AQs
74.83%
Wins 72.03%, ties 5.59%
A9o
25.17%
Wins 22.38%, ties 5.59%
AQs against A9o: the numbers
| Hand | Wins | Ties | Loses | Equity |
|---|---|---|---|---|
| AQs | 72.033 | 5.592 | 22.375 | 74.829 |
| A9o | 22.375 | 5.592 | 72.033 | 25.171 |
Here a suited hand (AQs) meets an offsuit hand (A9o). The two hands share a rank, and the one with the better other card dominates: it wins most kicker battles when that shared rank hits.
AQs is well ahead, and A9o needs a specific kind of board to catch up. 5.59% of boards are ties, so the equity of each hand is its win rate plus half of that.
For context, AQs sits at number 10 of 169 starting hands and A9o at number 25 when each is run against a random hand.
| Hand | Boards won, about | Boards tied, about | Boards lost, about |
|---|---|---|---|
| AQs | 44,403,000 | 3,447,000 | 13,793,000 |
| A9o | 13,793,000 | 3,447,000 | 44,403,000 |
The board total is exact, 36 deals at 1,712,304 boards each. Won, tied and lost counts are rounded to the nearest thousand from the five-decimal percentages.
| Hand | Equity as odds (to 1) | Wins one deal in | Loses one deal in | Pot odds needed to call (to 1) |
|---|---|---|---|---|
| AQs | 2.973 | 1.388 | 4.469 | 0.336 |
| A9o | 0.336 | 4.469 | 1.388 | 2.973 |
The last column is the break-even price: the pot odds a call needs to offer, as a ratio of pot to call.
Who is ahead on which flops
AQs prefers rainbow flops topped by a ten or better, where it holds 79.52%, and likes low rainbow flops (nine high or lower) least, where it holds 61.79%. AQs 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 | AQs wins | Ties | A9o wins | AQs equity |
|---|---|---|---|---|---|
| Rainbow, ten or higher | 23.905 | 77.767 | 3.515 | 18.718 | 79.524 |
| Rainbow, nine or lower | 7.042 | 59.573 | 4.436 | 35.991 | 61.791 |
| Two-tone | 46.527 | 73.813 | 3.528 | 22.659 | 75.577 |
| Monotone | 5.192 | 65.224 | 4.724 | 30.052 | 67.586 |
| Paired | 17.334 | 66.450 | 14.723 | 18.827 | 73.811 |
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
Relative to a random opponent, AQs changes by +8.62 points (baseline 66.21%) and A9o by -35.60 points (baseline 60.77%).
| Case | Equity here | Against a random hand | Change in points | Times the random-hand equity |
|---|---|---|---|---|
| AQs, all flops | 74.829 | 66.209 | +8.620 | 1.13019 |
| AQs, rainbow, ten or higher | 79.524 | 66.209 | +13.315 | 1.20111 |
| AQs, rainbow, nine or lower | 61.791 | 66.209 | -4.418 | 0.93327 |
| AQs, two-tone | 75.577 | 66.209 | +9.368 | 1.14149 |
| AQs, monotone | 67.586 | 66.209 | +1.377 | 1.02080 |
| AQs, paired | 73.811 | 66.209 | +7.602 | 1.11482 |
| A9o, all flops | 25.171 | 60.773 | -35.602 | 0.41418 |
| A9o, rainbow, ten or higher | 20.476 | 60.773 | -40.297 | 0.33693 |
| A9o, rainbow, nine or lower | 38.209 | 60.773 | -22.564 | 0.62872 |
| A9o, two-tone | 24.423 | 60.773 | -36.350 | 0.40187 |
| A9o, monotone | 32.414 | 60.773 | -28.359 | 0.53336 |
| A9o, paired | 26.189 | 60.773 | -34.584 | 0.43093 |
Does a shared suit matter?
When the hands share a suit, AQs holds 74.56%; when they do not, it holds 74.96%. AQs does better with no shared suit, by 0.40 points.
| Deals | Specific deals | Share of deals | AQs wins | Ties | A9o wins | AQs equity |
|---|---|---|---|---|---|---|
| Share a suit | 12 | 33.33 | 71.724 | 5.671 | 22.605 | 74.559 |
| No shared suit | 24 | 66.67 | 72.187 | 5.552 | 22.261 | 74.963 |
How often this matchup comes up
Out of 1,624,350 ways to deal two seats two cards each, 36 are AQs in one seat and A9o in the other (0.0022%); with the seats swapped too, 72 (0.0044%).
A worked example
With $100 from each side, the $200 pot is split on average as $149.66 for AQs and $50.34 for A9o; the first side gains $49.66 per all-in and the second gives up $49.66.
Run 1,000 deals and the tally comes out near 720 for AQs, 224 for A9o and 56 ties.
The same matchup from the other side
One page covers both views. From A9o's side the equity is 25.17%, and from AQs' side it is 74.83%.
Keep exploring
AsQs against Ah9d 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
Each figure is a complete count over boards. Take the 36 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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