A7s
57.10%
Wins 56.86%, ties 0.47%
Q9s
42.90%
Wins 42.67%, ties 0.47%
A7s against Q9s: the numbers
| Hand | Wins | Ties | Loses | Equity |
|---|---|---|---|---|
| A7s | 56.861 | 0.474 | 42.665 | 57.098 |
| Q9s | 42.665 | 0.474 | 56.861 | 42.902 |
A7s and Q9s are both suited hands. 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. 0.47% of boards are ties, so the equity of each hand is its win rate plus half of that.
By strength against a random hand, A7s holds place 24 of 169 and Q9s holds place 43.
| Hand | Boards won, about | Boards tied, about | Boards lost, about |
|---|---|---|---|
| A7s | 15,578,000 | 130,000 | 11,689,000 |
| Q9s | 11,689,000 | 130,000 | 15,578,000 |
16 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) |
|---|---|---|---|---|
| A7s | 1.331 | 1.759 | 2.344 | 0.751 |
| Q9s | 0.751 | 2.344 | 1.759 | 1.331 |
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
Paired flops are the best for A7s (62.18%); monotone flops are the worst (54.63%). A7s stays ahead on all five textures.
| Flop | Share of flops | A7s wins | Ties | Q9s wins | A7s equity |
|---|---|---|---|---|---|
| Rainbow, ten or higher | 24.543 | 56.231 | 0.163 | 43.606 | 56.312 |
| Rainbow, nine or lower | 6.366 | 56.587 | 0.611 | 42.802 | 56.892 |
| Two-tone | 46.727 | 55.844 | 0.231 | 43.925 | 55.959 |
| Monotone | 5.273 | 52.931 | 3.396 | 43.673 | 54.629 |
| Paired | 17.091 | 61.861 | 0.633 | 37.506 | 62.177 |
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
The table below sets each hand against its own random-hand baseline: a change of -3.88 points for A7s, from 60.98%, and -14.76 for Q9s, from 57.66%.
| Case | Equity here | Against a random hand | Change in points | Times the random-hand equity |
|---|---|---|---|---|
| A7s, all flops | 57.098 | 60.984 | -3.886 | 0.93628 |
| A7s, rainbow, ten or higher | 56.312 | 60.984 | -4.672 | 0.92339 |
| A7s, rainbow, nine or lower | 56.892 | 60.984 | -4.092 | 0.93290 |
| A7s, two-tone | 55.959 | 60.984 | -5.025 | 0.91760 |
| A7s, monotone | 54.629 | 60.984 | -6.355 | 0.89579 |
| A7s, paired | 62.177 | 60.984 | +1.193 | 1.01956 |
| Q9s, all flops | 42.902 | 57.664 | -14.762 | 0.74400 |
| Q9s, rainbow, ten or higher | 43.688 | 57.664 | -13.976 | 0.75763 |
| Q9s, rainbow, nine or lower | 43.108 | 57.664 | -14.556 | 0.74757 |
| Q9s, two-tone | 44.041 | 57.664 | -13.623 | 0.76375 |
| Q9s, monotone | 45.371 | 57.664 | -12.293 | 0.78682 |
| Q9s, paired | 37.823 | 57.664 | -19.841 | 0.65592 |
Does a shared suit matter?
Split by suits, the deals give A7s 58.96% when the hands overlap in a suit and 56.48% when they do not. A7s does better with a shared suit, by 2.48 points.
| Deals | Specific deals | Share of deals | A7s wins | Ties | Q9s wins | A7s equity |
|---|---|---|---|---|---|---|
| Share a suit | 4 | 25.00 | 58.689 | 0.550 | 40.761 | 58.964 |
| No shared suit | 12 | 75.00 | 56.251 | 0.449 | 43.300 | 56.476 |
How often this matchup comes up
Exactly 16 specific deals fit this matchup in one seat order, which is 0.0010% of 1,624,350; both orders together give 32, or 0.0020%.
A worked example
To see what the equity is worth, imagine $100 each in a $200 pot. A7s is worth $114.20 on average (+$14.20); Q9s is worth $85.80 (-$14.20).
Per 1,000 deals: A7s wins about 568, Q9s wins about 427, and about 5 end in a split pot.
The same matchup from the other side
Swap the hands and you get Q9s with 42.90% against A7s with 57.10%. We keep one page per matchup, with the better-ranked hand first.
Keep exploring
Open the calculator with As7s against Qh9h 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
The figures are counted, not estimated: 1,712,304 boards for every suit pattern of the 16 specific deals, with both seven-card hands compared each time. Equity gives half a win for a tie. For the flop rows, a board is counted once under each of the ten flops inside it.
Source: our own exact count from the GeorgeLiPoker poker math library. No outside data is used.
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