A9o
68.53%
Wins 67.55%, ties 1.96%
Q9s
31.47%
Wins 30.49%, ties 1.96%
A9o against Q9s: the numbers
| Hand | Wins | Ties | Loses | Equity |
|---|---|---|---|---|
| A9o | 67.547 | 1.957 | 30.496 | 68.525 |
| Q9s | 30.496 | 1.957 | 67.547 | 31.475 |
We compare an offsuit hand with a suited hand. 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.
That is a clear edge, 68.53% to 31.47%, but Q9s still wins often enough that one hand proves nothing. Split pots make up 1.96% of the boards, and both equity figures count them as half a win each.
A9o ranks number 25 of 169 starting hands, and Q9s ranks number 43, by equity against a random hand.
| Hand | Boards won, about | Boards tied, about | Boards lost, about |
|---|---|---|---|
| A9o | 41,638,000 | 1,206,000 | 18,799,000 |
| Q9s | 18,799,000 | 1,206,000 | 41,638,000 |
The total is exact: 36 specific deals times 1,712,304 boards. The three counts are approximate, worked out from the percentages to five decimals and 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) |
|---|---|---|---|---|
| A9o | 2.177 | 1.480 | 3.279 | 0.459 |
| Q9s | 0.459 | 3.279 | 1.480 | 2.177 |
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
The flop changes the picture. A9o does best on low rainbow flops (nine high or lower), at 82.47%, and worst on monotone flops, at 64.07%. A9o 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 | A9o wins | Ties | Q9s wins | A9o equity |
|---|---|---|---|---|---|
| Rainbow, ten or higher | 24.634 | 66.098 | 1.401 | 32.501 | 66.799 |
| Rainbow, nine or lower | 6.314 | 80.535 | 3.873 | 15.592 | 82.472 |
| Two-tone | 46.527 | 65.689 | 1.743 | 32.568 | 66.560 |
| Monotone | 5.192 | 62.484 | 3.174 | 34.342 | 64.071 |
| Paired | 17.333 | 71.378 | 2.256 | 26.366 | 72.506 |
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
Each hand has a baseline against a random hand: 60.77% for A9o, 57.66% for Q9s. Here the change is +7.76 and -26.19 points.
| Case | Equity here | Against a random hand | Change in points | Times the random-hand equity |
|---|---|---|---|---|
| A9o, all flops | 68.525 | 60.773 | +7.752 | 1.12756 |
| A9o, rainbow, ten or higher | 66.799 | 60.773 | +6.026 | 1.09916 |
| A9o, rainbow, nine or lower | 82.472 | 60.773 | +21.699 | 1.35705 |
| A9o, two-tone | 66.560 | 60.773 | +5.787 | 1.09522 |
| A9o, monotone | 64.071 | 60.773 | +3.298 | 1.05427 |
| A9o, paired | 72.506 | 60.773 | +11.733 | 1.19306 |
| Q9s, all flops | 31.475 | 57.664 | -26.189 | 0.54583 |
| Q9s, rainbow, ten or higher | 33.201 | 57.664 | -24.463 | 0.57577 |
| Q9s, rainbow, nine or lower | 17.528 | 57.664 | -40.136 | 0.30397 |
| Q9s, two-tone | 33.440 | 57.664 | -24.224 | 0.57991 |
| Q9s, monotone | 35.929 | 57.664 | -21.735 | 0.62308 |
| Q9s, paired | 27.494 | 57.664 | -30.170 | 0.47680 |
Does a shared suit matter?
Split by suits, the deals give A9o 69.61% when the hands overlap in a suit and 67.98% when they do not. A9o does better with a shared suit, by 1.63 points.
| Deals | Specific deals | Share of deals | A9o wins | Ties | Q9s wins | A9o equity |
|---|---|---|---|---|---|---|
| Share a suit | 12 | 33.33 | 68.597 | 2.030 | 29.373 | 69.612 |
| No shared suit | 24 | 66.67 | 67.022 | 1.920 | 31.058 | 67.982 |
How often this matchup comes up
This page stands for 36 specific-card matchups (0.0022% of 1,624,350 ordered deals), or 72 once you count the seats both ways (0.0044%).
A worked example
Take a $200 pot built from $100 each. A9o's equity of 68.53% is worth $137.06, a $37.06 edge, and Q9s' 31.47% is worth $62.94, which is $37.06 under its stake.
Run 1,000 deals and the tally comes out near 675 for A9o, 305 for Q9s and 20 ties.
The same matchup from the other side
One page covers both views. From Q9s' side the equity is 31.47%, and from A9o's side it is 68.53%.
Keep exploring
The calculator link fills in As9h against Qd9d, 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
We counted every case. Each suit pattern of the 36 specific A9o against Q9s deals meets all 1,712,304 boards, and the better five-card hand wins; a split pot is half a win each. The flop table reads each board under all ten of its three-card flops.
Source: our own exact count from the GeorgeLiPoker poker math library. No outside data is used.
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