AQs
70.55%
Wins 67.91%, ties 5.28%
ATs
29.45%
Wins 26.81%, ties 5.28%
AQs against ATs: the numbers
| Hand | Wins | Ties | Loses | Equity |
|---|---|---|---|---|
| AQs | 67.909 | 5.277 | 26.814 | 70.548 |
| ATs | 26.814 | 5.277 | 67.909 | 29.452 |
Here suited hands face each other, AQs on one side and ATs on the other. Sharing a rank is the signature of a dominated hand, since the weaker hand is usually out-kicked when the shared rank shows up.
AQs is the clear favorite, though ATs gets there on roughly one board in 3. A split pot comes up on 5.28% of boards, so the wins and the equity differ by half of that.
For context, AQs sits at number 10 of 169 starting hands and ATs at number 13 when each is run against a random hand.
| Hand | Boards won, about | Boards tied, about | Boards lost, about |
|---|---|---|---|
| AQs | 13,954,000 | 1,084,000 | 5,510,000 |
| ATs | 5,510,000 | 1,084,000 | 13,954,000 |
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) |
|---|---|---|---|---|
| AQs | 2.395 | 1.473 | 3.729 | 0.417 |
| ATs | 0.417 | 3.729 | 1.473 | 2.395 |
The last column is the smallest pot odds, written as a pot-to-call ratio, at which a call breaks even with this equity.
Who is ahead on which flops
By flop texture, AQs' equity runs from 64.18% on monotone flops up to 80.64% on low rainbow flops (nine high or lower). AQs 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 | ATs wins | AQs equity |
|---|---|---|---|---|---|
| Rainbow, ten or higher | 23.138 | 68.858 | 3.059 | 28.083 | 70.388 |
| Rainbow, nine or lower | 7.771 | 78.172 | 4.937 | 16.891 | 80.640 |
| Two-tone | 46.543 | 68.377 | 3.209 | 28.414 | 69.982 |
| Monotone | 5.215 | 61.595 | 5.168 | 33.237 | 64.179 |
| Paired | 17.333 | 62.685 | 13.975 | 23.340 | 69.672 |
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
Against one random hand instead, AQs holds 66.21% and ATs holds 64.60%. Facing each other changes that by +4.34 points for AQs and -35.15 points for ATs.
| Case | Equity here | Against a random hand | Change in points | Times the random-hand equity |
|---|---|---|---|---|
| AQs, all flops | 70.548 | 66.209 | +4.339 | 1.06553 |
| AQs, rainbow, ten or higher | 70.388 | 66.209 | +4.179 | 1.06312 |
| AQs, rainbow, nine or lower | 80.640 | 66.209 | +14.431 | 1.21796 |
| AQs, two-tone | 69.982 | 66.209 | +3.773 | 1.05699 |
| AQs, monotone | 64.179 | 66.209 | -2.030 | 0.96934 |
| AQs, paired | 69.672 | 66.209 | +3.463 | 1.05230 |
| ATs, all flops | 29.452 | 64.602 | -35.150 | 0.45590 |
| ATs, rainbow, ten or higher | 29.612 | 64.602 | -34.990 | 0.45838 |
| ATs, rainbow, nine or lower | 19.360 | 64.602 | -45.242 | 0.29968 |
| ATs, two-tone | 30.018 | 64.602 | -34.584 | 0.46466 |
| ATs, monotone | 35.821 | 64.602 | -28.781 | 0.55449 |
| ATs, paired | 30.328 | 64.602 | -34.274 | 0.46946 |
Does a shared suit matter?
These two classes cannot share a suit in any legal deal, so there is only one row to read: AQs holds 70.55% in every deal of this matchup.
| Deals | Specific deals | Share of deals | AQs wins | Ties | ATs wins | AQs equity |
|---|---|---|---|---|---|---|
| Share a suit | 0 | 0.00 | not possible | not possible | not possible | not possible |
| No shared suit | 12 | 100.00 | 67.909 | 5.277 | 26.814 | 70.548 |
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
A $100 all-in from each player makes a $200 pot, and the exact equity says AQs gets $141.10 of it on average and ATs gets $58.90.
Think in thousands: about 679 of 1,000 go to AQs, about 268 go to ATs, and about 53 are chopped.
The same matchup from the other side
ATs versus AQs is this same page seen from the other hand: 29.45% for ATs, 70.55% for AQs.
Keep exploring
Open the calculator with AsQs against AhTh 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
This is an exact count with no sampling. For the 12 ways to deal one AQs and one ATs 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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