AQs
29.88%
Wins 27.66%, ties 4.44%
AKo
70.12%
Wins 67.90%, ties 4.44%
AQs against AKo: the numbers
| Hand | Wins | Ties | Loses | Equity |
|---|---|---|---|---|
| AQs | 27.655 | 4.444 | 67.901 | 29.877 |
| AKo | 67.901 | 4.444 | 27.655 | 70.123 |
AQs, a suited hand, plays AKo, an offsuit hand. The two hands share a rank, and the one with the better other card dominates: it wins most kicker battles when that shared rank hits.
A lead of 40.24 points is large but not decisive: AQs still takes about 277 of every 1,000 deals. Of every 100 boards, about 4.44 are split pots, and the equity figures already include them.
In the ranking of all 169 starting hands, AQs is number 10 and AKo is number 12.
| Hand | Boards won, about | Boards tied, about | Boards lost, about |
|---|---|---|---|
| AQs | 17,047,000 | 2,739,000 | 41,856,000 |
| AKo | 41,856,000 | 2,739,000 | 17,047,000 |
The total is exact: 36 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) |
|---|---|---|---|---|
| AQs | 0.426 | 3.616 | 1.473 | 2.347 |
| AKo | 2.347 | 1.473 | 3.616 | 0.426 |
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: AKo holds 81.91% on low rainbow flops (nine high or lower) and 64.65% on monotone flops. AKo 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 | AQs wins | Ties | AKo wins | AQs equity |
|---|---|---|---|---|---|
| Rainbow, ten or higher | 23.177 | 29.100 | 1.975 | 68.925 | 30.087 |
| Rainbow, nine or lower | 7.771 | 15.381 | 5.427 | 79.192 | 18.095 |
| Two-tone | 46.527 | 29.608 | 2.671 | 67.721 | 30.944 |
| Monotone | 5.192 | 33.353 | 3.986 | 62.661 | 35.346 |
| Paired | 17.333 | 24.275 | 12.204 | 63.521 | 30.377 |
A rainbow flop shows three suits, a two-tone flop repeats one suit, a monotone flop is a single suit, and a paired flop repeats a rank.
Compared with a random hand
Start from the random-hand figures, 66.21% for AQs and 65.32% for AKo. This opponent changes them by -36.33 and +4.80 points.
| Case | Equity here | Against a random hand | Change in points | Times the random-hand equity |
|---|---|---|---|---|
| AQs, all flops | 29.877 | 66.209 | -36.332 | 0.45125 |
| AQs, rainbow, ten or higher | 30.087 | 66.209 | -36.122 | 0.45442 |
| AQs, rainbow, nine or lower | 18.095 | 66.209 | -48.114 | 0.27330 |
| AQs, two-tone | 30.944 | 66.209 | -35.265 | 0.46737 |
| AQs, monotone | 35.346 | 66.209 | -30.863 | 0.53385 |
| AQs, paired | 30.377 | 66.209 | -35.832 | 0.45880 |
| AKo, all flops | 70.123 | 65.320 | +4.803 | 1.07353 |
| AKo, rainbow, ten or higher | 69.913 | 65.320 | +4.593 | 1.07032 |
| AKo, rainbow, nine or lower | 81.905 | 65.320 | +16.585 | 1.25390 |
| AKo, two-tone | 69.056 | 65.320 | +3.736 | 1.05720 |
| AKo, monotone | 64.654 | 65.320 | -0.666 | 0.98980 |
| AKo, paired | 69.623 | 65.320 | +4.303 | 1.06588 |
Does a shared suit matter?
Two kinds of deal exist here. In 12 of them the hands share a suit and AKo holds 70.90%. In 24 they do not, and it holds 69.73%. AKo does better with a shared suit, by 1.17 points.
| Deals | Specific deals | Share of deals | AQs wins | Ties | AKo wins | AQs equity |
|---|---|---|---|---|---|---|
| Share a suit | 12 | 33.33 | 26.841 | 4.514 | 68.645 | 29.098 |
| No shared suit | 24 | 66.67 | 28.062 | 4.409 | 67.529 | 30.266 |
How often this matchup comes up
AQs against AKo is made up of 36 specific-card matchups in one seat order, 0.0022% of the 1,624,350 ordered deals, and 72 counting both seat orders, 0.0044%.
A worked example
Put $100 each into a $200 pot and deal every board once: AKo averages $140.24 back, ahead of its $100 by $40.24, while AQs averages $59.76, short of its $100 by $40.24.
Over a long run, 1,000 deals split into about 679 for AKo, 277 for AQs and 44 tied.
The same matchup from the other side
One page covers both views. From AKo's side the equity is 70.12%, and from AQs' side it is 29.88%.
Keep exploring
The calculator link fills in AsQs against AhKd, 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
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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