A9s
62.51%
Wins 62.26%, ties 0.50%
75s
37.49%
Wins 37.24%, ties 0.50%
A9s against 75s: the numbers
| Hand | Wins | Ties | Loses | Equity |
|---|---|---|---|---|
| A9s | 62.262 | 0.503 | 37.235 | 62.514 |
| 75s | 37.235 | 0.503 | 62.262 | 37.486 |
Both hands are suited hands: A9s and 75s. 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. Ties are 0.50% of the outcomes here; each tied board gives both hands half the pot.
In the ranking of all 169 starting hands, A9s is number 18 and 75s is number 124.
| Hand | Boards won, about | Boards tied, about | Boards lost, about |
|---|---|---|---|
| A9s | 17,058,000 | 138,000 | 10,201,000 |
| 75s | 10,201,000 | 138,000 | 17,058,000 |
Exact total: 16 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) |
|---|---|---|---|---|
| A9s | 1.668 | 1.606 | 2.686 | 0.600 |
| 75s | 0.600 | 2.686 | 1.606 | 1.668 |
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
Rainbow flops topped by a ten or better are the best for A9s (66.40%); low rainbow flops (nine high or lower) are the worst (45.87%). Watch for low rainbow flops (nine high or lower): on those flops 75s holds the better equity.
| Flop | Share of flops | A9s wins | Ties | 75s wins | A9s equity |
|---|---|---|---|---|---|
| Rainbow, ten or higher | 25.220 | 66.284 | 0.225 | 33.491 | 66.396 |
| Rainbow, nine or lower | 5.689 | 45.600 | 0.547 | 53.853 | 45.873 |
| Two-tone | 46.727 | 61.594 | 0.259 | 38.147 | 61.723 |
| Monotone | 5.273 | 57.912 | 3.436 | 38.652 | 59.630 |
| Paired | 17.091 | 65.045 | 0.661 | 34.294 | 65.376 |
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
The table below sets each hand against its own random-hand baseline: a change of -0.27 points for A9s, from 62.78%, and -6.19 for 75s, from 43.68%.
| Case | Equity here | Against a random hand | Change in points | Times the random-hand equity |
|---|---|---|---|---|
| A9s, all flops | 62.514 | 62.781 | -0.267 | 0.99575 |
| A9s, rainbow, ten or higher | 66.396 | 62.781 | +3.615 | 1.05758 |
| A9s, rainbow, nine or lower | 45.873 | 62.781 | -16.908 | 0.73068 |
| A9s, two-tone | 61.723 | 62.781 | -1.058 | 0.98315 |
| A9s, monotone | 59.630 | 62.781 | -3.151 | 0.94981 |
| A9s, paired | 65.376 | 62.781 | +2.595 | 1.04133 |
| 75s, all flops | 37.486 | 43.676 | -6.190 | 0.85827 |
| 75s, rainbow, ten or higher | 33.604 | 43.676 | -10.072 | 0.76939 |
| 75s, rainbow, nine or lower | 54.127 | 43.676 | +10.451 | 1.23928 |
| 75s, two-tone | 38.277 | 43.676 | -5.399 | 0.87639 |
| 75s, monotone | 40.370 | 43.676 | -3.306 | 0.92431 |
| 75s, paired | 34.624 | 43.676 | -9.052 | 0.79275 |
Does a shared suit matter?
Looking only at deals where the hands share a suit, A9s has 64.81%; looking only at deals where they do not, 61.75%. A9s does better with a shared suit, by 3.06 points.
| Deals | Specific deals | Share of deals | A9s wins | Ties | 75s wins | A9s equity |
|---|---|---|---|---|---|---|
| Share a suit | 4 | 25.00 | 64.517 | 0.580 | 34.903 | 64.807 |
| No shared suit | 12 | 75.00 | 61.511 | 0.477 | 38.012 | 61.749 |
How often this matchup comes up
Exactly 16 specific deals fit this matchup in one seat order, which is 0.0010% of 1,624,350; both orders together give 32, or 0.0020%.
A worked example
Put $100 each into a $200 pot and deal every board once: A9s averages $125.02 back, ahead of its $100 by $25.02, while 75s averages $74.98, short of its $100 by $25.02.
Over a long run, 1,000 deals split into about 623 for A9s, 372 for 75s and 5 tied.
The same matchup from the other side
Swap the hands and you get 75s with 37.49% against A9s with 62.51%. We keep one page per matchup, with the better-ranked hand first.
Keep exploring
As9s 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
All 1,712,304 five-card boards are dealt for every suit pattern among the 16 specific deals of A9s against 75s, 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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