ATo
68.61%
Wins 67.69%, ties 1.83%
QTs
31.39%
Wins 30.48%, ties 1.83%
ATo against QTs: the numbers
| Hand | Wins | Ties | Loses | Equity |
|---|---|---|---|---|
| ATo | 67.693 | 1.834 | 30.473 | 68.610 |
| QTs | 30.473 | 1.834 | 67.693 | 31.390 |
ATo and QTs are an offsuit hand and a suited hand, in that order. 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, 68.61% to 31.39%, but QTs still wins often enough that one hand proves nothing. Of every 100 boards, about 1.83 are split pots, and the equity figures already include them.
Ranked by equity against a random hand, ATo is number 19 of the 169 starting hands and QTs is number 34.
| Hand | Boards won, about | Boards tied, about | Boards lost, about |
|---|---|---|---|
| ATo | 41,728,000 | 1,131,000 | 18,784,000 |
| QTs | 18,784,000 | 1,131,000 | 41,728,000 |
36 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) |
|---|---|---|---|---|
| ATo | 2.186 | 1.477 | 3.282 | 0.458 |
| QTs | 0.458 | 3.282 | 1.477 | 2.186 |
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
Break the boards down by their first three cards and ATo is strongest on low rainbow flops (nine high or lower) (80.74%) and weakest on monotone flops (64.20%). 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 | QTs wins | ATo equity |
|---|---|---|---|---|---|
| Rainbow, ten or higher | 23.177 | 65.767 | 1.406 | 32.827 | 66.470 |
| Rainbow, nine or lower | 7.771 | 79.355 | 2.768 | 17.877 | 80.739 |
| Two-tone | 46.527 | 65.853 | 1.616 | 32.531 | 66.661 |
| Monotone | 5.192 | 62.635 | 3.121 | 34.244 | 64.196 |
| Paired | 17.333 | 71.494 | 2.187 | 26.319 | 72.587 |
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
Compared with a random opponent, this matchup shifts ATo from 62.72% by +5.89 points and QTs from 59.47% by -28.08 points.
| Case | Equity here | Against a random hand | Change in points | Times the random-hand equity |
|---|---|---|---|---|
| ATo, all flops | 68.610 | 62.722 | +5.888 | 1.09387 |
| ATo, rainbow, ten or higher | 66.470 | 62.722 | +3.748 | 1.05976 |
| ATo, rainbow, nine or lower | 80.739 | 62.722 | +18.017 | 1.28725 |
| ATo, two-tone | 66.661 | 62.722 | +3.939 | 1.06280 |
| ATo, monotone | 64.196 | 62.722 | +1.474 | 1.02350 |
| ATo, paired | 72.587 | 62.722 | +9.865 | 1.15728 |
| QTs, all flops | 31.390 | 59.468 | -28.078 | 0.52785 |
| QTs, rainbow, ten or higher | 33.530 | 59.468 | -25.938 | 0.56383 |
| QTs, rainbow, nine or lower | 19.261 | 59.468 | -40.207 | 0.32389 |
| QTs, two-tone | 33.339 | 59.468 | -26.129 | 0.56062 |
| QTs, monotone | 35.804 | 59.468 | -23.664 | 0.60207 |
| QTs, paired | 27.413 | 59.468 | -32.055 | 0.46097 |
Does a shared suit matter?
Does suit overlap move the numbers? ATo has 69.64% when the hands share a suit and 68.09% when they do not. ATo does better with a shared suit, by 1.55 points.
| Deals | Specific deals | Share of deals | ATo wins | Ties | QTs wins | ATo equity |
|---|---|---|---|---|---|---|
| Share a suit | 12 | 33.33 | 68.686 | 1.910 | 29.404 | 69.641 |
| No shared suit | 24 | 66.67 | 67.196 | 1.796 | 31.008 | 68.094 |
How often this matchup comes up
You will meet this exact matchup 0.0044% of the time in a random heads-up deal: 72 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 ATo gets $137.22 of it on average and QTs gets $62.78.
Scaled to 1,000 deals, that is roughly 677 wins for ATo, 305 for QTs and 18 chopped pots.
The same matchup from the other side
One page covers both views. From QTs' side the equity is 31.39%, and from ATo's side it is 68.61%.
Keep exploring
AsTh against QdTd is a ready-made deal for the calculator, with no suit in common between the hands. The neighboring matchups below replace one hand with another of similar strength.
How this was computed
All 1,712,304 five-card boards are dealt for every suit pattern among the 36 specific deals of ATo against QTs, 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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