A3s
56.99%
Wins 56.71%, ties 0.56%
75s
43.01%
Wins 42.73%, ties 0.56%
A3s against 75s: the numbers
| Hand | Wins | Ties | Loses | Equity |
|---|---|---|---|---|
| A3s | 56.711 | 0.557 | 42.732 | 56.989 |
| 75s | 42.732 | 0.557 | 56.711 | 43.011 |
Each side holds one of the suited hands: A3s and 75s. 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. Split pots make up 0.56% of the boards, and both equity figures count them as half a win each.
In the ranking of all 169 starting hands, A3s is number 38 and 75s is number 124.
| Hand | Boards won, about | Boards tied, about | Boards lost, about |
|---|---|---|---|
| A3s | 15,537,000 | 153,000 | 11,707,000 |
| 75s | 11,707,000 | 153,000 | 15,537,000 |
The board total is exact, 16 deals at 1,712,304 boards each. Won, tied and lost counts are rounded to the nearest thousand from the five-decimal percentages.
| Hand | Equity as odds (to 1) | Wins one deal in | Loses one deal in | Pot odds needed to call (to 1) |
|---|---|---|---|---|
| A3s | 1.325 | 1.763 | 2.340 | 0.755 |
| 75s | 0.755 | 2.340 | 1.763 | 1.325 |
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
A3s prefers paired flops, where it holds 62.78%, and likes low rainbow flops (nine high or lower) least, where it holds 36.23%. 75s is ahead on low rainbow flops (nine high or lower), even though it trails A3s when every flop is counted.
| Flop | Share of flops | A3s wins | Ties | 75s wins | A3s equity |
|---|---|---|---|---|---|
| Rainbow, ten or higher | 25.220 | 60.497 | 0.258 | 39.245 | 60.626 |
| Rainbow, nine or lower | 5.689 | 35.846 | 0.761 | 63.393 | 36.227 |
| Two-tone | 46.727 | 55.561 | 0.316 | 44.123 | 55.719 |
| Monotone | 5.273 | 52.748 | 3.477 | 43.775 | 54.487 |
| Paired | 17.091 | 62.437 | 0.686 | 36.877 | 62.780 |
Rainbow flops have three suits, two-tone flops repeat one suit, monotone flops are all one suit, and paired flops repeat a rank.
Compared with a random hand
Relative to a random opponent, A3s changes by -1.23 points (baseline 58.22%) and 75s by -0.67 points (baseline 43.68%).
| Case | Equity here | Against a random hand | Change in points | Times the random-hand equity |
|---|---|---|---|---|
| A3s, all flops | 56.989 | 58.220 | -1.231 | 0.97886 |
| A3s, rainbow, ten or higher | 60.626 | 58.220 | +2.406 | 1.04133 |
| A3s, rainbow, nine or lower | 36.227 | 58.220 | -21.993 | 0.62224 |
| A3s, two-tone | 55.719 | 58.220 | -2.501 | 0.95704 |
| A3s, monotone | 54.487 | 58.220 | -3.733 | 0.93588 |
| A3s, paired | 62.780 | 58.220 | +4.560 | 1.07832 |
| 75s, all flops | 43.011 | 43.676 | -0.665 | 0.98477 |
| 75s, rainbow, ten or higher | 39.374 | 43.676 | -4.302 | 0.90150 |
| 75s, rainbow, nine or lower | 63.773 | 43.676 | +20.097 | 1.46014 |
| 75s, two-tone | 44.281 | 43.676 | +0.605 | 1.01385 |
| 75s, monotone | 45.513 | 43.676 | +1.837 | 1.04206 |
| 75s, paired | 37.220 | 43.676 | -6.456 | 0.85218 |
Does a shared suit matter?
Of the deals of this matchup, 4 share a suit (A3s at 58.84%) and 12 do not (56.37%). A3s does better with a shared suit, by 2.47 points.
| Deals | Specific deals | Share of deals | A3s wins | Ties | 75s wins | A3s equity |
|---|---|---|---|---|---|---|
| Share a suit | 4 | 25.00 | 58.516 | 0.640 | 40.844 | 58.836 |
| No shared suit | 12 | 75.00 | 56.109 | 0.529 | 43.362 | 56.374 |
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
With $100 from each side, the $200 pot is split on average as $113.98 for A3s and $86.02 for 75s; the first side gains $13.98 per all-in and the second gives up $13.98.
Scaled to 1,000 deals, that is roughly 567 wins for A3s, 427 for 75s and 6 chopped pots.
The same matchup from the other side
75s against A3s adds nothing new: it is 43.01% for 75s and 56.99% for A3s, the same figures reversed.
Keep exploring
As3s 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 A3s 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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