A9s
59.13%
Wins 58.91%, ties 0.44%
QTo
40.87%
Wins 40.65%, ties 0.44%
A9s against QTo: the numbers
| Hand | Wins | Ties | Loses | Equity |
|---|---|---|---|---|
| A9s | 58.905 | 0.443 | 40.652 | 59.126 |
| QTo | 40.652 | 0.443 | 58.905 | 40.874 |
One side is a suited hand, the other is an offsuit hand. With no overlap in ranks, every card that pairs one hand is a card that does not pair the other.
The lead is steady rather than large, and the flop still has plenty of say in who wins. 0.44% of boards are ties, so the equity of each hand is its win rate plus half of that.
For context, A9s sits at number 18 of 169 starting hands and QTo at number 47 when each is run against a random hand.
| Hand | Boards won, about | Boards tied, about | Boards lost, about |
|---|---|---|---|
| A9s | 48,414,000 | 364,000 | 33,412,000 |
| QTo | 33,412,000 | 364,000 | 48,414,000 |
Exact total: 48 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) |
|---|---|---|---|---|
| A9s | 1.447 | 1.698 | 2.460 | 0.691 |
| QTo | 0.691 | 2.460 | 1.698 | 1.447 |
The final column gives the least the pot must offer for each unit called for a call to break even at this equity.
Who is ahead on which flops
Break the boards down by their first three cards and A9s is strongest on low rainbow flops (nine high or lower) (74.86%) and weakest on rainbow flops topped by a ten or better (51.94%). A9s 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 | A9s wins | Ties | QTo wins | A9s equity |
|---|---|---|---|---|---|
| Rainbow, ten or higher | 23.988 | 51.865 | 0.149 | 47.986 | 51.939 |
| Rainbow, nine or lower | 7.042 | 74.470 | 0.772 | 24.758 | 74.856 |
| Two-tone | 46.667 | 58.563 | 0.265 | 41.172 | 58.696 |
| Monotone | 5.212 | 54.564 | 2.364 | 43.072 | 55.746 |
| Paired | 17.091 | 64.631 | 0.620 | 34.749 | 64.941 |
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 A9s from 62.78% by -3.65 points and QTo from 57.29% by -16.42 points.
| Case | Equity here | Against a random hand | Change in points | Times the random-hand equity |
|---|---|---|---|---|
| A9s, all flops | 59.126 | 62.781 | -3.655 | 0.94178 |
| A9s, rainbow, ten or higher | 51.939 | 62.781 | -10.842 | 0.82730 |
| A9s, rainbow, nine or lower | 74.856 | 62.781 | +12.075 | 1.19234 |
| A9s, two-tone | 58.696 | 62.781 | -4.085 | 0.93493 |
| A9s, monotone | 55.746 | 62.781 | -7.035 | 0.88794 |
| A9s, paired | 64.941 | 62.781 | +2.160 | 1.03441 |
| QTo, all flops | 40.874 | 57.291 | -16.417 | 0.71345 |
| QTo, rainbow, ten or higher | 48.061 | 57.291 | -9.230 | 0.83889 |
| QTo, rainbow, nine or lower | 25.144 | 57.291 | -32.147 | 0.43888 |
| QTo, two-tone | 41.304 | 57.291 | -15.987 | 0.72095 |
| QTo, monotone | 44.254 | 57.291 | -13.037 | 0.77244 |
| QTo, paired | 35.059 | 57.291 | -22.232 | 0.61195 |
Does a shared suit matter?
Two kinds of deal exist here. In 24 of them the hands share a suit and A9s holds 58.79%. In 24 they do not, and it holds 59.46%. A9s does better with no shared suit, by 0.67 points.
| Deals | Specific deals | Share of deals | A9s wins | Ties | QTo wins | A9s equity |
|---|---|---|---|---|---|---|
| Share a suit | 24 | 50.00 | 58.547 | 0.484 | 40.969 | 58.789 |
| No shared suit | 24 | 50.00 | 59.263 | 0.402 | 40.335 | 59.464 |
How often this matchup comes up
Counting specific cards, A9s against QTo appears in 48 of the 1,624,350 ordered heads-up deals (0.0030%), and in 96 when the seats are swapped too (0.0059%).
A worked example
A $100 all-in from each player makes a $200 pot, and the exact equity says A9s gets $118.26 of it on average and QTo gets $81.74.
Over a long run, 1,000 deals split into about 589 for A9s, 407 for QTo and 4 tied.
The same matchup from the other side
QTo versus A9s is this same page seen from the other hand: 40.87% for QTo, 59.13% for A9s.
Keep exploring
Open the calculator with As9s against QhTd 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
Method: exact enumeration. The 48 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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