A4s
57.57%
Wins 57.30%, ties 0.55%
75s
42.43%
Wins 42.15%, ties 0.55%
A4s against 75s: the numbers
| Hand | Wins | Ties | Loses | Equity |
|---|---|---|---|---|
| A4s | 57.298 | 0.550 | 42.152 | 57.573 |
| 75s | 42.152 | 0.550 | 57.298 | 42.427 |
Two suited hands meet here: A4s against 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. 0.55% of boards are ties, so the equity of each hand is its win rate plus half of that.
By strength against a random hand, A4s holds place 35 of 169 and 75s holds place 124.
| Hand | Boards won, about | Boards tied, about | Boards lost, about |
|---|---|---|---|
| A4s | 15,698,000 | 151,000 | 11,548,000 |
| 75s | 11,548,000 | 151,000 | 15,698,000 |
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) |
|---|---|---|---|---|
| A4s | 1.357 | 1.745 | 2.372 | 0.737 |
| 75s | 0.737 | 2.372 | 1.745 | 1.357 |
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
The flop changes the picture. A4s does best on paired flops, at 63.14%, and worst on low rainbow flops (nine high or lower), at 37.94%. 75s is ahead on low rainbow flops (nine high or lower), even though it trails A4s when every flop is counted.
| Flop | Share of flops | A4s wins | Ties | 75s wins | A4s equity |
|---|---|---|---|---|---|
| Rainbow, ten or higher | 25.220 | 60.976 | 0.258 | 38.766 | 61.105 |
| Rainbow, nine or lower | 5.689 | 37.583 | 0.713 | 61.704 | 37.940 |
| Two-tone | 46.727 | 56.167 | 0.309 | 43.524 | 56.321 |
| Monotone | 5.273 | 53.156 | 3.472 | 43.372 | 54.892 |
| Paired | 17.091 | 62.803 | 0.682 | 36.515 | 63.144 |
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, A4s changes by -1.46 points (baseline 59.03%) and 75s by -1.25 points (baseline 43.68%).
| Case | Equity here | Against a random hand | Change in points | Times the random-hand equity |
|---|---|---|---|---|
| A4s, all flops | 57.573 | 59.034 | -1.461 | 0.97525 |
| A4s, rainbow, ten or higher | 61.105 | 59.034 | +2.071 | 1.03508 |
| A4s, rainbow, nine or lower | 37.940 | 59.034 | -21.094 | 0.64268 |
| A4s, two-tone | 56.321 | 59.034 | -2.713 | 0.95404 |
| A4s, monotone | 54.892 | 59.034 | -4.142 | 0.92984 |
| A4s, paired | 63.144 | 59.034 | +4.110 | 1.06962 |
| 75s, all flops | 42.427 | 43.676 | -1.249 | 0.97140 |
| 75s, rainbow, ten or higher | 38.895 | 43.676 | -4.781 | 0.89053 |
| 75s, rainbow, nine or lower | 62.060 | 43.676 | +18.384 | 1.42092 |
| 75s, two-tone | 43.679 | 43.676 | +0.003 | 1.00007 |
| 75s, monotone | 45.108 | 43.676 | +1.432 | 1.03279 |
| 75s, paired | 36.856 | 43.676 | -6.820 | 0.84385 |
Does a shared suit matter?
Split by suits, the deals give A4s 59.51% when the hands overlap in a suit and 56.93% when they do not. A4s does better with a shared suit, by 2.58 points.
| Deals | Specific deals | Share of deals | A4s wins | Ties | 75s wins | A4s equity |
|---|---|---|---|---|---|---|
| Share a suit | 4 | 25.00 | 59.192 | 0.631 | 40.177 | 59.508 |
| No shared suit | 12 | 75.00 | 56.666 | 0.523 | 42.811 | 56.927 |
How often this matchup comes up
The class pair covers 16 combinations of specific cards in a fixed seat order, 0.0010% of 1,624,350, and 32 (0.0020%) in either order.
A worked example
Say each player puts $100 in before the flop, making a $200 pot. On average A4s takes back $115.14 of it, which is $15.14 more than it put in, and 75s takes back $84.86, $15.14 less than it put in.
Per 1,000 deals: A4s wins about 573, 75s wins about 422, and about 5 end in a split pot.
The same matchup from the other side
The reversed view, 75s against A4s, shows 42.43% for 75s and 57.57% for A4s. It is the same count, so it redirects here.
Keep exploring
As4s 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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