AQs
74.66%
Wins 71.90%, ties 5.52%
ATo
25.34%
Wins 22.58%, ties 5.52%
AQs against ATo: the numbers
| Hand | Wins | Ties | Loses | Equity |
|---|---|---|---|---|
| AQs | 71.900 | 5.519 | 22.581 | 74.660 |
| ATo | 22.581 | 5.519 | 71.900 | 25.340 |
The matchup pits a suited hand against an offsuit hand. Sharing a rank is the signature of a dominated hand, since the weaker hand is usually out-kicked when the shared rank shows up.
That is a clear edge, 74.66% to 25.34%, but ATo still wins often enough that one hand proves nothing. 5.52% of boards are ties, so the equity of each hand is its win rate plus half of that.
Place 10 of 169 belongs to AQs and place 19 belongs to ATo in the ranking against a random hand.
| Hand | Boards won, about | Boards tied, about | Boards lost, about |
|---|---|---|---|
| AQs | 44,321,000 | 3,402,000 | 13,920,000 |
| ATo | 13,920,000 | 3,402,000 | 44,321,000 |
Exact total: 36 deals times 1,712,304 boards. The other three counts come from the five-decimal percentages and are rounded to the nearest thousand, so read them as approximate.
| Hand | Equity as odds (to 1) | Wins one deal in | Loses one deal in | Pot odds needed to call (to 1) |
|---|---|---|---|---|
| AQs | 2.946 | 1.391 | 4.429 | 0.339 |
| ATo | 0.339 | 4.429 | 1.391 | 2.946 |
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
If you know the kind of flop that came, the numbers shift: AQs holds 83.62% on low rainbow flops (nine high or lower) and 67.36% on monotone flops. 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 | ATo wins | AQs equity |
|---|---|---|---|---|---|
| Rainbow, ten or higher | 23.177 | 71.042 | 3.126 | 25.832 | 72.605 |
| Rainbow, nine or lower | 7.771 | 81.057 | 5.125 | 13.818 | 83.620 |
| Two-tone | 46.527 | 73.674 | 3.441 | 22.885 | 75.394 |
| Monotone | 5.192 | 65.026 | 4.669 | 30.305 | 67.360 |
| Paired | 17.333 | 66.241 | 14.727 | 19.032 | 73.605 |
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
Start from the random-hand figures, 66.21% for AQs and 62.72% for ATo. This opponent changes them by +8.45 and -37.38 points.
| Case | Equity here | Against a random hand | Change in points | Times the random-hand equity |
|---|---|---|---|---|
| AQs, all flops | 74.660 | 66.209 | +8.451 | 1.12764 |
| AQs, rainbow, ten or higher | 72.605 | 66.209 | +6.396 | 1.09660 |
| AQs, rainbow, nine or lower | 83.620 | 66.209 | +17.411 | 1.26297 |
| AQs, two-tone | 75.394 | 66.209 | +9.185 | 1.13873 |
| AQs, monotone | 67.360 | 66.209 | +1.151 | 1.01738 |
| AQs, paired | 73.605 | 66.209 | +7.396 | 1.11171 |
| ATo, all flops | 25.340 | 62.722 | -37.382 | 0.40400 |
| ATo, rainbow, ten or higher | 27.395 | 62.722 | -35.327 | 0.43677 |
| ATo, rainbow, nine or lower | 16.380 | 62.722 | -46.342 | 0.26115 |
| ATo, two-tone | 24.606 | 62.722 | -38.116 | 0.39230 |
| ATo, monotone | 32.640 | 62.722 | -30.082 | 0.52039 |
| ATo, paired | 26.395 | 62.722 | -36.327 | 0.42083 |
Does a shared suit matter?
Does suit overlap move the numbers? AQs has 74.44% when the hands share a suit and 74.77% when they do not. AQs does better with no shared suit, by 0.33 points.
| Deals | Specific deals | Share of deals | AQs wins | Ties | ATo wins | AQs equity |
|---|---|---|---|---|---|---|
| Share a suit | 12 | 33.33 | 71.640 | 5.600 | 22.760 | 74.440 |
| No shared suit | 24 | 66.67 | 72.030 | 5.478 | 22.492 | 74.769 |
How often this matchup comes up
How often does it happen? 36 of the 1,624,350 ordered deals (0.0022%) are AQs against ATo, and 72 (0.0044%) if either hand may sit in either seat.
A worked example
Try it with money: two players each put in $100 and the whole board runs out every possible way. AQs averages $149.32 from the $200, up $49.32; ATo averages $50.68, down $49.32.
Think in thousands: about 719 of 1,000 go to AQs, about 226 go to ATo, and about 55 are chopped.
The same matchup from the other side
If you came looking for ATo against AQs, the numbers are the same with the hands swapped: 25.34% and 74.66%.
Keep exploring
Try AsQs against AhTd in the calculator: the hands share no suit, and every card can be changed. The links after it are the closest matchups in the ranking.
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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