A4s
56.75%
Wins 56.47%, ties 0.56%
65s
43.25%
Wins 42.97%, ties 0.56%
A4s against 65s: the numbers
| Hand | Wins | Ties | Loses | Equity |
|---|---|---|---|---|
| A4s | 56.468 | 0.562 | 42.970 | 56.749 |
| 65s | 42.970 | 0.562 | 56.468 | 43.251 |
A4s meets 65s, and both are suited hands. The two hands share no rank, which makes this a pure matchup of card strength, straight chances and flush chances.
A 13.50 point lead is real, and 65s still takes about 430 of every 1,000 deals outright. 0.56% of boards are ties, so the equity of each hand is its win rate plus half of that.
The hand ranking puts A4s at 35 and 65s at 128 out of 169 starting hands.
| Hand | Boards won, about | Boards tied, about | Boards lost, about |
|---|---|---|---|
| A4s | 15,470,000 | 154,000 | 11,772,000 |
| 65s | 11,772,000 | 154,000 | 15,470,000 |
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 | 1.312 | 1.771 | 2.327 | 0.762 |
| 65s | 0.762 | 2.327 | 1.771 | 1.312 |
The last column is the break-even price: the pot odds a call needs to offer, as a ratio of pot to call.
Who is ahead on which flops
By flop texture, A4s' equity runs from 34.84% on low rainbow flops (nine high or lower) up to 62.72% on paired flops. Low rainbow flops (nine high or lower) favor 65s, the hand that is behind overall.
| Flop | Share of flops | A4s wins | Ties | 65s wins | A4s equity |
|---|---|---|---|---|---|
| Rainbow, ten or higher | 25.220 | 60.488 | 0.255 | 39.257 | 60.615 |
| Rainbow, nine or lower | 5.689 | 34.430 | 0.813 | 64.757 | 34.837 |
| Two-tone | 46.727 | 55.277 | 0.321 | 44.402 | 55.437 |
| Monotone | 5.273 | 52.434 | 3.500 | 44.066 | 54.184 |
| Paired | 17.091 | 62.374 | 0.686 | 36.940 | 62.717 |
A rainbow flop shows three suits, a two-tone flop repeats one suit, a monotone flop is a single suit, and a paired flop repeats a rank.
Compared with a random hand
Relative to a random opponent, A4s changes by -2.28 points (baseline 59.03%) and 65s by +0.12 points (baseline 43.13%).
| Case | Equity here | Against a random hand | Change in points | Times the random-hand equity |
|---|---|---|---|---|
| A4s, all flops | 56.749 | 59.034 | -2.285 | 0.96129 |
| A4s, rainbow, ten or higher | 60.615 | 59.034 | +1.581 | 1.02678 |
| A4s, rainbow, nine or lower | 34.837 | 59.034 | -24.197 | 0.59012 |
| A4s, two-tone | 55.437 | 59.034 | -3.597 | 0.93907 |
| A4s, monotone | 54.184 | 59.034 | -4.850 | 0.91784 |
| A4s, paired | 62.717 | 59.034 | +3.683 | 1.06239 |
| 65s, all flops | 43.251 | 43.133 | +0.118 | 1.00274 |
| 65s, rainbow, ten or higher | 39.385 | 43.133 | -3.748 | 0.91311 |
| 65s, rainbow, nine or lower | 65.163 | 43.133 | +22.030 | 1.51075 |
| 65s, two-tone | 44.563 | 43.133 | +1.430 | 1.03315 |
| 65s, monotone | 45.816 | 43.133 | +2.683 | 1.06220 |
| 65s, paired | 37.283 | 43.133 | -5.850 | 0.86437 |
Does a shared suit matter?
Looking only at deals where the hands share a suit, A4s has 58.61%; looking only at deals where they do not, 56.13%. A4s does better with a shared suit, by 2.48 points.
| Deals | Specific deals | Share of deals | A4s wins | Ties | 65s wins | A4s equity |
|---|---|---|---|---|---|---|
| Share a suit | 4 | 25.00 | 58.285 | 0.642 | 41.073 | 58.606 |
| No shared suit | 12 | 75.00 | 55.863 | 0.535 | 43.602 | 56.130 |
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
Put $100 each into a $200 pot and deal every board once: A4s averages $113.50 back, ahead of its $100 by $13.50, while 65s averages $86.50, short of its $100 by $13.50.
Out of 1,000 deals you should see around 565 outright wins for A4s, 430 for 65s, and 5 split pots.
The same matchup from the other side
65s against A4s adds nothing new: it is 43.25% for 65s and 56.75% for A4s, the same figures reversed.
Keep exploring
The calculator link fills in As4s against 6h5h, 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
This is an exact count with no sampling. For the 16 ways to deal one A4s and one 65s 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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