AA
91.87%
Wins 91.23%, ties 1.27%
ATo
8.13%
Wins 7.50%, ties 1.27%
AA against ATo: the numbers
| Hand | Wins | Ties | Loses | Equity |
|---|---|---|---|---|
| AA | 91.228 | 1.274 | 7.498 | 91.865 |
| ATo | 7.498 | 1.274 | 91.228 | 8.135 |
AA and ATo are a pocket pair and an offsuit hand, in that order. The pair already holds one of the other hand's ranks, and that overlap cuts down the cards the other hand can pair with.
This is one of the lopsided matchups: ATo wins only 7.50% of the boards outright. Ties are 1.27% of the outcomes here; each tied board gives both hands half the pot.
The hand ranking puts AA at 1 and ATo at 19 out of 169 starting hands.
| Hand | Boards won, about | Boards tied, about | Boards lost, about |
|---|---|---|---|
| AA | 56,236,000 | 785,000 | 4,622,000 |
| ATo | 4,622,000 | 785,000 | 56,236,000 |
The board total is exact, 36 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) |
|---|---|---|---|---|
| AA | 11.293 | 1.096 | 13.337 | 0.089 |
| ATo | 0.089 | 13.337 | 1.096 | 11.293 |
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
By flop texture, AA's equity runs from 82.81% on monotone flops up to 95.82% on low rainbow flops (nine high or lower). AA stays ahead on all five textures.
| Flop | Share of flops | AA wins | Ties | ATo wins | AA equity |
|---|---|---|---|---|---|
| Rainbow, ten or higher | 23.053 | 91.580 | 1.088 | 7.332 | 92.124 |
| Rainbow, nine or lower | 7.771 | 94.513 | 2.605 | 2.882 | 95.815 |
| Two-tone | 46.215 | 91.110 | 1.401 | 7.489 | 91.811 |
| Monotone | 5.130 | 81.830 | 1.953 | 16.217 | 82.807 |
| Paired | 17.831 | 92.351 | 0.407 | 7.242 | 92.554 |
Rainbow flops have three suits, two-tone flops repeat one suit, monotone flops are all one suit, and paired flops repeat a rank.
Compared with a random hand
Start from the random-hand figures, 85.20% for AA and 62.72% for ATo. This opponent changes them by +6.67 and -54.59 points.
| Case | Equity here | Against a random hand | Change in points | Times the random-hand equity |
|---|---|---|---|---|
| AA, all flops | 91.865 | 85.204 | +6.661 | 1.07818 |
| AA, rainbow, ten or higher | 92.124 | 85.204 | +6.920 | 1.08122 |
| AA, rainbow, nine or lower | 95.815 | 85.204 | +10.611 | 1.12454 |
| AA, two-tone | 91.811 | 85.204 | +6.607 | 1.07754 |
| AA, monotone | 82.807 | 85.204 | -2.397 | 0.97187 |
| AA, paired | 92.554 | 85.204 | +7.350 | 1.08626 |
| ATo, all flops | 8.135 | 62.722 | -54.587 | 0.12970 |
| ATo, rainbow, ten or higher | 7.876 | 62.722 | -54.846 | 0.12557 |
| ATo, rainbow, nine or lower | 4.185 | 62.722 | -58.537 | 0.06672 |
| ATo, two-tone | 8.189 | 62.722 | -54.533 | 0.13056 |
| ATo, monotone | 17.193 | 62.722 | -45.529 | 0.27411 |
| ATo, paired | 7.446 | 62.722 | -55.276 | 0.11871 |
Does a shared suit matter?
Split by suits, the deals give AA 92.15% when the hands overlap in a suit and 91.29% when they do not. AA does better with a shared suit, by 0.86 points.
| Deals | Specific deals | Share of deals | AA wins | Ties | ATo wins | AA equity |
|---|---|---|---|---|---|---|
| Share a suit | 24 | 66.67 | 91.502 | 1.305 | 7.193 | 92.154 |
| No shared suit | 12 | 33.33 | 90.681 | 1.210 | 8.109 | 91.286 |
How often this matchup comes up
How often does it happen? 36 of the 1,624,350 ordered deals (0.0022%) are AA against ATo, and 72 (0.0044%) if either hand may sit in either seat.
A worked example
A $100 all-in from each player makes a $200 pot, and the exact equity says AA gets $183.74 of it on average and ATo gets $16.26.
Over a long run, 1,000 deals split into about 912 for AA, 75 for ATo and 13 tied.
The same matchup from the other side
One page covers both views. From ATo's side the equity is 8.13%, and from AA's side it is 91.87%.
Keep exploring
Open the calculator with AsAh against AdTc 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
Each figure is a complete count over boards. Take the 36 specific deals, group them by suit pattern, deal all 1,712,304 boards against each, and compare the two seven-card hands. Equity counts a tie as half a win; the flop rows use every one of a board's ten flops.
Source: our own exact count from the GeorgeLiPoker poker math library. No outside data is used.
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