A9s
61.22%
Wins 60.99%, ties 0.47%
76s
38.78%
Wins 38.54%, ties 0.47%
A9s against 76s: the numbers
| Hand | Wins | Ties | Loses | Equity |
|---|---|---|---|---|
| A9s | 60.992 | 0.465 | 38.543 | 61.224 |
| 76s | 38.543 | 0.465 | 60.992 | 38.776 |
Two suited hands meet here: A9s against 76s. With no overlap in ranks, every card that pairs one hand is a card that does not pair the other.
A 22.44 point lead is real, and 76s still takes about 385 of every 1,000 deals outright. Ties are part of the picture: 0.47% of boards end in a split pot, and each side counts that as half a win.
A9s ranks number 18 of 169 starting hands, and 76s ranks number 115, by equity against a random hand.
| Hand | Boards won, about | Boards tied, about | Boards lost, about |
|---|---|---|---|
| A9s | 16,710,000 | 127,000 | 10,560,000 |
| 76s | 10,560,000 | 127,000 | 16,710,000 |
The total is exact: 16 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) |
|---|---|---|---|---|
| A9s | 1.579 | 1.640 | 2.595 | 0.633 |
| 76s | 0.633 | 2.595 | 1.640 | 1.579 |
In the last column, a pot-to-call ratio at or above the figure makes a call break even or better at this equity.
Who is ahead on which flops
The flop changes the picture. A9s does best on rainbow flops topped by a ten or better, at 65.08%, and worst on low rainbow flops (nine high or lower), at 43.58%. Low rainbow flops (nine high or lower) favor 76s, the hand that is behind overall.
| Flop | Share of flops | A9s wins | Ties | 76s wins | A9s equity |
|---|---|---|---|---|---|
| Rainbow, ten or higher | 25.220 | 64.980 | 0.189 | 34.831 | 65.075 |
| Rainbow, nine or lower | 5.689 | 43.363 | 0.437 | 56.200 | 43.582 |
| Two-tone | 46.727 | 60.267 | 0.216 | 39.517 | 60.375 |
| Monotone | 5.273 | 56.868 | 3.401 | 39.731 | 58.569 |
| Paired | 17.091 | 64.226 | 0.657 | 35.117 | 64.555 |
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
Against one random hand instead, A9s holds 62.78% and 76s holds 45.37%. Facing each other changes that by -1.56 points for A9s and -6.59 points for 76s.
| Case | Equity here | Against a random hand | Change in points | Times the random-hand equity |
|---|---|---|---|---|
| A9s, all flops | 61.224 | 62.781 | -1.557 | 0.97520 |
| A9s, rainbow, ten or higher | 65.075 | 62.781 | +2.294 | 1.03654 |
| A9s, rainbow, nine or lower | 43.582 | 62.781 | -19.199 | 0.69419 |
| A9s, two-tone | 60.375 | 62.781 | -2.406 | 0.96168 |
| A9s, monotone | 58.569 | 62.781 | -4.212 | 0.93291 |
| A9s, paired | 64.555 | 62.781 | +1.774 | 1.02826 |
| 76s, all flops | 38.776 | 45.372 | -6.596 | 0.85462 |
| 76s, rainbow, ten or higher | 34.925 | 45.372 | -10.447 | 0.76975 |
| 76s, rainbow, nine or lower | 56.418 | 45.372 | +11.046 | 1.24345 |
| 76s, two-tone | 39.625 | 45.372 | -5.747 | 0.87334 |
| 76s, monotone | 41.431 | 45.372 | -3.941 | 0.91314 |
| 76s, paired | 35.445 | 45.372 | -9.927 | 0.78121 |
Does a shared suit matter?
Does suit overlap move the numbers? A9s has 63.40% when the hands share a suit and 60.50% when they do not. A9s does better with a shared suit, by 2.90 points.
| Deals | Specific deals | Share of deals | A9s wins | Ties | 76s wins | A9s equity |
|---|---|---|---|---|---|---|
| Share a suit | 4 | 25.00 | 63.128 | 0.539 | 36.333 | 63.397 |
| No shared suit | 12 | 75.00 | 60.279 | 0.441 | 39.280 | 60.500 |
How often this matchup comes up
A9s against 76s is made up of 16 specific-card matchups in one seat order, 0.0010% of the 1,624,350 ordered deals, and 32 counting both seat orders, 0.0020%.
A worked example
Put $100 each into a $200 pot and deal every board once: A9s averages $122.44 back, ahead of its $100 by $22.44, while 76s averages $77.56, short of its $100 by $22.44.
Run 1,000 deals and the tally comes out near 610 for A9s, 385 for 76s and 5 ties.
The same matchup from the other side
The mirror image, 76s against A9s, is 38.78% to 61.22%, and its address redirects to this page.
Keep exploring
Open the calculator with As9s against 7h6h 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
This is an exact count with no sampling. For the 16 ways to deal one A9s and one 76s without reusing a card, grouped by suit pattern, every one of the 1,712,304 possible boards is dealt and both seven-card hands are compared. A tie counts as half a win in the equity column, and each board is counted once under each of its ten three-card flops.
Source: our own exact count from the GeorgeLiPoker poker math library. No outside data is used.
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