A9o
58.85%
Wins 58.65%, ties 0.41%
87s
41.15%
Wins 40.94%, ties 0.41%
A9o against 87s: the numbers
| Hand | Wins | Ties | Loses | Equity |
|---|---|---|---|---|
| A9o | 58.651 | 0.406 | 40.943 | 58.854 |
| 87s | 40.943 | 0.406 | 58.651 | 41.146 |
A9o, an offsuit hand, plays 87s, a suited hand. The two hands share no rank, which makes this a pure matchup of card strength, straight chances and flush chances.
That is a modest edge, the kind that shows up over many hands and is easy to miss in one. Of every 100 boards, about 0.41 are split pots, and the equity figures already include them.
By strength against a random hand, A9o holds place 25 of 169 and 87s holds place 100.
| Hand | Boards won, about | Boards tied, about | Boards lost, about |
|---|---|---|---|
| A9o | 48,206,000 | 334,000 | 33,651,000 |
| 87s | 33,651,000 | 334,000 | 48,206,000 |
Exact total: 48 deals times 1,712,304 boards. The other three counts come from the five-decimal percentages and are rounded to the nearest thousand, so read them as approximate.
| Hand | Equity as odds (to 1) | Wins one deal in | Loses one deal in | Pot odds needed to call (to 1) |
|---|---|---|---|---|
| A9o | 1.430 | 1.705 | 2.442 | 0.699 |
| 87s | 0.699 | 2.442 | 1.705 | 1.430 |
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
Across the five flop textures A9o's equity moves by 17.82 points, from 45.21% on low rainbow flops (nine high or lower) to 63.03% on rainbow flops topped by a ten or better. A9o is the favorite overall but falls behind on low rainbow flops (nine high or lower).
| Flop | Share of flops | A9o wins | Ties | 87s wins | A9o equity |
|---|---|---|---|---|---|
| Rainbow, ten or higher | 25.341 | 62.925 | 0.204 | 36.871 | 63.027 |
| Rainbow, nine or lower | 5.689 | 45.037 | 0.348 | 54.615 | 45.211 |
| Two-tone | 46.667 | 56.984 | 0.218 | 42.798 | 57.093 |
| Monotone | 5.212 | 56.108 | 2.343 | 41.549 | 57.279 |
| Paired | 17.091 | 62.172 | 0.649 | 37.179 | 62.496 |
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
Relative to a random opponent, A9o changes by -1.92 points (baseline 60.77%) and 87s by -6.79 points (baseline 47.94%).
| Case | Equity here | Against a random hand | Change in points | Times the random-hand equity |
|---|---|---|---|---|
| A9o, all flops | 58.854 | 60.773 | -1.919 | 0.96842 |
| A9o, rainbow, ten or higher | 63.027 | 60.773 | +2.254 | 1.03709 |
| A9o, rainbow, nine or lower | 45.211 | 60.773 | -15.562 | 0.74393 |
| A9o, two-tone | 57.093 | 60.773 | -3.680 | 0.93945 |
| A9o, monotone | 57.279 | 60.773 | -3.494 | 0.94251 |
| A9o, paired | 62.496 | 60.773 | +1.723 | 1.02835 |
| 87s, all flops | 41.146 | 47.936 | -6.790 | 0.85835 |
| 87s, rainbow, ten or higher | 36.973 | 47.936 | -10.963 | 0.77130 |
| 87s, rainbow, nine or lower | 54.789 | 47.936 | +6.853 | 1.14296 |
| 87s, two-tone | 42.907 | 47.936 | -5.029 | 0.89509 |
| 87s, monotone | 42.721 | 47.936 | -5.215 | 0.89121 |
| 87s, paired | 37.504 | 47.936 | -10.432 | 0.78238 |
Does a shared suit matter?
Two kinds of deal exist here. In 24 of them the hands share a suit and A9o holds 59.50%. In 24 they do not, and it holds 58.21%. A9o does better with a shared suit, by 1.29 points.
| Deals | Specific deals | Share of deals | A9o wins | Ties | 87s wins | A9o equity |
|---|---|---|---|---|---|---|
| Share a suit | 24 | 50.00 | 59.274 | 0.447 | 40.279 | 59.497 |
| No shared suit | 24 | 50.00 | 58.028 | 0.365 | 41.607 | 58.211 |
How often this matchup comes up
Exactly 48 specific deals fit this matchup in one seat order, which is 0.0030% of 1,624,350; both orders together give 96, or 0.0059%.
A worked example
Try it with money: two players each put in $100 and the whole board runs out every possible way. A9o averages $117.70 from the $200, up $17.70; 87s averages $82.30, down $17.70.
In 1,000 deals of exactly this matchup, expect about 587 won outright by A9o, about 409 won outright by 87s and about 4 split.
The same matchup from the other side
If you came looking for 87s against A9o, the numbers are the same with the hands swapped: 41.15% and 58.85%.
Keep exploring
Open the calculator with As9h against 8d7d 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 48 ways to deal one A9o and one 87s 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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