ATs
68.06%
Wins 63.13%, ties 9.86%
A3s
31.94%
Wins 27.01%, ties 9.86%
ATs against A3s: the numbers
| Hand | Wins | Ties | Loses | Equity |
|---|---|---|---|---|
| ATs | 63.132 | 9.862 | 27.006 | 68.063 |
| A3s | 27.006 | 9.862 | 63.132 | 31.937 |
This is a contest between two suited hands, ATs and A3s. Sharing a rank is the signature of a dominated hand, since the weaker hand is usually out-kicked when the shared rank shows up.
ATs is well ahead, and A3s needs a specific kind of board to catch up. Of every 100 boards, about 9.86 are split pots, and the equity figures already include them.
In the ranking of all 169 starting hands, ATs is number 13 and A3s is number 38.
| Hand | Boards won, about | Boards tied, about | Boards lost, about |
|---|---|---|---|
| ATs | 12,972,000 | 2,026,000 | 5,549,000 |
| A3s | 5,549,000 | 2,026,000 | 12,972,000 |
12 specific deals times 1,712,304 boards gives the exact total. The won, tied and lost counts are approximations from the five-decimal percentages, 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) |
|---|---|---|---|---|
| ATs | 2.131 | 1.584 | 3.703 | 0.469 |
| A3s | 0.469 | 3.703 | 1.584 | 2.131 |
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
Rainbow flops topped by a ten or better are the best for ATs (74.37%); low rainbow flops (nine high or lower) are the worst (57.26%). ATs 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 | ATs wins | Ties | A3s wins | ATs equity |
|---|---|---|---|---|---|
| Rainbow, ten or higher | 23.867 | 70.150 | 8.446 | 21.404 | 74.373 |
| Rainbow, nine or lower | 7.042 | 55.253 | 4.016 | 40.731 | 57.261 |
| Two-tone | 46.543 | 64.490 | 6.740 | 28.770 | 67.860 |
| Monotone | 5.215 | 58.898 | 7.855 | 33.247 | 62.825 |
| Paired | 17.333 | 54.297 | 23.173 | 22.530 | 65.884 |
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
Compared with a random opponent, this matchup shifts ATs from 64.60% by +3.46 points and A3s from 58.22% by -26.28 points.
| Case | Equity here | Against a random hand | Change in points | Times the random-hand equity |
|---|---|---|---|---|
| ATs, all flops | 68.063 | 64.602 | +3.461 | 1.05357 |
| ATs, rainbow, ten or higher | 74.373 | 64.602 | +9.771 | 1.15125 |
| ATs, rainbow, nine or lower | 57.261 | 64.602 | -7.341 | 0.88637 |
| ATs, two-tone | 67.860 | 64.602 | +3.258 | 1.05043 |
| ATs, monotone | 62.825 | 64.602 | -1.777 | 0.97249 |
| ATs, paired | 65.884 | 64.602 | +1.282 | 1.01984 |
| A3s, all flops | 31.937 | 58.220 | -26.283 | 0.54856 |
| A3s, rainbow, ten or higher | 25.627 | 58.220 | -32.593 | 0.44018 |
| A3s, rainbow, nine or lower | 42.739 | 58.220 | -15.481 | 0.73409 |
| A3s, two-tone | 32.140 | 58.220 | -26.080 | 0.55204 |
| A3s, monotone | 37.175 | 58.220 | -21.045 | 0.63853 |
| A3s, paired | 34.116 | 58.220 | -24.104 | 0.58598 |
Does a shared suit matter?
For this pair the shared-suit row is empty: the two hands cannot both own a card of one suit without reusing a card.
| Deals | Specific deals | Share of deals | ATs wins | Ties | A3s wins | ATs equity |
|---|---|---|---|---|---|---|
| Share a suit | 0 | 0.00 | not possible | not possible | not possible | not possible |
| No shared suit | 12 | 100.00 | 63.132 | 9.862 | 27.006 | 68.063 |
How often this matchup comes up
This page stands for 12 specific-card matchups (0.0007% of 1,624,350 ordered deals), or 24 once you count the seats both ways (0.0015%).
A worked example
A $100 all-in from each player makes a $200 pot, and the exact equity says ATs gets $136.12 of it on average and A3s gets $63.88.
Per 1,000 deals: ATs wins about 631, A3s wins about 270, and about 99 end in a split pot.
The same matchup from the other side
A3s against ATs adds nothing new: it is 31.94% for A3s and 68.06% for ATs, the same figures reversed.
Keep exploring
AsTs against Ah3h 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
All 1,712,304 five-card boards are dealt for every suit pattern among the 12 specific deals of ATs against A3s, 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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