AA
87.49%
Wins 86.85%, ties 1.30%
A3s
12.51%
Wins 11.85%, ties 1.30%
AA against A3s: the numbers
| Hand | Wins | Ties | Loses | Equity |
|---|---|---|---|---|
| AA | 86.845 | 1.296 | 11.859 | 87.493 |
| A3s | 11.859 | 1.296 | 86.845 | 12.507 |
One side is a pocket pair, the other is a suited hand. One hand holds a card of the same rank as the pair, which removes a card the pair needs and makes the pair a bigger favorite.
A gap this wide means A3s is in trouble before the flop and has few good runouts. Split pots make up 1.30% of the boards, and both equity figures count them as half a win each.
In the ranking of all 169 starting hands, AA is number 1 and A3s is number 38.
| Hand | Boards won, about | Boards tied, about | Boards lost, about |
|---|---|---|---|
| AA | 17,845,000 | 266,000 | 2,437,000 |
| A3s | 2,437,000 | 266,000 | 17,845,000 |
The total is exact: 12 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) |
|---|---|---|---|---|
| AA | 6.996 | 1.151 | 8.432 | 0.143 |
| A3s | 0.143 | 8.432 | 1.151 | 6.996 |
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, AA's equity runs from 77.40% on monotone flops up to 92.61% on rainbow flops topped by a ten or better. AA stays ahead on all five textures, but the swing between them is large, so how the flop looks matters a great deal.
| Flop | Share of flops | AA wins | Ties | A3s wins | AA equity |
|---|---|---|---|---|---|
| Rainbow, ten or higher | 23.740 | 92.004 | 1.219 | 6.777 | 92.613 |
| Rainbow, nine or lower | 7.042 | 84.420 | 2.544 | 13.036 | 85.692 |
| Two-tone | 46.236 | 85.348 | 1.375 | 13.277 | 86.036 |
| Monotone | 5.151 | 76.210 | 2.370 | 21.420 | 77.395 |
| Paired | 17.831 | 87.887 | 0.393 | 11.720 | 88.084 |
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
Start from the random-hand figures, 85.20% for AA and 58.22% for A3s. This opponent changes them by +2.29 and -45.71 points.
| Case | Equity here | Against a random hand | Change in points | Times the random-hand equity |
|---|---|---|---|---|
| AA, all flops | 87.493 | 85.204 | +2.289 | 1.02686 |
| AA, rainbow, ten or higher | 92.613 | 85.204 | +7.409 | 1.08696 |
| AA, rainbow, nine or lower | 85.692 | 85.204 | +0.488 | 1.00573 |
| AA, two-tone | 86.036 | 85.204 | +0.832 | 1.00976 |
| AA, monotone | 77.395 | 85.204 | -7.809 | 0.90835 |
| AA, paired | 88.084 | 85.204 | +2.880 | 1.03380 |
| A3s, all flops | 12.507 | 58.220 | -45.713 | 0.21482 |
| A3s, rainbow, ten or higher | 7.387 | 58.220 | -50.833 | 0.12688 |
| A3s, rainbow, nine or lower | 14.308 | 58.220 | -43.912 | 0.24576 |
| A3s, two-tone | 13.964 | 58.220 | -44.256 | 0.23985 |
| A3s, monotone | 22.605 | 58.220 | -35.615 | 0.38827 |
| A3s, paired | 11.916 | 58.220 | -46.304 | 0.20467 |
Does a shared suit matter?
These two classes cannot share a suit in any legal deal, so there is only one row to read: AA holds 87.49% in every deal of this matchup.
| Deals | Specific deals | Share of deals | AA wins | Ties | A3s wins | AA equity |
|---|---|---|---|---|---|---|
| Share a suit | 0 | 0.00 | not possible | not possible | not possible | not possible |
| No shared suit | 12 | 100.00 | 86.845 | 1.296 | 11.859 | 87.493 |
How often this matchup comes up
Exactly 12 specific deals fit this matchup in one seat order, which is 0.0007% of 1,624,350; both orders together give 24, or 0.0015%.
A worked example
Say each player puts $100 in before the flop, making a $200 pot. On average AA takes back $174.98 of it, which is $74.98 more than it put in, and A3s takes back $25.02, $74.98 less than it put in.
Think in thousands: about 868 of 1,000 go to AA, about 119 go to A3s, and about 13 are chopped.
The same matchup from the other side
The mirror image, A3s against AA, is 12.51% to 87.49%, and its address redirects to this page.
Keep exploring
Open the calculator with AsAh against Ad3d already entered, a deal with no shared suit, and change any card to try your own hand. The matchups after it each swap one hand for a nearby one in the ranking.
How this was computed
This is an exact count with no sampling. For the 12 ways to deal one AA and one A3s 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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