A3s
56.53%
Wins 56.22%, ties 0.61%
54s
43.47%
Wins 43.17%, ties 0.61%
A3s against 54s: the numbers
| Hand | Wins | Ties | Loses | Equity |
|---|---|---|---|---|
| A3s | 56.220 | 0.611 | 43.169 | 56.526 |
| 54s | 43.169 | 0.611 | 56.220 | 43.474 |
A3s and 54s are both suited hands. The two hands share no rank, which makes this a pure matchup of card strength, straight chances and flush chances.
The lead is steady rather than large, and the flop still has plenty of say in who wins. A split pot comes up on 0.61% of boards, so the wins and the equity differ by half of that.
The hand ranking puts A3s at 38 and 54s at 136 out of 169 starting hands.
| Hand | Boards won, about | Boards tied, about | Boards lost, about |
|---|---|---|---|
| A3s | 15,403,000 | 167,000 | 11,827,000 |
| 54s | 11,827,000 | 167,000 | 15,403,000 |
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 | 1.300 | 1.779 | 2.316 | 0.769 |
| 54s | 0.769 | 2.316 | 1.779 | 1.300 |
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
Across the five flop textures A3s' equity moves by 27.71 points, from 35.20% on low rainbow flops (nine high or lower) to 62.91% on paired flops. On low rainbow flops (nine high or lower) the numbers flip and 54s is the one ahead.
| Flop | Share of flops | A3s wins | Ties | 54s wins | A3s equity |
|---|---|---|---|---|---|
| Rainbow, ten or higher | 25.220 | 59.971 | 0.282 | 39.747 | 60.112 |
| Rainbow, nine or lower | 5.689 | 34.695 | 1.015 | 64.290 | 35.203 |
| Two-tone | 46.727 | 54.952 | 0.371 | 44.677 | 55.137 |
| Monotone | 5.273 | 52.192 | 3.589 | 44.219 | 53.986 |
| Paired | 17.091 | 62.562 | 0.698 | 36.740 | 62.911 |
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
Compared with a random opponent, this matchup shifts A3s from 58.22% by -1.69 points and 54s from 41.45% by +2.02 points.
| Case | Equity here | Against a random hand | Change in points | Times the random-hand equity |
|---|---|---|---|---|
| A3s, all flops | 56.526 | 58.220 | -1.694 | 0.97090 |
| A3s, rainbow, ten or higher | 60.112 | 58.220 | +1.892 | 1.03250 |
| A3s, rainbow, nine or lower | 35.203 | 58.220 | -23.017 | 0.60465 |
| A3s, two-tone | 55.137 | 58.220 | -3.083 | 0.94705 |
| A3s, monotone | 53.986 | 58.220 | -4.234 | 0.92728 |
| A3s, paired | 62.911 | 58.220 | +4.691 | 1.08057 |
| 54s, all flops | 43.474 | 41.453 | +2.021 | 1.04875 |
| 54s, rainbow, ten or higher | 39.888 | 41.453 | -1.565 | 0.96225 |
| 54s, rainbow, nine or lower | 64.797 | 41.453 | +23.344 | 1.56314 |
| 54s, two-tone | 44.863 | 41.453 | +3.410 | 1.08226 |
| 54s, monotone | 46.014 | 41.453 | +4.561 | 1.11003 |
| 54s, paired | 37.089 | 41.453 | -4.364 | 0.89472 |
Does a shared suit matter?
When the hands share a suit, A3s holds 58.36%; when they do not, it holds 55.92%. A3s does better with a shared suit, by 2.44 points.
| Deals | Specific deals | Share of deals | A3s wins | Ties | 54s wins | A3s equity |
|---|---|---|---|---|---|---|
| Share a suit | 4 | 25.00 | 58.010 | 0.692 | 41.298 | 58.356 |
| No shared suit | 12 | 75.00 | 55.623 | 0.584 | 43.793 | 55.915 |
How often this matchup comes up
You will meet this exact matchup 0.0020% of the time in a random heads-up deal: 32 of 1,624,350, counting either seat order.
A worked example
Try it with money: two players each put in $100 and the whole board runs out every possible way. A3s averages $113.06 from the $200, up $13.06; 54s averages $86.94, down $13.06.
Over a long run, 1,000 deals split into about 562 for A3s, 432 for 54s and 6 tied.
The same matchup from the other side
If you came looking for 54s against A3s, the numbers are the same with the hands swapped: 43.47% and 56.53%.
Keep exploring
As3s against 5h4h 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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