A3s
57.36%
Wins 57.07%, ties 0.58%
64s
42.64%
Wins 42.35%, ties 0.58%
A3s against 64s: the numbers
| Hand | Wins | Ties | Loses | Equity |
|---|---|---|---|---|
| A3s | 57.074 | 0.579 | 42.347 | 57.363 |
| 64s | 42.347 | 0.579 | 57.074 | 42.637 |
The matchup is suited hands on both sides, A3s against 64s. The two hands share no rank, which makes this a pure matchup of card strength, straight chances and flush chances.
A 14.72 point lead is real, and 64s still takes about 423 of every 1,000 deals outright. A split pot comes up on 0.58% of boards, so the wins and the equity differ by half of that.
For context, A3s sits at number 38 of 169 starting hands and 64s at number 138 when each is run against a random hand.
| Hand | Boards won, about | Boards tied, about | Boards lost, about |
|---|---|---|---|
| A3s | 15,636,000 | 159,000 | 11,602,000 |
| 64s | 11,602,000 | 159,000 | 15,636,000 |
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) |
|---|---|---|---|---|
| A3s | 1.345 | 1.752 | 2.361 | 0.743 |
| 64s | 0.743 | 2.361 | 1.752 | 1.345 |
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
Split by what the flop looks like, A3s peaks at 63.36% on paired flops and bottoms out at 35.93% on low rainbow flops (nine high or lower). The lead reverses on low rainbow flops (nine high or lower): there 64s is the favorite even though A3s is ahead overall.
| Flop | Share of flops | A3s wins | Ties | 64s wins | A3s equity |
|---|---|---|---|---|---|
| Rainbow, ten or higher | 25.220 | 61.038 | 0.255 | 38.707 | 61.165 |
| Rainbow, nine or lower | 5.689 | 35.461 | 0.934 | 63.605 | 35.928 |
| Two-tone | 46.727 | 55.862 | 0.338 | 43.800 | 56.031 |
| Monotone | 5.273 | 52.910 | 3.513 | 43.577 | 54.667 |
| Paired | 17.091 | 63.014 | 0.694 | 36.292 | 63.361 |
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
Start from the random-hand figures, 58.22% for A3s and 41.33% for 64s. This opponent changes them by -0.86 and +1.31 points.
| Case | Equity here | Against a random hand | Change in points | Times the random-hand equity |
|---|---|---|---|---|
| A3s, all flops | 57.363 | 58.220 | -0.857 | 0.98528 |
| A3s, rainbow, ten or higher | 61.165 | 58.220 | +2.945 | 1.05058 |
| A3s, rainbow, nine or lower | 35.928 | 58.220 | -22.292 | 0.61711 |
| A3s, two-tone | 56.031 | 58.220 | -2.189 | 0.96240 |
| A3s, monotone | 54.667 | 58.220 | -3.553 | 0.93897 |
| A3s, paired | 63.361 | 58.220 | +5.141 | 1.08830 |
| 64s, all flops | 42.637 | 41.333 | +1.304 | 1.03155 |
| 64s, rainbow, ten or higher | 38.835 | 41.333 | -2.498 | 0.93956 |
| 64s, rainbow, nine or lower | 64.072 | 41.333 | +22.739 | 1.55014 |
| 64s, two-tone | 43.969 | 41.333 | +2.636 | 1.06377 |
| 64s, monotone | 45.333 | 41.333 | +4.000 | 1.09677 |
| 64s, paired | 36.639 | 41.333 | -4.694 | 0.88643 |
Does a shared suit matter?
Does suit overlap move the numbers? A3s has 59.28% when the hands share a suit and 56.73% when they do not. A3s does better with a shared suit, by 2.55 points.
| Deals | Specific deals | Share of deals | A3s wins | Ties | 64s wins | A3s equity |
|---|---|---|---|---|---|---|
| Share a suit | 4 | 25.00 | 58.947 | 0.661 | 40.392 | 59.277 |
| No shared suit | 12 | 75.00 | 56.449 | 0.552 | 42.999 | 56.725 |
How often this matchup comes up
Out of 1,624,350 ways to deal two seats two cards each, 16 are A3s in one seat and 64s in the other (0.0010%); with the seats swapped too, 32 (0.0020%).
A worked example
Say each player puts $100 in before the flop, making a $200 pot. On average A3s takes back $114.72 of it, which is $14.72 more than it put in, and 64s takes back $85.28, $14.72 less than it put in.
A thousand deals look like this: A3s takes 571, 64s takes 423, 6 are ties.
The same matchup from the other side
The mirror image, 64s against A3s, is 42.64% to 57.36%, and its address redirects to this page.
Keep exploring
Try As3s against 6h4h in the calculator: the hands share no suit, and every card can be changed. The links after it are the closest matchups in the ranking.
How this was computed
Each figure is a complete count over boards. Take the 16 specific deals, group them by suit pattern, deal all 1,712,304 boards against each, and compare the two seven-card hands. Equity counts a tie as half a win; the flop rows use every one of a board's ten flops.
Source: our own exact count from the GeorgeLiPoker poker math library. No outside data is used.
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