AQs vs T9s: preflop equity

Dealt all in against each other, AQs takes 62.18% of the pot on average and T9s takes the other 37.82%.

AQs

62.18%

Wins 61.94%, ties 0.49%

T9s

37.82%

Wins 37.57%, ties 0.49%

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

AQs against T9s: the numbers

Exact preflop results for AQs against T9s, in percent
HandWinsTiesLosesEquity
AQs61.9400.48837.57262.184
T9s37.5720.48861.94037.816

This is a contest between two suited hands, AQs and T9s. Neither hand shares a rank with the other, so this is a contest of high cards, connection and suits.

A 24.36 point lead is real, and T9s still takes about 376 of every 1,000 deals outright. Split pots make up 0.49% of the boards, and both equity figures count them as half a win each.

Ranked by equity against a random hand, AQs is number 10 of the 169 starting hands and T9s is number 64.

Boards behind the percentages: 27,396,864 counted in all
HandBoards won, aboutBoards tied, aboutBoards lost, about
AQs16,970,000134,00010,294,000
T9s10,294,000134,00016,970,000

16 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.

AQs against T9s read as odds
HandEquity as odds (to 1)Wins one deal inLoses one deal inPot odds needed to call (to 1)
AQs1.6441.6142.6620.608
T9s0.6082.6621.6141.644

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: AQs holds 64.85% on rainbow flops topped by a ten or better and 53.69% on low rainbow flops (nine high or lower). AQs stays ahead on all five textures.

AQs against T9s by flop texture, in percent
FlopShare of flopsAQs winsTiesT9s winsAQs equity
Rainbow, ten or higher23.86764.7800.14135.07964.850
Rainbow, nine or lower7.04253.3190.74445.93753.691
Two-tone46.72761.3200.24838.43261.444
Monotone5.27357.7063.40438.89059.408
Paired17.09164.5320.62034.84864.842

Flop types: rainbow means three different suits, two-tone means one suit twice, monotone means one suit three times, paired means a repeated rank.

Compared with a random hand

Relative to a random opponent, AQs changes by -4.03 points (baseline 66.21%) and T9s by -16.21 points (baseline 54.03%).

AQs and T9s here compared with each against a random hand, in percent
CaseEquity hereAgainst a random handChange in pointsTimes the random-hand equity
AQs, all flops62.18466.209-4.0250.93921
AQs, rainbow, ten or higher64.85066.209-1.3590.97947
AQs, rainbow, nine or lower53.69166.209-12.5180.81093
AQs, two-tone61.44466.209-4.7650.92803
AQs, monotone59.40866.209-6.8010.89728
AQs, paired64.84266.209-1.3670.97935
T9s, all flops37.81654.028-16.2120.69993
T9s, rainbow, ten or higher35.15054.028-18.8780.65059
T9s, rainbow, nine or lower46.30954.028-7.7190.85713
T9s, two-tone38.55654.028-15.4720.71363
T9s, monotone40.59254.028-13.4360.75131
T9s, paired35.15854.028-18.8700.65074

Does a shared suit matter?

Two kinds of deal exist here. In 4 of them the hands share a suit and AQs holds 64.45%. In 12 they do not, and it holds 61.43%. AQs does better with a shared suit, by 3.02 points.

AQs against T9s by suit overlap, in percent
DealsSpecific dealsShare of dealsAQs winsTiesT9s winsAQs equity
Share a suit425.0064.1690.56435.26764.451
No shared suit1275.0061.1980.46238.34061.429

How often this matchup comes up

Out of 1,624,350 ways to deal two seats two cards each, 16 are AQs in one seat and T9s in the other (0.0010%); with the seats swapped too, 32 (0.0020%).

A worked example

Say each player puts $100 in before the flop, making a $200 pot. On average AQs takes back $124.36 of it, which is $24.36 more than it put in, and T9s takes back $75.64, $24.36 less than it put in.

Think in thousands: about 619 of 1,000 go to AQs, about 376 go to T9s, and about 5 are chopped.

The same matchup from the other side

Read it from the other side: T9s against AQs is the same matchup with the numbers swapped, so T9s holds 37.82% and AQs holds 62.18%. That address sends you back to this page.

The calculator link fills in AsQs against Th9h, 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

We counted every case. Each suit pattern of the 16 specific AQs against T9s deals meets all 1,712,304 boards, and the better five-card hand wins; a split pot is half a win each. The flop table reads each board under all ten of its three-card flops.

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

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