AJs vs ATs: preflop equity

If AJs and ATs get all the chips in before the flop, AJs owns 69.87% of the pot in the long run and ATs owns 30.13%.

AJs

69.87%

Wins 66.22%, ties 7.31%

ATs

30.13%

Wins 26.47%, ties 7.31%

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

AJs against ATs: the numbers

Exact preflop results for AJs against ATs, in percent
HandWinsTiesLosesEquity
AJs66.2197.30526.47669.872
ATs26.4767.30566.21930.128

Each side holds one of the suited hands: AJs and ATs. Sharing a rank is the signature of a dominated hand, since the weaker hand is usually out-kicked when the shared rank shows up.

A lead of 39.74 points is large but not decisive: ATs still takes about 265 of every 1,000 deals. The tie share is 7.31%: on those boards the pot is chopped and neither hand wins outright.

Place 11 of 169 belongs to AJs and place 13 belongs to ATs in the ranking against a random hand.

Boards behind the percentages: 20,547,648 counted in all
HandBoards won, aboutBoards tied, aboutBoards lost, about
AJs13,606,0001,501,0005,440,000
ATs5,440,0001,501,00013,606,000

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.

AJs against ATs read as odds
HandEquity as odds (to 1)Wins one deal inLoses one deal inPot odds needed to call (to 1)
AJs2.3191.5103.7770.431
ATs0.4313.7771.5102.319

The last column is the smallest pot odds, written as a pot-to-call ratio, at which a call breaks even with this equity.

Who is ahead on which flops

Low rainbow flops (nine high or lower) are the best for AJs (81.20%); monotone flops are the worst (63.82%). AJs stays ahead on all five textures, but the swing between them is large, so how the flop looks matters a great deal.

AJs against ATs by flop texture, in percent
FlopShare of flopsAJs winsTiesATs winsAJs equity
Rainbow, ten or higher23.13866.9115.40927.68069.615
Rainbow, nine or lower7.77178.7664.87216.36281.202
Two-tone46.54367.1764.77428.05069.563
Monotone5.21560.6546.34133.00563.824
Paired17.33358.77918.01023.21167.784

Rainbow flops have three suits, two-tone flops repeat one suit, monotone flops are all one suit, and paired flops repeat a rank.

Compared with a random hand

A random hand would give AJs 65.39% and ATs 64.60%. Against each other the change is +4.48 points for AJs and -34.47 for ATs.

AJs and ATs here compared with each against a random hand, in percent
CaseEquity hereAgainst a random handChange in pointsTimes the random-hand equity
AJs, all flops69.87265.393+4.4791.06849
AJs, rainbow, ten or higher69.61565.393+4.2221.06456
AJs, rainbow, nine or lower81.20265.393+15.8091.24175
AJs, two-tone69.56365.393+4.1701.06377
AJs, monotone63.82465.393-1.5690.97601
AJs, paired67.78465.393+2.3911.03656
ATs, all flops30.12864.602-34.4740.46636
ATs, rainbow, ten or higher30.38564.602-34.2170.47034
ATs, rainbow, nine or lower18.79864.602-45.8040.29098
ATs, two-tone30.43764.602-34.1650.47115
ATs, monotone36.17664.602-28.4260.55998
ATs, paired32.21664.602-32.3860.49868

Does a shared suit matter?

A shared suit is impossible for this matchup, so AJs' 69.87% is the answer for every suit pattern.

AJs against ATs by suit overlap, in percent
DealsSpecific dealsShare of dealsAJs winsTiesATs winsAJs equity
Share a suit00.00not possiblenot possiblenot possiblenot possible
No shared suit12100.0066.2197.30526.47669.872

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

Put $100 each into a $200 pot and deal every board once: AJs averages $139.74 back, ahead of its $100 by $39.74, while ATs averages $60.26, short of its $100 by $39.74.

Per 1,000 deals: AJs wins about 662, ATs wins about 265, and about 73 end in a split pot.

The same matchup from the other side

The mirror image, ATs against AJs, is 30.13% to 69.87%, and its address redirects to this page.

AsJs against AhTh 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

The page is built from a full enumeration: 1,712,304 boards, every suit pattern of the 12 specific deals, both seven-card hands evaluated. A tie is worth half a win to each hand, and a board is tallied under each of its ten possible flops for the texture rows.

Source: our own exact count from the GeorgeLiPoker poker math library. No outside data is used.

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