Q9s
43.15%
Wins 42.88%, ties 0.53%
A2s
56.85%
Wins 56.59%, ties 0.53%
Q9s against A2s: the numbers
| Hand | Wins | Ties | Loses | Equity |
|---|---|---|---|---|
| Q9s | 42.878 | 0.534 | 56.588 | 43.145 |
| A2s | 56.588 | 0.534 | 42.878 | 56.855 |
Q9s meets A2s, and both are suited hands. With no overlap in ranks, every card that pairs one hand is a card that does not pair the other.
A 13.70 point lead is real, and Q9s still takes about 429 of every 1,000 deals outright. About 0.53% of boards chop the pot, which is why equity sits slightly above the win figure for both hands.
By strength against a random hand, Q9s holds place 43 of 169 and A2s holds place 46.
| Hand | Boards won, about | Boards tied, about | Boards lost, about |
|---|---|---|---|
| Q9s | 11,747,000 | 146,000 | 15,503,000 |
| A2s | 15,503,000 | 146,000 | 11,747,000 |
The board total is exact, 16 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) |
|---|---|---|---|---|
| Q9s | 0.759 | 2.332 | 1.767 | 1.318 |
| A2s | 1.318 | 1.767 | 2.332 | 0.759 |
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
Split by what the flop looks like, A2s peaks at 62.09% on paired flops and bottoms out at 54.48% on monotone flops. A2s stays ahead on all five textures.
| Flop | Share of flops | Q9s wins | Ties | A2s wins | Q9s equity |
|---|---|---|---|---|---|
| Rainbow, ten or higher | 24.543 | 43.734 | 0.162 | 56.104 | 43.815 |
| Rainbow, nine or lower | 6.366 | 43.687 | 0.990 | 55.323 | 44.182 |
| Two-tone | 46.727 | 44.151 | 0.296 | 55.553 | 44.299 |
| Monotone | 5.273 | 43.798 | 3.442 | 52.760 | 45.519 |
| Paired | 17.091 | 37.581 | 0.653 | 61.766 | 37.908 |
Flop types: rainbow means three different suits, two-tone means one suit twice, monotone means one suit three times, paired means a repeated rank.
Compared with a random hand
Each hand has a baseline against a random hand: 57.66% for Q9s, 57.38% for A2s. Here the change is -14.51 and -0.53 points.
| Case | Equity here | Against a random hand | Change in points | Times the random-hand equity |
|---|---|---|---|---|
| Q9s, all flops | 43.145 | 57.664 | -14.519 | 0.74821 |
| Q9s, rainbow, ten or higher | 43.815 | 57.664 | -13.849 | 0.75983 |
| Q9s, rainbow, nine or lower | 44.182 | 57.664 | -13.482 | 0.76620 |
| Q9s, two-tone | 44.299 | 57.664 | -13.365 | 0.76823 |
| Q9s, monotone | 45.519 | 57.664 | -12.145 | 0.78938 |
| Q9s, paired | 37.908 | 57.664 | -19.756 | 0.65739 |
| A2s, all flops | 56.855 | 57.379 | -0.524 | 0.99087 |
| A2s, rainbow, ten or higher | 56.185 | 57.379 | -1.194 | 0.97919 |
| A2s, rainbow, nine or lower | 55.818 | 57.379 | -1.561 | 0.97279 |
| A2s, two-tone | 55.701 | 57.379 | -1.678 | 0.97076 |
| A2s, monotone | 54.481 | 57.379 | -2.898 | 0.94949 |
| A2s, paired | 62.092 | 57.379 | +4.713 | 1.08214 |
Does a shared suit matter?
Of the deals of this matchup, 4 share a suit (A2s at 58.70%) and 12 do not (56.24%). A2s does better with a shared suit, by 2.46 points.
| Deals | Specific deals | Share of deals | Q9s wins | Ties | A2s wins | Q9s equity |
|---|---|---|---|---|---|---|
| Share a suit | 4 | 25.00 | 40.992 | 0.617 | 58.391 | 41.301 |
| No shared suit | 12 | 75.00 | 43.506 | 0.507 | 55.987 | 43.760 |
How often this matchup comes up
You will meet this exact matchup 0.0020% of the time in a random heads-up deal: 32 of 1,624,350, counting either seat order.
A worked example
Worked example: both players commit $100, so $200 sits in the middle. Over every board, A2s' average share is $113.70 (a gain of $13.70) and Q9s' is $86.30 (a loss of $13.70).
Run 1,000 deals and the tally comes out near 566 for A2s, 429 for Q9s and 5 ties.
The same matchup from the other side
Read it from the other side: A2s against Q9s is the same matchup with the numbers swapped, so A2s holds 56.85% and Q9s holds 43.15%. That address sends you back to this page.
Keep exploring
Open the calculator with Qs9s against Ah2h 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 16 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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