A9o vs T9o: preflop equity

Over all 1,712,304 boards that can follow this deal, A9o finishes with 69.33% of the pot and T9o with 30.67%.

A9o

69.33%

Wins 68.43%, ties 1.80%

T9o

30.67%

Wins 29.77%, ties 1.80%

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

A9o against T9o: the numbers

Exact preflop results for A9o against T9o, in percent
HandWinsTiesLosesEquity
A9o68.4291.79929.77269.329
T9o29.7721.79968.42930.671

A9o meets T9o, and both are offsuit hands. Sharing a rank is the signature of a dominated hand, since the weaker hand is usually out-kicked when the shared rank shows up.

That is a clear edge, 69.33% to 30.67%, but T9o still wins often enough that one hand proves nothing. Split pots make up 1.80% of the boards, and both equity figures count them as half a win each.

In the ranking of all 169 starting hands, A9o is number 25 and T9o is number 78.

Boards behind the percentages: 184,928,832 counted in all
HandBoards won, aboutBoards tied, aboutBoards lost, about
A9o126,545,0003,327,00055,057,000
T9o55,057,0003,327,000126,545,000

108 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.

A9o against T9o read as odds
HandEquity as odds (to 1)Wins one deal inLoses one deal inPot odds needed to call (to 1)
A9o2.2601.4613.3590.442
T9o0.4423.3591.4612.260

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: A9o holds 77.87% on low rainbow flops (nine high or lower) and 64.69% on monotone flops. A9o stays ahead on all five textures.

A9o against T9o by flop texture, in percent
FlopShare of flopsA9o winsTiesT9o winsA9o equity
Rainbow, ten or higher24.73165.5681.65732.77566.397
Rainbow, nine or lower6.31476.9391.86221.19977.870
Two-tone46.47767.4661.63530.89968.284
Monotone5.14463.4332.51934.04864.693
Paired17.33473.4772.20424.31974.579

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

Each hand has a baseline against a random hand: 60.77% for A9o, 51.53% for T9o. Here the change is +8.56 and -20.86 points.

A9o and T9o here compared with each against a random hand, in percent
CaseEquity hereAgainst a random handChange in pointsTimes the random-hand equity
A9o, all flops69.32960.773+8.5561.14079
A9o, rainbow, ten or higher66.39760.773+5.6241.09254
A9o, rainbow, nine or lower77.87060.773+17.0971.28133
A9o, two-tone68.28460.773+7.5111.12359
A9o, monotone64.69360.773+3.9201.06450
A9o, paired74.57960.773+13.8061.22717
T9o, all flops30.67151.532-20.8610.59518
T9o, rainbow, ten or higher33.60351.532-17.9290.65208
T9o, rainbow, nine or lower22.13051.532-29.4020.42944
T9o, two-tone31.71651.532-19.8160.61546
T9o, monotone35.30751.532-16.2250.68515
T9o, paired25.42151.532-26.1110.49331

Does a shared suit matter?

Does suit overlap move the numbers? A9o has 69.41% when the hands share a suit and 69.04% when they do not. A9o does better with a shared suit, by 0.37 points.

A9o against T9o by suit overlap, in percent
DealsSpecific dealsShare of dealsA9o winsTiesT9o winsA9o equity
Share a suit8477.7868.5001.82429.67669.412
No shared suit2422.2268.1811.71230.10769.037

How often this matchup comes up

The class pair covers 108 combinations of specific cards in a fixed seat order, 0.0066% of 1,624,350, and 216 (0.0133%) in either order.

A worked example

Worked example: both players commit $100, so $200 sits in the middle. Over every board, A9o's average share is $138.66 (a gain of $38.66) and T9o's is $61.34 (a loss of $38.66).

A thousand deals look like this: A9o takes 684, T9o takes 298, 18 are ties.

The same matchup from the other side

The mirror image, T9o against A9o, is 30.67% to 69.33%, and its address redirects to this page.

Try As9h against Td9c 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

Nothing here is simulated. The 108 deals of A9o against T9o fall into a few suit patterns, each dealt against all 1,712,304 boards, with both best five-card hands compared on every board. Ties give each hand half a win, and the flop rows count a board under each of its ten flops.

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

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