ATo vs T9s: preflop equity

The exact count puts ATo at 67.90% and T9s at 32.10% when the two hands see all five board cards.

ATo

67.90%

Wins 66.83%, ties 2.15%

T9s

32.10%

Wins 31.02%, ties 2.15%

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

ATo against T9s: the numbers

Exact preflop results for ATo against T9s, in percent
HandWinsTiesLosesEquity
ATo66.8282.15231.02067.904
T9s31.0202.15266.82832.096

One side is an offsuit hand, the other is a suited hand. 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, 67.90% to 32.10%, but T9s still wins often enough that one hand proves nothing. Ties are part of the picture: 2.15% of boards end in a split pot, and each side counts that as half a win.

In the ranking of all 169 starting hands, ATo is number 19 and T9s is number 64.

Boards behind the percentages: 61,642,944 counted in all
HandBoards won, aboutBoards tied, aboutBoards lost, about
ATo41,195,0001,327,00019,122,000
T9s19,122,0001,327,00041,195,000

Exact total: 36 deals times 1,712,304 boards. The other three counts come from the five-decimal percentages and are rounded to the nearest thousand, so read them as approximate.

ATo against T9s read as odds
HandEquity as odds (to 1)Wins one deal inLoses one deal inPot odds needed to call (to 1)
ATo2.1161.4963.2240.473
T9s0.4733.2241.4962.116

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

Across the five flop textures ATo's equity moves by 17.83 points, from 55.46% on low rainbow flops (nine high or lower) to 73.29% on rainbow flops topped by a ten or better. ATo stays ahead on all five textures, but the swing between them is large, so how the flop looks matters a great deal.

ATo against T9s by flop texture, in percent
FlopShare of flopsATo winsTiesT9s winsATo equity
Rainbow, ten or higher23.90572.3491.88425.76773.291
Rainbow, nine or lower7.04254.0212.86843.11155.455
Two-tone46.52764.9131.96033.12765.893
Monotone5.19261.9233.38934.68863.617
Paired17.33471.0272.37426.59972.214

Read the flop types this way: rainbow has three suits, two-tone has two cards of one suit, monotone has three, and paired repeats a rank.

Compared with a random hand

Start from the random-hand figures, 62.72% for ATo and 54.03% for T9s. This opponent changes them by +5.18 and -21.93 points.

ATo and T9s here compared with each against a random hand, in percent
CaseEquity hereAgainst a random handChange in pointsTimes the random-hand equity
ATo, all flops67.90462.722+5.1821.08262
ATo, rainbow, ten or higher73.29162.722+10.5691.16851
ATo, rainbow, nine or lower55.45562.722-7.2670.88414
ATo, two-tone65.89362.722+3.1711.05056
ATo, monotone63.61762.722+0.8951.01427
ATo, paired72.21462.722+9.4921.15133
T9s, all flops32.09654.028-21.9320.59406
T9s, rainbow, ten or higher26.70954.028-27.3190.49435
T9s, rainbow, nine or lower44.54554.028-9.4830.82448
T9s, two-tone34.10754.028-19.9210.63128
T9s, monotone36.38354.028-17.6450.67341
T9s, paired27.78654.028-26.2420.51429

Does a shared suit matter?

When the hands share a suit, ATo holds 68.95%; when they do not, it holds 67.38%. ATo does better with a shared suit, by 1.57 points.

ATo against T9s by suit overlap, in percent
DealsSpecific dealsShare of dealsATo winsTiesT9s winsATo equity
Share a suit1233.3367.8322.24129.92768.952
No shared suit2466.6766.3262.10731.56767.380

How often this matchup comes up

Exactly 36 specific deals fit this matchup in one seat order, which is 0.0022% of 1,624,350; both orders together give 72, or 0.0044%.

A worked example

Worked example: both players commit $100, so $200 sits in the middle. Over every board, ATo's average share is $135.80 (a gain of $35.80) and T9s' is $64.20 (a loss of $35.80).

Run 1,000 deals and the tally comes out near 668 for ATo, 310 for T9s and 22 ties.

The same matchup from the other side

If you came looking for T9s against ATo, the numbers are the same with the hands swapped: 32.10% and 67.90%.

The calculator link fills in AsTh against Td9d, 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

The page is built from a full enumeration: 1,712,304 boards, every suit pattern of the 36 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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