ATs vs A2s: preflop equity

In equity, ATs against A2s stands at 68.48% to 31.52%, a gap of 36.96 points.

ATs

68.48%

Wins 63.51%, ties 9.95%

A2s

31.52%

Wins 26.54%, ties 9.95%

Equity counts a tie as half a win. Exact over every board.

ATs against A2s: the numbers

Exact preflop results for ATs against A2s, in percent
HandWinsTiesLosesEquity
ATs63.5089.95026.54268.483
A2s26.5429.95063.50831.517

ATs meets A2s, and both are suited hands. Because the hands share one rank, the one with the higher kicker is ahead when that rank pairs and the other hand is mostly drawing.

That is a clear edge, 68.48% to 31.52%, but A2s still wins often enough that one hand proves nothing. A split pot comes up on 9.95% of boards, so the wins and the equity differ by half of that.

The hand ranking puts ATs at 13 and A2s at 46 out of 169 starting hands.

Boards behind the percentages: 20,547,648 counted in all
HandBoards won, aboutBoards tied, aboutBoards lost, about
ATs13,049,0002,044,0005,454,000
A2s5,454,0002,044,00013,049,000

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.

ATs against A2s read as odds
HandEquity as odds (to 1)Wins one deal inLoses one deal inPot odds needed to call (to 1)
ATs2.1731.5753.7680.460
A2s0.4603.7681.5752.173

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

If you know the kind of flop that came, the numbers shift: ATs holds 74.65% on rainbow flops topped by a ten or better and 58.49% on low rainbow flops (nine high or lower). ATs stays ahead on all five textures, but the swing between them is large, so how the flop looks matters a great deal.

ATs against A2s by flop texture, in percent
FlopShare of flopsATs winsTiesA2s winsATs equity
Rainbow, ten or higher23.86770.4038.48421.11374.645
Rainbow, nine or lower7.04256.4054.16239.43358.486
Two-tone46.54364.8836.79828.31968.282
Monotone5.21559.1717.90132.92863.121
Paired17.33354.51023.40222.08866.211

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

A random hand would give ATs 64.60% and A2s 57.38%. Against each other the change is +3.88 points for ATs and -25.86 for A2s.

ATs and A2s here compared with each against a random hand, in percent
CaseEquity hereAgainst a random handChange in pointsTimes the random-hand equity
ATs, all flops68.48364.602+3.8811.06008
ATs, rainbow, ten or higher74.64564.602+10.0431.15546
ATs, rainbow, nine or lower58.48664.602-6.1160.90533
ATs, two-tone68.28264.602+3.6801.05696
ATs, monotone63.12164.602-1.4810.97708
ATs, paired66.21164.602+1.6091.02491
A2s, all flops31.51757.379-25.8620.54928
A2s, rainbow, ten or higher25.35557.379-32.0240.44189
A2s, rainbow, nine or lower41.51457.379-15.8650.72351
A2s, two-tone31.71857.379-25.6610.55278
A2s, monotone36.87957.379-20.5000.64273
A2s, paired33.78957.379-23.5900.58887

Does a shared suit matter?

The hands cannot hold a suit in common here, which leaves a single case and a single number: 68.48% for ATs.

ATs against A2s by suit overlap, in percent
DealsSpecific dealsShare of dealsATs winsTiesA2s winsATs equity
Share a suit00.00not possiblenot possiblenot possiblenot possible
No shared suit12100.0063.5089.95026.54268.483

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 ATs takes back $136.96 of it, which is $36.96 more than it put in, and A2s takes back $63.04, $36.96 less than it put in.

In 1,000 deals of exactly this matchup, expect about 635 won outright by ATs, about 265 won outright by A2s and about 100 split.

The same matchup from the other side

A2s against ATs adds nothing new: it is 31.52% for A2s and 68.48% for ATs, the same figures reversed.

Try AsTs against Ah2h in the calculator: the hands share no suit, and every card can be changed. The links after it are the closest matchups in the ranking.

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 A2s, 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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