A2s
56.20%
Wins 55.92%, ties 0.56%
75s
43.80%
Wins 43.52%, ties 0.56%
A2s against 75s: the numbers
| Hand | Wins | Ties | Loses | Equity |
|---|---|---|---|---|
| A2s | 55.916 | 0.563 | 43.521 | 56.198 |
| 75s | 43.521 | 0.563 | 55.916 | 43.802 |
Each side holds one of the suited hands: A2s and 75s. With no overlap in ranks, every card that pairs one hand is a card that does not pair the other.
A2s is ahead, but 75s is far from dead: it takes 435 of every 1,000 deals outright. Ties are 0.56% of the outcomes here; each tied board gives both hands half the pot.
By strength against a random hand, A2s holds place 46 of 169 and 75s holds place 124.
| Hand | Boards won, about | Boards tied, about | Boards lost, about |
|---|---|---|---|
| A2s | 15,319,000 | 154,000 | 11,923,000 |
| 75s | 11,923,000 | 154,000 | 15,319,000 |
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) |
|---|---|---|---|---|
| A2s | 1.283 | 1.788 | 2.298 | 0.779 |
| 75s | 0.779 | 2.298 | 1.788 | 1.283 |
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. A2s does best on paired flops, at 62.32%, and worst on low rainbow flops (nine high or lower), at 33.80%. 75s takes over on low rainbow flops (nine high or lower), so the favorite before the flop is the underdog on those boards.
| Flop | Share of flops | A2s wins | Ties | 75s wins | A2s equity |
|---|---|---|---|---|---|
| Rainbow, ten or higher | 25.220 | 59.868 | 0.258 | 39.874 | 59.997 |
| Rainbow, nine or lower | 5.689 | 33.398 | 0.808 | 65.794 | 33.802 |
| Two-tone | 46.727 | 54.731 | 0.323 | 44.946 | 54.892 |
| Monotone | 5.273 | 52.172 | 3.481 | 44.347 | 53.913 |
| Paired | 17.091 | 61.974 | 0.690 | 37.336 | 62.319 |
A rainbow flop shows three suits, a two-tone flop repeats one suit, a monotone flop is a single suit, and a paired flop repeats a rank.
Compared with a random hand
Start from the random-hand figures, 57.38% for A2s and 43.68% for 75s. This opponent changes them by -1.18 and +0.12 points.
| Case | Equity here | Against a random hand | Change in points | Times the random-hand equity |
|---|---|---|---|---|
| A2s, all flops | 56.198 | 57.379 | -1.181 | 0.97942 |
| A2s, rainbow, ten or higher | 59.997 | 57.379 | +2.618 | 1.04563 |
| A2s, rainbow, nine or lower | 33.802 | 57.379 | -23.577 | 0.58910 |
| A2s, two-tone | 54.892 | 57.379 | -2.487 | 0.95666 |
| A2s, monotone | 53.913 | 57.379 | -3.466 | 0.93959 |
| A2s, paired | 62.319 | 57.379 | +4.940 | 1.08609 |
| 75s, all flops | 43.802 | 43.676 | +0.126 | 1.00288 |
| 75s, rainbow, ten or higher | 40.003 | 43.676 | -3.673 | 0.91590 |
| 75s, rainbow, nine or lower | 66.198 | 43.676 | +22.522 | 1.51566 |
| 75s, two-tone | 45.108 | 43.676 | +1.432 | 1.03279 |
| 75s, monotone | 46.087 | 43.676 | +2.411 | 1.05520 |
| 75s, paired | 37.681 | 43.676 | -5.995 | 0.86274 |
Does a shared suit matter?
Looking only at deals where the hands share a suit, A2s has 57.94%; looking only at deals where they do not, 55.62%. A2s does better with a shared suit, by 2.32 points.
| Deals | Specific deals | Share of deals | A2s wins | Ties | 75s wins | A2s equity |
|---|---|---|---|---|---|---|
| Share a suit | 4 | 25.00 | 57.611 | 0.648 | 41.741 | 57.935 |
| No shared suit | 12 | 75.00 | 55.351 | 0.535 | 44.114 | 55.618 |
How often this matchup comes up
Counting specific cards, A2s against 75s appears in 16 of the 1,624,350 ordered heads-up deals (0.0010%), and in 32 when the seats are swapped too (0.0020%).
A worked example
A $100 all-in from each player makes a $200 pot, and the exact equity says A2s gets $112.40 of it on average and 75s gets $87.60.
Out of 1,000 deals you should see around 559 outright wins for A2s, 435 for 75s, and 6 split pots.
The same matchup from the other side
Read it from the other side: 75s against A2s is the same matchup with the numbers swapped, so 75s holds 43.80% and A2s holds 56.20%. That address sends you back to this page.
Keep exploring
As2s against 7h5h 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
The figures are counted, not estimated: 1,712,304 boards for every suit pattern of the 16 specific deals, with both seven-card hands compared each time. Equity gives half a win for a tie. For the flop rows, a board is counted once under each of the ten flops inside it.
Source: our own exact count from the GeorgeLiPoker poker math library. No outside data is used.
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