A9o
58.67%
Wins 58.46%, ties 0.42%
76s
41.33%
Wins 41.12%, ties 0.42%
A9o against 76s: the numbers
| Hand | Wins | Ties | Loses | Equity |
|---|---|---|---|---|
| A9o | 58.458 | 0.416 | 41.126 | 58.666 |
| 76s | 41.126 | 0.416 | 58.458 | 41.334 |
A9o and 76s are an offsuit hand and a suited hand, in that order. The two hands share no rank, which makes this a pure matchup of card strength, straight chances and flush chances.
A9o is ahead, but 76s is far from dead: it takes 411 of every 1,000 deals outright. 0.42% of boards are ties, so the equity of each hand is its win rate plus half of that.
For context, A9o sits at number 25 of 169 starting hands and 76s at number 115 when each is run against a random hand.
| Hand | Boards won, about | Boards tied, about | Boards lost, about |
|---|---|---|---|
| A9o | 48,047,000 | 342,000 | 33,802,000 |
| 76s | 33,802,000 | 342,000 | 48,047,000 |
The board total is exact, 48 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) |
|---|---|---|---|---|
| A9o | 1.419 | 1.711 | 2.432 | 0.705 |
| 76s | 0.705 | 2.432 | 1.711 | 1.419 |
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
Across the five flop textures A9o's equity moves by 22.14 points, from 41.47% on low rainbow flops (nine high or lower) to 63.61% on rainbow flops topped by a ten or better. Low rainbow flops (nine high or lower) favor 76s, the hand that is behind overall.
| Flop | Share of flops | A9o wins | Ties | 76s wins | A9o equity |
|---|---|---|---|---|---|
| Rainbow, ten or higher | 25.341 | 63.511 | 0.192 | 36.297 | 63.607 |
| Rainbow, nine or lower | 5.689 | 41.245 | 0.455 | 58.300 | 41.472 |
| Two-tone | 46.667 | 56.779 | 0.227 | 42.994 | 56.893 |
| Monotone | 5.212 | 55.979 | 2.356 | 41.665 | 57.157 |
| Paired | 17.091 | 62.037 | 0.657 | 37.306 | 62.365 |
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, 45.37% for 76s. Here the change is -2.10 and -4.04 points.
| Case | Equity here | Against a random hand | Change in points | Times the random-hand equity |
|---|---|---|---|---|
| A9o, all flops | 58.666 | 60.773 | -2.107 | 0.96533 |
| A9o, rainbow, ten or higher | 63.607 | 60.773 | +2.834 | 1.04663 |
| A9o, rainbow, nine or lower | 41.472 | 60.773 | -19.301 | 0.68241 |
| A9o, two-tone | 56.893 | 60.773 | -3.880 | 0.93616 |
| A9o, monotone | 57.157 | 60.773 | -3.616 | 0.94050 |
| A9o, paired | 62.365 | 60.773 | +1.592 | 1.02620 |
| 76s, all flops | 41.334 | 45.372 | -4.038 | 0.91100 |
| 76s, rainbow, ten or higher | 36.393 | 45.372 | -8.979 | 0.80210 |
| 76s, rainbow, nine or lower | 58.528 | 45.372 | +13.156 | 1.28996 |
| 76s, two-tone | 43.107 | 45.372 | -2.265 | 0.95008 |
| 76s, monotone | 42.843 | 45.372 | -2.529 | 0.94426 |
| 76s, paired | 37.635 | 45.372 | -7.737 | 0.82948 |
Does a shared suit matter?
Suit overlap shows up in the numbers. With a suit in common A9o has 59.32% equity, and with none in common it has 58.01%. A9o does better with a shared suit, by 1.31 points.
| Deals | Specific deals | Share of deals | A9o wins | Ties | 76s wins | A9o equity |
|---|---|---|---|---|---|---|
| Share a suit | 24 | 50.00 | 59.094 | 0.456 | 40.450 | 59.322 |
| No shared suit | 24 | 50.00 | 57.822 | 0.375 | 41.803 | 58.010 |
How often this matchup comes up
The class pair covers 48 combinations of specific cards in a fixed seat order, 0.0030% of 1,624,350, and 96 (0.0059%) in either order.
A worked example
Try it with money: two players each put in $100 and the whole board runs out every possible way. A9o averages $117.34 from the $200, up $17.34; 76s averages $82.66, down $17.34.
A thousand deals look like this: A9o takes 585, 76s takes 411, 4 are ties.
The same matchup from the other side
If you came looking for 76s against A9o, the numbers are the same with the hands swapped: 41.33% and 58.67%.
Keep exploring
Open the calculator with As9h against 7d6d 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
All 1,712,304 five-card boards are dealt for every suit pattern among the 48 specific deals of A9o against 76s, and both hands are scored on each. That is a full count, so the percentages are exact. Ties are half a win each, and each board appears once per flop it contains.
Source: our own exact count from the GeorgeLiPoker poker math library. No outside data is used.
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