AA
87.46%
Wins 86.84%, ties 1.25%
AQs
12.54%
Wins 11.91%, ties 1.25%
AA against AQs: the numbers
| Hand | Wins | Ties | Loses | Equity |
|---|---|---|---|---|
| AA | 86.838 | 1.245 | 11.917 | 87.461 |
| AQs | 11.917 | 1.245 | 86.838 | 12.539 |
AA and AQs are a pocket pair and a suited hand, in that order. The non-pair hand shares a rank with the pair, so two of its outs for pairing are blocked by the pair itself.
A gap this wide means AQs is in trouble before the flop and has few good runouts. A split pot comes up on 1.25% of boards, so the wins and the equity differ by half of that.
Among the 169 starting hands, AA is number 1 and AQs is number 10 by strength against a random hand.
| Hand | Boards won, about | Boards tied, about | Boards lost, about |
|---|---|---|---|
| AA | 17,843,000 | 256,000 | 2,449,000 |
| AQs | 2,449,000 | 256,000 | 17,843,000 |
The total is exact: 12 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) |
|---|---|---|---|---|
| AA | 6.975 | 1.152 | 8.391 | 0.143 |
| AQs | 0.143 | 8.391 | 1.152 | 6.975 |
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
The flop changes the picture. AA does best on low rainbow flops (nine high or lower), at 94.74%, and worst on monotone flops, at 77.38%. 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 | AQs wins | AA equity |
|---|---|---|---|---|---|
| Rainbow, ten or higher | 23.011 | 89.228 | 1.007 | 9.765 | 89.732 |
| Rainbow, nine or lower | 7.771 | 93.350 | 2.773 | 3.877 | 94.736 |
| Two-tone | 46.236 | 85.348 | 1.314 | 13.338 | 86.005 |
| Monotone | 5.151 | 76.210 | 2.333 | 21.457 | 77.376 |
| Paired | 17.831 | 87.852 | 0.393 | 11.755 | 88.048 |
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
How much does the opponent matter? Compared with its random-hand 85.20%, AA changes by +2.26 points, and AQs, from 66.21%, by -53.67.
| Case | Equity here | Against a random hand | Change in points | Times the random-hand equity |
|---|---|---|---|---|
| AA, all flops | 87.461 | 85.204 | +2.257 | 1.02649 |
| AA, rainbow, ten or higher | 89.732 | 85.204 | +4.528 | 1.05314 |
| AA, rainbow, nine or lower | 94.736 | 85.204 | +9.532 | 1.11187 |
| AA, two-tone | 86.005 | 85.204 | +0.801 | 1.00940 |
| AA, monotone | 77.376 | 85.204 | -7.828 | 0.90813 |
| AA, paired | 88.048 | 85.204 | +2.844 | 1.03338 |
| AQs, all flops | 12.539 | 66.209 | -53.670 | 0.18939 |
| AQs, rainbow, ten or higher | 10.268 | 66.209 | -55.941 | 0.15508 |
| AQs, rainbow, nine or lower | 5.264 | 66.209 | -60.945 | 0.07951 |
| AQs, two-tone | 13.995 | 66.209 | -52.214 | 0.21138 |
| AQs, monotone | 22.624 | 66.209 | -43.585 | 0.34171 |
| AQs, paired | 11.952 | 66.209 | -54.257 | 0.18052 |
Does a shared suit matter?
The hands cannot hold a suit in common here, which leaves a single case and a single number: 87.46% for AA.
| Deals | Specific deals | Share of deals | AA wins | Ties | AQs wins | AA equity |
|---|---|---|---|---|---|---|
| Share a suit | 0 | 0.00 | not possible | not possible | not possible | not possible |
| No shared suit | 12 | 100.00 | 86.838 | 1.245 | 11.917 | 87.461 |
How often this matchup comes up
You will meet this exact matchup 0.0015% of the time in a random heads-up deal: 24 of 1,624,350, counting either seat order.
A worked example
To see what the equity is worth, imagine $100 each in a $200 pot. AA is worth $174.92 on average (+$74.92); AQs is worth $25.08 (-$74.92).
Over a long run, 1,000 deals split into about 868 for AA, 119 for AQs and 13 tied.
The same matchup from the other side
AQs versus AA is this same page seen from the other hand: 12.54% for AQs, 87.46% for AA.
Keep exploring
Open the calculator with AsAh against AdQd 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
Nothing here is simulated. The 12 deals of AA against AQs fall into a few suit patterns, each dealt against all 1,712,304 boards, with both best five-card hands compared on every board. Ties give each hand half a win, and the flop rows count a board under each of its ten flops.
Source: our own exact count from the GeorgeLiPoker poker math library. No outside data is used.
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