|---|---|---|---|---|
| Share a suit | 12 | 50.00 | 48.924 | 0.715 | 50.361 | 49.282 |
| No shared suit | 12 | 50.00 | 49.289 | 0.677 | 50.034 | 49.627 |
How often this matchup comes up
This page stands for 24 specific-card matchups (0.0015% of 1,624,350 ordered deals), or 48 once you count the seats both ways (0.0030%).
A worked example
A $100 all-in from each player makes a $200 pot, and the exact equity says 22 gets $101.10 of it on average and A3s gets $98.90.
Per 1,000 deals: 22 wins about 502, A3s wins about 491, and about 7 end in a split pot.
The same matchup from the other side
One page covers both views. From 22's side the equity is 50.55%, and from A3s' side it is 49.45%.
Keep exploring
The calculator link fills in As3s against 2h2d, a deal where the two hands share no suit. Change any card to test your own hand. The neighboring matchups below swap one of the two hands for one of similar strength.
How this was computed
This is an exact count with no sampling. For the 24 ways to deal one A3s and one 22 without reusing a card, grouped by suit pattern, every one of the 1,712,304 possible boards is dealt and both seven-card hands are compared. A tie counts as half a win in the equity column, and each board is counted once under each of its ten three-card flops.
Source: our own exact count from the GeorgeLiPoker poker math library. No outside data is used.
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