A9o vs 33: preflop equity

A9o

46.43%

Wins 46.17%, ties 0.51%

53.57%

Wins 53.32%, ties 0.51%

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

A9o against 33: the numbers

Exact preflop results for A9o against 33, in percent
Hand	Wins	Ties	Loses	Equity
A9o	46.170	0.514	53.316	46.427
33	53.316	0.514	46.170	53.573

A9o is an offsuit hand and 33 is a pocket pair. This is a pair against two overcards, a matchup that stays close because the other hand only needs one of its ranks to appear.

This is close to even money, with 33 a little ahead. A split pot comes up on 0.51% of boards, so the wins and the equity differ by half of that.

Among the 169 starting hands, A9o is number 25 and 33 is number 66 by strength against a random hand.

Boards behind the percentages: 123,285,888 counted in all
Hand	Boards won, about	Boards tied, about	Boards lost, about
A9o	56,921,000	634,000	65,731,000
33	65,731,000	634,000	56,921,000

Exact total: 72 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.

A9o against 33 read as odds
Hand	Equity as odds (to 1)	Wins one deal in	Loses one deal in	Pot odds needed to call (to 1)
A9o	0.867	2.166	1.876	1.154
33	1.154	1.876	2.166	0.867

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

Across the five flop textures 33's equity moves by 9.29 points, from 50.71% on monotone flops to 60.00% on low rainbow flops (nine high or lower). 33 stays ahead on all five textures.

A9o against 33 by flop texture, in percent
Flop	Share of flops	A9o wins	Ties	33 wins	A9o equity
Rainbow, ten or higher	25.341	47.218	0.252	52.530	47.344
Rainbow, nine or lower	5.689	39.547	0.897	59.556	39.996
Two-tone	46.485	46.169	0.356	53.475	46.347
Monotone	5.151	48.172	2.244	49.584	49.294
Paired	17.334	46.220	0.681	53.099	46.561

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

Against one random hand instead, A9o holds 60.77% and 33 holds 53.69%. Facing each other changes that by -14.34 points for A9o and -0.12 points for 33.

A9o and 33 here compared with each against a random hand, in percent
Case	Equity here	Against a random hand	Change in points	Times the random-hand equity
A9o, all flops	46.427	60.773	-14.346	0.76394
A9o, rainbow, ten or higher	47.344	60.773	-13.429	0.77903
A9o, rainbow, nine or lower	39.996	60.773	-20.777	0.65812
A9o, two-tone	46.347	60.773	-14.426	0.76262
A9o, monotone	49.294	60.773	-11.479	0.81112
A9o, paired	46.561	60.773	-14.212	0.76615
33, all flops	53.573	53.693	-0.120	0.99777
33, rainbow, ten or higher	52.656	53.693	-1.037	0.98069
33, rainbow, nine or lower	60.004	53.693	+6.311	1.11754
33, two-tone	53.653	53.693	-0.040	0.99926
33, monotone	50.706	53.693	-2.987	0.94437
33, paired	53.439	53.693	-0.254	0.99527

Does a shared suit matter?

Of the deals of this matchup, 60 share a suit (33 at 53.49%) and 12 do not (53.97%). 33 does better with no shared suit, by 0.48 points.

A9o against 33 by suit overlap, in percent
Deals	Specific deals	Share of deals	A9o wins	Ties	33 wins	A9o equity
Share a suit	60	83.33	46.243	0.525	53.232	46.506
No shared suit	12	16.67	45.803	0.460	53.737	46.033

How often this matchup comes up

Exactly 72 specific deals fit this matchup in one seat order, which is 0.0044% of 1,624,350; both orders together give 144, or 0.0089%.

A worked example

A $100 all-in from each player makes a $200 pot, and the exact equity says 33 gets $107.14 of it on average and A9o gets $92.86.

Scaled to 1,000 deals, that is roughly 533 wins for 33, 462 for A9o and 5 chopped pots.

The same matchup from the other side

33 versus A9o is this same page seen from the other hand: 53.57% for 33, 46.43% for A9o.

Try As9h against 3d3c 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

Each figure is a complete count over boards. Take the 72 specific deals, group them by suit pattern, deal all 1,712,304 boards against each, and compare the two seven-card hands. Equity counts a tie as half a win; the flop rows use every one of a board's ten flops.

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

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