AQo
59.12%
Wins 58.91%, ties 0.42%
87s
40.88%
Wins 40.67%, ties 0.42%
AQo against 87s: the numbers
| Hand | Wins | Ties | Loses | Equity |
|---|---|---|---|---|
| AQo | 58.907 | 0.418 | 40.675 | 59.116 |
| 87s | 40.675 | 0.418 | 58.907 | 40.884 |
One side is an offsuit hand, the other is a suited hand. With no overlap in ranks, every card that pairs one hand is a card that does not pair the other.
That is a modest edge, the kind that shows up over many hands and is easy to miss in one. The tie share is 0.42%: on those boards the pot is chopped and neither hand wins outright.
Ranked by equity against a random hand, AQo is number 14 of the 169 starting hands and 87s is number 100.
| Hand | Boards won, about | Boards tied, about | Boards lost, about |
|---|---|---|---|
| AQo | 48,416,000 | 344,000 | 33,431,000 |
| 87s | 33,431,000 | 344,000 | 48,416,000 |
The total is exact: 48 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) |
|---|---|---|---|---|
| AQo | 1.446 | 1.698 | 2.459 | 0.692 |
| 87s | 0.692 | 2.459 | 1.698 | 1.446 |
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
Break the boards down by their first three cards and AQo is strongest on rainbow flops topped by a ten or better (66.66%) and weakest on low rainbow flops (nine high or lower) (35.11%). Watch for low rainbow flops (nine high or lower): on those flops 87s holds the better equity.
| Flop | Share of flops | AQo wins | Ties | 87s wins | AQo equity |
|---|---|---|---|---|---|
| Rainbow, ten or higher | 24.717 | 66.574 | 0.168 | 33.258 | 66.658 |
| Rainbow, nine or lower | 6.313 | 34.825 | 0.559 | 64.616 | 35.105 |
| Two-tone | 46.667 | 57.394 | 0.235 | 42.371 | 57.512 |
| Monotone | 5.212 | 56.441 | 2.357 | 41.202 | 57.620 |
| Paired | 17.091 | 61.597 | 0.637 | 37.766 | 61.916 |
Flop types: rainbow means three different suits, two-tone means one suit twice, monotone means one suit three times, paired means a repeated rank.
Compared with a random hand
Relative to a random opponent, AQo changes by -5.31 points (baseline 64.43%) and 87s by -7.06 points (baseline 47.94%).
| Case | Equity here | Against a random hand | Change in points | Times the random-hand equity |
|---|---|---|---|---|
| AQo, all flops | 59.116 | 64.432 | -5.316 | 0.91749 |
| AQo, rainbow, ten or higher | 66.658 | 64.432 | +2.226 | 1.03455 |
| AQo, rainbow, nine or lower | 35.105 | 64.432 | -29.327 | 0.54484 |
| AQo, two-tone | 57.512 | 64.432 | -6.920 | 0.89260 |
| AQo, monotone | 57.620 | 64.432 | -6.812 | 0.89428 |
| AQo, paired | 61.916 | 64.432 | -2.516 | 0.96095 |
| 87s, all flops | 40.884 | 47.936 | -7.052 | 0.85289 |
| 87s, rainbow, ten or higher | 33.342 | 47.936 | -14.594 | 0.69555 |
| 87s, rainbow, nine or lower | 64.895 | 47.936 | +16.959 | 1.35378 |
| 87s, two-tone | 42.488 | 47.936 | -5.448 | 0.88635 |
| 87s, monotone | 42.380 | 47.936 | -5.556 | 0.88410 |
| 87s, paired | 38.084 | 47.936 | -9.852 | 0.79448 |
Does a shared suit matter?
The suit split reads 59.81% for AQo with a shared suit and 58.42% without one. AQo does better with a shared suit, by 1.39 points.
| Deals | Specific deals | Share of deals | AQo wins | Ties | 87s wins | AQo equity |
|---|---|---|---|---|---|---|
| Share a suit | 24 | 50.00 | 59.579 | 0.459 | 39.962 | 59.808 |
| No shared suit | 24 | 50.00 | 58.235 | 0.377 | 41.388 | 58.424 |
How often this matchup comes up
How often does it happen? 48 of the 1,624,350 ordered deals (0.0030%) are AQo against 87s, and 96 (0.0059%) if either hand may sit in either seat.
A worked example
A $100 all-in from each player makes a $200 pot, and the exact equity says AQo gets $118.24 of it on average and 87s gets $81.76.
Scaled to 1,000 deals, that is roughly 589 wins for AQo, 407 for 87s and 4 chopped pots.
The same matchup from the other side
The mirror image, 87s against AQo, is 40.88% to 59.12%, and its address redirects to this page.
Keep exploring
AsQh against 8d7d is a ready-made deal for the calculator, with no suit in common between the hands. The neighboring matchups below replace one hand with another of similar strength.
How this was computed
Nothing here is simulated. The 48 deals of AQo against 87s fall into a few suit patterns, each dealt against all 1,712,304 boards, with both best five-card hands compared on every board. Ties give each hand half a win, and the flop rows count a board under each of its ten flops.
Source: our own exact count from the GeorgeLiPoker poker math library. No outside data is used.
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