AQo
72.73%
Wins 72.00%, ties 1.46%
QTo
27.27%
Wins 26.54%, ties 1.46%
AQo against QTo: the numbers
| Hand | Wins | Ties | Loses | Equity |
|---|---|---|---|---|
| AQo | 72.003 | 1.459 | 26.538 | 72.733 |
| QTo | 26.538 | 1.459 | 72.003 | 27.267 |
The matchup is offsuit hands on both sides, AQo against QTo. Because the hands share one rank, the one with the higher kicker is ahead when that rank pairs and the other hand is mostly drawing.
AQo is the clear favorite, though QTo gets there on roughly one board in 4. Ties are 1.46% of the outcomes here; each tied board gives both hands half the pot.
Place 14 of 169 belongs to AQo and place 47 belongs to QTo in the ranking against a random hand.
| Hand | Boards won, about | Boards tied, about | Boards lost, about |
|---|---|---|---|
| AQo | 133,154,000 | 2,698,000 | 49,076,000 |
| QTo | 49,076,000 | 2,698,000 | 133,154,000 |
108 specific deals times 1,712,304 boards gives the exact total. The won, tied and lost counts are approximations from the five-decimal percentages, 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) |
|---|---|---|---|---|
| AQo | 2.667 | 1.389 | 3.768 | 0.375 |
| QTo | 0.375 | 3.768 | 1.389 | 2.667 |
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
By flop texture, AQo's equity runs from 68.63% on rainbow flops topped by a ten or better up to 82.87% on low rainbow flops (nine high or lower). AQo stays ahead on all five textures.
| Flop | Share of flops | AQo wins | Ties | QTo wins | AQo equity |
|---|---|---|---|---|---|
| Rainbow, ten or higher | 23.275 | 67.966 | 1.322 | 30.712 | 68.627 |
| Rainbow, nine or lower | 7.771 | 82.287 | 1.169 | 16.544 | 82.872 |
| Two-tone | 46.477 | 71.261 | 1.236 | 27.503 | 71.879 |
| Monotone | 5.144 | 68.024 | 2.240 | 29.736 | 69.144 |
| Paired | 17.333 | 75.984 | 2.139 | 21.877 | 77.053 |
Flop types: rainbow means three different suits, two-tone means one suit twice, monotone means one suit three times, paired means a repeated rank.
Compared with a random hand
Relative to a random opponent, AQo changes by +8.30 points (baseline 64.43%) and QTo by -30.02 points (baseline 57.29%).
| Case | Equity here | Against a random hand | Change in points | Times the random-hand equity |
|---|---|---|---|---|
| AQo, all flops | 72.733 | 64.432 | +8.301 | 1.12883 |
| AQo, rainbow, ten or higher | 68.627 | 64.432 | +4.195 | 1.06511 |
| AQo, rainbow, nine or lower | 82.872 | 64.432 | +18.440 | 1.28619 |
| AQo, two-tone | 71.879 | 64.432 | +7.447 | 1.11558 |
| AQo, monotone | 69.144 | 64.432 | +4.712 | 1.07313 |
| AQo, paired | 77.053 | 64.432 | +12.621 | 1.19588 |
| QTo, all flops | 27.267 | 57.291 | -30.024 | 0.47594 |
| QTo, rainbow, ten or higher | 31.373 | 57.291 | -25.918 | 0.54761 |
| QTo, rainbow, nine or lower | 17.128 | 57.291 | -40.163 | 0.29896 |
| QTo, two-tone | 28.121 | 57.291 | -29.170 | 0.49084 |
| QTo, monotone | 30.856 | 57.291 | -26.435 | 0.53858 |
| QTo, paired | 22.947 | 57.291 | -34.344 | 0.40053 |
Does a shared suit matter?
Does suit overlap move the numbers? AQo has 72.90% when the hands share a suit and 72.16% when they do not. AQo does better with a shared suit, by 0.74 points.
| Deals | Specific deals | Share of deals | AQo wins | Ties | QTo wins | AQo equity |
|---|---|---|---|---|---|---|
| Share a suit | 84 | 77.78 | 72.156 | 1.483 | 26.361 | 72.897 |
| No shared suit | 24 | 22.22 | 71.467 | 1.378 | 27.155 | 72.156 |
How often this matchup comes up
Counting specific cards, AQo against QTo appears in 108 of the 1,624,350 ordered heads-up deals (0.0066%), and in 216 when the seats are swapped too (0.0133%).
A worked example
Say each player puts $100 in before the flop, making a $200 pot. On average AQo takes back $145.46 of it, which is $45.46 more than it put in, and QTo takes back $54.54, $45.46 less than it put in.
A thousand deals look like this: AQo takes 720, QTo takes 265, 15 are ties.
The same matchup from the other side
QTo versus AQo is this same page seen from the other hand: 27.27% for QTo, 72.73% for AQo.
Keep exploring
The calculator link fills in AsQh against QdTc, 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
Each figure is a complete count over boards. Take the 108 specific deals, group them by suit pattern, deal all 1,712,304 boards against each, and compare the two seven-card hands. Equity counts a tie as half a win; the flop rows use every one of a board's ten flops.
Source: our own exact count from the GeorgeLiPoker poker math library. No outside data is used.
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