A3s
54.40%
Wins 54.14%, ties 0.51%
87s
45.60%
Wins 45.35%, ties 0.51%
A3s against 87s: the numbers
| Hand | Wins | Ties | Loses | Equity |
|---|---|---|---|---|
| A3s | 54.140 | 0.509 | 45.351 | 54.395 |
| 87s | 45.351 | 0.509 | 54.140 | 45.605 |
A3s and 87s are both suited hands. Neither hand shares a rank with the other, so this is a contest of high cards, connection and suits.
A3s leads by less than 9 points of equity, so the result of any one deal is close to a toss-up. A split pot comes up on 0.51% of boards, so the wins and the equity differ by half of that.
For context, A3s sits at number 38 of 169 starting hands and 87s at number 100 when each is run against a random hand.
| Hand | Boards won, about | Boards tied, about | Boards lost, about |
|---|---|---|---|
| A3s | 14,833,000 | 139,000 | 12,425,000 |
| 87s | 12,425,000 | 139,000 | 14,833,000 |
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) |
|---|---|---|---|---|
| A3s | 1.193 | 1.847 | 2.205 | 0.838 |
| 87s | 0.838 | 2.205 | 1.847 | 1.193 |
The final column gives the least the pot must offer for each unit called for a call to break even at this equity.
Who is ahead on which flops
Paired flops are the best for A3s (60.64%); low rainbow flops (nine high or lower) are the worst (34.51%). A3s is the favorite overall but falls behind on low rainbow flops (nine high or lower).
| Flop | Share of flops | A3s wins | Ties | 87s wins | A3s equity |
|---|---|---|---|---|---|
| Rainbow, ten or higher | 25.220 | 57.285 | 0.221 | 42.494 | 57.395 |
| Rainbow, nine or lower | 5.689 | 34.216 | 0.586 | 65.198 | 34.509 |
| Two-tone | 46.727 | 52.986 | 0.265 | 46.749 | 53.118 |
| Monotone | 5.273 | 50.843 | 3.431 | 45.726 | 52.558 |
| Paired | 17.091 | 60.305 | 0.674 | 39.021 | 60.642 |
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
Compared with a random opponent, this matchup shifts A3s from 58.22% by -3.82 points and 87s from 47.94% by -2.34 points.
| Case | Equity here | Against a random hand | Change in points | Times the random-hand equity |
|---|---|---|---|---|
| A3s, all flops | 54.395 | 58.220 | -3.825 | 0.93430 |
| A3s, rainbow, ten or higher | 57.395 | 58.220 | -0.825 | 0.98583 |
| A3s, rainbow, nine or lower | 34.509 | 58.220 | -23.711 | 0.59273 |
| A3s, two-tone | 53.118 | 58.220 | -5.102 | 0.91237 |
| A3s, monotone | 52.558 | 58.220 | -5.662 | 0.90275 |
| A3s, paired | 60.642 | 58.220 | +2.422 | 1.04160 |
| 87s, all flops | 45.605 | 47.936 | -2.331 | 0.95137 |
| 87s, rainbow, ten or higher | 42.605 | 47.936 | -5.331 | 0.88879 |
| 87s, rainbow, nine or lower | 65.491 | 47.936 | +17.555 | 1.36622 |
| 87s, two-tone | 46.882 | 47.936 | -1.054 | 0.97801 |
| 87s, monotone | 47.442 | 47.936 | -0.494 | 0.98969 |
| 87s, paired | 39.358 | 47.936 | -8.578 | 0.82105 |
Does a shared suit matter?
Does suit overlap move the numbers? A3s has 55.93% when the hands share a suit and 53.88% when they do not. A3s does better with a shared suit, by 2.05 points.
| Deals | Specific deals | Share of deals | A3s wins | Ties | 87s wins | A3s equity |
|---|---|---|---|---|---|---|
| Share a suit | 4 | 25.00 | 55.639 | 0.590 | 43.771 | 55.934 |
| No shared suit | 12 | 75.00 | 53.641 | 0.481 | 45.878 | 53.882 |
How often this matchup comes up
How often does it happen? 16 of the 1,624,350 ordered deals (0.0010%) are A3s against 87s, and 32 (0.0020%) if either hand may sit in either seat.
A worked example
To see what the equity is worth, imagine $100 each in a $200 pot. A3s is worth $108.80 on average (+$8.80); 87s is worth $91.20 (-$8.80).
Scaled to 1,000 deals, that is roughly 541 wins for A3s, 454 for 87s and 5 chopped pots.
The same matchup from the other side
If you came looking for 87s against A3s, the numbers are the same with the hands swapped: 45.60% and 54.40%.
Keep exploring
Open the calculator with As3s against 8h7h 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 page is built from a full enumeration: 1,712,304 boards, every suit pattern of the 16 specific deals, both seven-card hands evaluated. A tie is worth half a win to each hand, and a board is tallied under each of its ten possible flops for the texture rows.
Source: our own exact count from the GeorgeLiPoker poker math library. No outside data is used.
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