AKo
73.74%
Wins 71.42%, ties 4.65%
ATo
26.26%
Wins 23.93%, ties 4.65%
AKo against ATo: the numbers
| Hand | Wins | Ties | Loses | Equity |
|---|---|---|---|---|
| AKo | 71.416 | 4.647 | 23.937 | 73.739 |
| ATo | 23.937 | 4.647 | 71.416 | 26.261 |
AKo and ATo are both offsuit hands. Sharing a rank is the signature of a dominated hand, since the weaker hand is usually out-kicked when the shared rank shows up.
A lead of 47.48 points is large but not decisive: ATo still takes about 239 of every 1,000 deals. A split pot comes up on 4.65% of boards, so the wins and the equity differ by half of that.
Ranked by equity against a random hand, AKo is number 12 of the 169 starting hands and ATo is number 19.
| Hand | Boards won, about | Boards tied, about | Boards lost, about |
|---|---|---|---|
| AKo | 132,069,000 | 8,594,000 | 44,266,000 |
| ATo | 44,266,000 | 8,594,000 | 132,069,000 |
The total is exact: 108 specific deals times 1,712,304 boards. The three counts are approximate, worked out from the percentages to five decimals and 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) |
|---|---|---|---|---|
| AKo | 2.808 | 1.400 | 4.178 | 0.356 |
| ATo | 0.356 | 4.178 | 1.400 | 2.808 |
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
AKo prefers low rainbow flops (nine high or lower), where it holds 82.83%, and likes monotone flops least, where it holds 68.55%. AKo stays ahead on all five textures.
| Flop | Share of flops | AKo wins | Ties | ATo wins | AKo equity |
|---|---|---|---|---|---|
| Rainbow, ten or higher | 23.275 | 70.710 | 2.077 | 27.213 | 71.749 |
| Rainbow, nine or lower | 7.771 | 80.162 | 5.332 | 14.506 | 82.828 |
| Two-tone | 46.477 | 72.419 | 2.841 | 24.740 | 73.840 |
| Monotone | 5.144 | 66.647 | 3.806 | 29.547 | 68.550 |
| Paired | 17.333 | 67.166 | 12.887 | 19.947 | 73.609 |
Read the flop types this way: rainbow has three suits, two-tone has two cards of one suit, monotone has three, and paired repeats a rank.
Compared with a random hand
Each hand has a baseline against a random hand: 65.32% for AKo, 62.72% for ATo. Here the change is +8.42 and -36.46 points.
| Case | Equity here | Against a random hand | Change in points | Times the random-hand equity |
|---|---|---|---|---|
| AKo, all flops | 73.739 | 65.320 | +8.419 | 1.12889 |
| AKo, rainbow, ten or higher | 71.749 | 65.320 | +6.429 | 1.09842 |
| AKo, rainbow, nine or lower | 82.828 | 65.320 | +17.508 | 1.26803 |
| AKo, two-tone | 73.840 | 65.320 | +8.520 | 1.13043 |
| AKo, monotone | 68.550 | 65.320 | +3.230 | 1.04945 |
| AKo, paired | 73.609 | 65.320 | +8.289 | 1.12690 |
| ATo, all flops | 26.261 | 62.722 | -36.461 | 0.41869 |
| ATo, rainbow, ten or higher | 28.251 | 62.722 | -34.471 | 0.45042 |
| ATo, rainbow, nine or lower | 17.172 | 62.722 | -45.550 | 0.27378 |
| ATo, two-tone | 26.160 | 62.722 | -36.562 | 0.41708 |
| ATo, monotone | 31.450 | 62.722 | -31.272 | 0.50142 |
| ATo, paired | 26.391 | 62.722 | -36.331 | 0.42076 |
Does a shared suit matter?
Does suit overlap move the numbers? AKo has 73.84% when the hands share a suit and 73.37% when they do not. AKo does better with a shared suit, by 0.47 points.
| Deals | Specific deals | Share of deals | AKo wins | Ties | ATo wins | AKo equity |
|---|---|---|---|---|---|---|
| Share a suit | 84 | 77.78 | 71.509 | 4.671 | 23.820 | 73.844 |
| No shared suit | 24 | 22.22 | 71.090 | 4.566 | 24.344 | 73.373 |
How often this matchup comes up
The class pair covers 108 combinations of specific cards in a fixed seat order, 0.0066% of 1,624,350, and 216 (0.0133%) in either order.
A worked example
To see what the equity is worth, imagine $100 each in a $200 pot. AKo is worth $147.48 on average (+$47.48); ATo is worth $52.52 (-$47.48).
Per 1,000 deals: AKo wins about 714, ATo wins about 239, and about 47 end in a split pot.
The same matchup from the other side
Read it from the other side: ATo against AKo is the same matchup with the numbers swapped, so ATo holds 26.26% and AKo holds 73.74%. That address sends you back to this page.
Keep exploring
AsKh against AdTc is a ready-made deal for the calculator, with no suit in common between the hands. The neighboring matchups below replace one hand with another of similar strength.
How this was computed
The page is built from a full enumeration: 1,712,304 boards, every suit pattern of the 108 specific deals, both seven-card hands evaluated. A tie is worth half a win to each hand, and a board is tallied under each of its ten possible flops for the texture rows.
Source: our own exact count from the GeorgeLiPoker poker math library. No outside data is used.
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