ATo
72.57%
Wins 71.63%, ties 1.88%
QTo
27.43%
Wins 26.49%, ties 1.88%
ATo against QTo: the numbers
| Hand | Wins | Ties | Loses | Equity |
|---|---|---|---|---|
| ATo | 71.625 | 1.880 | 26.495 | 72.565 |
| QTo | 26.495 | 1.880 | 71.625 | 27.435 |
Here offsuit hands face each other, ATo on one side and QTo 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.
A lead of 45.14 points is large but not decisive: QTo still takes about 265 of every 1,000 deals. A split pot comes up on 1.88% of boards, so the wins and the equity differ by half of that.
In the ranking of all 169 starting hands, ATo is number 19 and QTo is number 47.
| Hand | Boards won, about | Boards tied, about | Boards lost, about |
|---|---|---|---|
| ATo | 132,455,000 | 3,477,000 | 48,997,000 |
| QTo | 48,997,000 | 3,477,000 | 132,455,000 |
Exact total: 108 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) |
|---|---|---|---|---|
| ATo | 2.645 | 1.396 | 3.774 | 0.378 |
| QTo | 0.378 | 3.774 | 1.396 | 2.645 |
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
Break the boards down by their first three cards and ATo is strongest on low rainbow flops (nine high or lower) (83.73%) and weakest on monotone flops (67.23%). ATo 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 | ATo wins | Ties | QTo wins | ATo equity |
|---|---|---|---|---|---|
| Rainbow, ten or higher | 23.275 | 67.812 | 1.440 | 30.748 | 68.532 |
| Rainbow, nine or lower | 7.771 | 82.287 | 2.886 | 14.827 | 83.730 |
| Two-tone | 46.477 | 70.892 | 1.733 | 27.375 | 71.759 |
| Monotone | 5.144 | 65.932 | 2.586 | 31.482 | 67.225 |
| Paired | 17.333 | 75.623 | 2.202 | 22.175 | 76.724 |
Rainbow flops have three suits, two-tone flops repeat one suit, monotone flops are all one suit, and paired flops repeat a rank.
Compared with a random hand
Start from the random-hand figures, 62.72% for ATo and 57.29% for QTo. This opponent changes them by +9.85 and -29.86 points.
| Case | Equity here | Against a random hand | Change in points | Times the random-hand equity |
|---|---|---|---|---|
| ATo, all flops | 72.565 | 62.722 | +9.843 | 1.15693 |
| ATo, rainbow, ten or higher | 68.532 | 62.722 | +5.810 | 1.09263 |
| ATo, rainbow, nine or lower | 83.730 | 62.722 | +21.008 | 1.33494 |
| ATo, two-tone | 71.759 | 62.722 | +9.037 | 1.14408 |
| ATo, monotone | 67.225 | 62.722 | +4.503 | 1.07179 |
| ATo, paired | 76.724 | 62.722 | +14.002 | 1.22324 |
| QTo, all flops | 27.435 | 57.291 | -29.856 | 0.47887 |
| QTo, rainbow, ten or higher | 31.468 | 57.291 | -25.823 | 0.54927 |
| QTo, rainbow, nine or lower | 16.270 | 57.291 | -41.021 | 0.28399 |
| QTo, two-tone | 28.241 | 57.291 | -29.050 | 0.49294 |
| QTo, monotone | 32.775 | 57.291 | -24.516 | 0.57208 |
| QTo, paired | 23.276 | 57.291 | -34.015 | 0.40628 |
Does a shared suit matter?
The suit split reads 72.66% for ATo with a shared suit and 72.23% without one. ATo does better with a shared suit, by 0.43 points.
| Deals | Specific deals | Share of deals | ATo wins | Ties | QTo wins | ATo equity |
|---|---|---|---|---|---|---|
| Share a suit | 84 | 77.78 | 71.708 | 1.905 | 26.387 | 72.661 |
| No shared suit | 24 | 22.22 | 71.334 | 1.793 | 26.873 | 72.231 |
How often this matchup comes up
This page stands for 108 specific-card matchups (0.0066% of 1,624,350 ordered deals), or 216 once you count the seats both ways (0.0133%).
A worked example
Put $100 each into a $200 pot and deal every board once: ATo averages $145.14 back, ahead of its $100 by $45.14, while QTo averages $54.86, short of its $100 by $45.14.
Think in thousands: about 716 of 1,000 go to ATo, about 265 go to QTo, and about 19 are chopped.
The same matchup from the other side
QTo versus ATo is this same page seen from the other hand: 27.43% for QTo, 72.57% for ATo.
Keep exploring
Open the calculator with AsTh against QdTc 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
All 1,712,304 five-card boards are dealt for every suit pattern among the 108 specific deals of ATo against QTo, and both hands are scored on each. That is a full count, so the percentages are exact. Ties are half a win each, and each board appears once per flop it contains.
Source: our own exact count from the GeorgeLiPoker poker math library. No outside data is used.
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