A4s
61.02%
Wins 60.71%, ties 0.61%
53s
38.98%
Wins 38.68%, ties 0.61%
A4s against 53s: the numbers
| Hand | Wins | Ties | Loses | Equity |
|---|---|---|---|---|
| A4s | 60.711 | 0.612 | 38.677 | 61.017 |
| 53s | 38.677 | 0.612 | 60.711 | 38.983 |
The matchup is suited hands on both sides, A4s against 53s. Neither hand shares a rank with the other, so this is a contest of high cards, connection and suits.
A4s is ahead, but 53s is far from dead: it takes 387 of every 1,000 deals outright. About 0.61% of boards chop the pot, which is why equity sits slightly above the win figure for both hands.
The hand ranking puts A4s at 35 and 53s at 146 out of 169 starting hands.
| Hand | Boards won, about | Boards tied, about | Boards lost, about |
|---|---|---|---|
| A4s | 16,633,000 | 168,000 | 10,596,000 |
| 53s | 10,596,000 | 168,000 | 16,633,000 |
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) |
|---|---|---|---|---|
| A4s | 1.565 | 1.647 | 2.586 | 0.639 |
| 53s | 0.639 | 2.586 | 1.647 | 1.565 |
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
Paired flops are the best for A4s (65.47%); low rainbow flops (nine high or lower) are the worst (44.31%). On low rainbow flops (nine high or lower) the numbers flip and 53s is the one ahead.
| Flop | Share of flops | A4s wins | Ties | 53s wins | A4s equity |
|---|---|---|---|---|---|
| Rainbow, ten or higher | 25.220 | 64.352 | 0.281 | 35.367 | 64.493 |
| Rainbow, nine or lower | 5.689 | 43.795 | 1.024 | 55.181 | 44.307 |
| Two-tone | 46.727 | 59.717 | 0.372 | 39.911 | 59.903 |
| Monotone | 5.273 | 56.057 | 3.597 | 40.346 | 57.856 |
| Paired | 17.091 | 65.123 | 0.698 | 34.179 | 65.472 |
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
Start from the random-hand figures, 59.03% for A4s and 39.69% for 53s. This opponent changes them by +1.99 and -0.71 points.
| Case | Equity here | Against a random hand | Change in points | Times the random-hand equity |
|---|---|---|---|---|
| A4s, all flops | 61.017 | 59.034 | +1.983 | 1.03359 |
| A4s, rainbow, ten or higher | 64.493 | 59.034 | +5.459 | 1.09247 |
| A4s, rainbow, nine or lower | 44.307 | 59.034 | -14.727 | 0.75053 |
| A4s, two-tone | 59.903 | 59.034 | +0.869 | 1.01472 |
| A4s, monotone | 57.856 | 59.034 | -1.178 | 0.98005 |
| A4s, paired | 65.472 | 59.034 | +6.438 | 1.10906 |
| 53s, all flops | 38.983 | 39.693 | -0.710 | 0.98211 |
| 53s, rainbow, ten or higher | 35.507 | 39.693 | -4.186 | 0.89454 |
| 53s, rainbow, nine or lower | 55.693 | 39.693 | +16.000 | 1.40309 |
| 53s, two-tone | 40.097 | 39.693 | +0.404 | 1.01018 |
| 53s, monotone | 42.144 | 39.693 | +2.451 | 1.06175 |
| 53s, paired | 34.528 | 39.693 | -5.165 | 0.86988 |
Does a shared suit matter?
Split by suits, the deals give A4s 63.27% when the hands overlap in a suit and 60.27% when they do not. A4s does better with a shared suit, by 3.00 points.
| Deals | Specific deals | Share of deals | A4s wins | Ties | 53s wins | A4s equity |
|---|---|---|---|---|---|---|
| Share a suit | 4 | 25.00 | 62.924 | 0.692 | 36.384 | 63.270 |
| No shared suit | 12 | 75.00 | 59.973 | 0.585 | 39.442 | 60.266 |
How often this matchup comes up
Counting specific cards, A4s against 53s appears in 16 of the 1,624,350 ordered heads-up deals (0.0010%), and in 32 when the seats are swapped too (0.0020%).
A worked example
With $100 from each side, the $200 pot is split on average as $122.04 for A4s and $77.96 for 53s; the first side gains $22.04 per all-in and the second gives up $22.04.
Think in thousands: about 607 of 1,000 go to A4s, about 387 go to 53s, and about 6 are chopped.
The same matchup from the other side
Swap the hands and you get 53s with 38.98% against A4s with 61.02%. We keep one page per matchup, with the better-ranked hand first.
Keep exploring
The calculator link fills in As4s against 5h3h, a deal where the two hands share no suit. Change any card to test your own hand. The neighboring matchups below swap one of the two hands for one 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 A4s against 53s, 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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