A7s
60.32%
Wins 47.76%, ties 25.11%
A4s
39.68%
Wins 27.13%, ties 25.11%
A7s against A4s: the numbers
| Hand | Wins | Ties | Loses | Equity |
|---|---|---|---|---|
| A7s | 47.763 | 25.105 | 27.132 | 60.315 |
| A4s | 27.132 | 25.105 | 47.763 | 39.685 |
Each side holds one of the suited hands: A7s and A4s. Because the hands share one rank, the one with the higher kicker is ahead when that rank pairs and the other hand is mostly drawing.
That is a modest edge, the kind that shows up over many hands and is easy to miss in one. Split pots make up 25.11% of the boards, and both equity figures count them as half a win each.
Among the 169 starting hands, A7s is number 24 and A4s is number 35 by strength against a random hand.
| Hand | Boards won, about | Boards tied, about | Boards lost, about |
|---|---|---|---|
| A7s | 9,814,000 | 5,158,000 | 5,575,000 |
| A4s | 5,575,000 | 5,158,000 | 9,814,000 |
Exact total: 12 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) |
|---|---|---|---|---|
| A7s | 1.520 | 2.094 | 3.686 | 0.658 |
| A4s | 0.658 | 3.686 | 2.094 | 1.520 |
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
The flop changes the picture. A7s does best on low rainbow flops (nine high or lower), at 62.52%, and worst on paired flops, at 56.18%. A7s stays ahead on all five textures.
| Flop | Share of flops | A7s wins | Ties | A4s wins | A7s equity |
|---|---|---|---|---|---|
| Rainbow, ten or higher | 24.526 | 48.786 | 27.101 | 24.113 | 62.337 |
| Rainbow, nine or lower | 6.383 | 57.798 | 9.444 | 32.758 | 62.520 |
| Two-tone | 46.543 | 50.413 | 20.716 | 28.871 | 60.771 |
| Monotone | 5.215 | 48.966 | 17.665 | 33.369 | 57.799 |
| Paired | 17.333 | 35.143 | 42.070 | 22.787 | 56.178 |
Read the flop types this way: rainbow has three suits, two-tone has two cards of one suit, monotone has three, and paired repeats a rank.
Compared with a random hand
Against one random hand instead, A7s holds 60.98% and A4s holds 59.03%. Facing each other changes that by -0.66 points for A7s and -19.35 points for A4s.
| Case | Equity here | Against a random hand | Change in points | Times the random-hand equity |
|---|---|---|---|---|
| A7s, all flops | 60.315 | 60.984 | -0.669 | 0.98903 |
| A7s, rainbow, ten or higher | 62.337 | 60.984 | +1.353 | 1.02219 |
| A7s, rainbow, nine or lower | 62.520 | 60.984 | +1.536 | 1.02519 |
| A7s, two-tone | 60.771 | 60.984 | -0.213 | 0.99651 |
| A7s, monotone | 57.799 | 60.984 | -3.185 | 0.94777 |
| A7s, paired | 56.178 | 60.984 | -4.806 | 0.92119 |
| A4s, all flops | 39.685 | 59.034 | -19.349 | 0.67224 |
| A4s, rainbow, ten or higher | 37.663 | 59.034 | -21.371 | 0.63799 |
| A4s, rainbow, nine or lower | 37.480 | 59.034 | -21.554 | 0.63489 |
| A4s, two-tone | 39.229 | 59.034 | -19.805 | 0.66452 |
| A4s, monotone | 42.201 | 59.034 | -16.833 | 0.71486 |
| A4s, paired | 43.822 | 59.034 | -15.212 | 0.74232 |
Does a shared suit matter?
The hands cannot hold a suit in common here, which leaves a single case and a single number: 60.32% for A7s.
| Deals | Specific deals | Share of deals | A7s wins | Ties | A4s wins | A7s equity |
|---|---|---|---|---|---|---|
| Share a suit | 0 | 0.00 | not possible | not possible | not possible | not possible |
| No shared suit | 12 | 100.00 | 47.763 | 25.105 | 27.132 | 60.315 |
How often this matchup comes up
How often does it happen? 12 of the 1,624,350 ordered deals (0.0007%) are A7s against A4s, and 24 (0.0015%) if either hand may sit in either seat.
A worked example
Take a $200 pot built from $100 each. A7s' equity of 60.32% is worth $120.64, a $20.64 edge, and A4s' 39.68% is worth $79.36, which is $20.64 under its stake.
Out of 1,000 deals you should see around 478 outright wins for A7s, 271 for A4s, and 251 split pots.
The same matchup from the other side
One page covers both views. From A4s' side the equity is 39.68%, and from A7s' side it is 60.32%.
Keep exploring
As7s against Ah4h 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
This is an exact count with no sampling. For the 12 ways to deal one A7s and one A4s without reusing a card, grouped by suit pattern, every one of the 1,712,304 possible boards is dealt and both seven-card hands are compared. A tie counts as half a win in the equity column, and each board is counted once under each of its ten three-card flops.
Source: our own exact count from the GeorgeLiPoker poker math library. No outside data is used.
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