A9o vs 22: preflop equity

Counting every board, the equity split is 52.85% for 22 and 47.15% for A9o, so 22 leads by 5.70 points.

A9o

47.15%

Wins 46.87%, ties 0.57%

22

52.85%

Wins 52.56%, ties 0.57%

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

A9o against 22: the numbers

Exact preflop results for A9o against 22, in percent
HandWinsTiesLosesEquity
A9o46.8660.57452.56047.153
2252.5600.57446.86652.847

A9o is an offsuit hand and 22 is a pocket pair. One hand holds a pair and the other holds two cards that both outrank it, which keeps the equity closer than most people expect.

22 leads by less than 6 points of equity, so the result of any one deal is close to a toss-up. 0.57% of boards are ties, so the equity of each hand is its win rate plus half of that.

The hand ranking puts A9o at 25 and 22 at 87 out of 169 starting hands.

Boards behind the percentages: 123,285,888 counted in all
HandBoards won, aboutBoards tied, aboutBoards lost, about
A9o57,779,000708,00064,799,000
2264,799,000708,00057,779,000

The board total is exact, 72 deals at 1,712,304 boards each. Won, tied and lost counts are rounded to the nearest thousand from the five-decimal percentages.

A9o against 22 read as odds
HandEquity as odds (to 1)Wins one deal inLoses one deal inPot odds needed to call (to 1)
A9o0.8922.1341.9031.121
221.1211.9032.1340.892

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

Split by what the flop looks like, 22 peaks at 59.05% on low rainbow flops (nine high or lower) and bottoms out at 50.12% on monotone flops. 22 stays ahead on all five textures.

A9o against 22 by flop texture, in percent
FlopShare of flopsA9o winsTies22 winsA9o equity
Rainbow, ten or higher25.34147.5170.25252.23147.643
Rainbow, nine or lower5.68940.4081.09458.49840.955
Two-tone46.48546.5690.39053.04146.764
Monotone5.15148.5632.63148.80649.879
Paired17.33448.3290.75450.91748.706

A rainbow flop shows three suits, a two-tone flop repeats one suit, a monotone flop is a single suit, and a paired flop repeats a rank.

Compared with a random hand

Each hand has a baseline against a random hand: 60.77% for A9o, 50.33% for 22. Here the change is -13.62 and +2.52 points.

A9o and 22 here compared with each against a random hand, in percent
CaseEquity hereAgainst a random handChange in pointsTimes the random-hand equity
A9o, all flops47.15360.773-13.6200.77589
A9o, rainbow, ten or higher47.64360.773-13.1300.78395
A9o, rainbow, nine or lower40.95560.773-19.8180.67390
A9o, two-tone46.76460.773-14.0090.76949
A9o, monotone49.87960.773-10.8940.82074
A9o, paired48.70660.773-12.0670.80144
22, all flops52.84750.334+2.5131.04993
22, rainbow, ten or higher52.35750.334+2.0231.04019
22, rainbow, nine or lower59.04550.334+8.7111.17306
22, two-tone53.23650.334+2.9021.05765
22, monotone50.12150.334-0.2130.99577
22, paired51.29450.334+0.9601.01907

Does a shared suit matter?

Does suit overlap move the numbers? 22 has 52.77% when the hands share a suit and 53.24% when they do not. 22 does better with no shared suit, by 0.47 points.

A9o against 22 by suit overlap, in percent
DealsSpecific dealsShare of dealsA9o winsTies22 winsA9o equity
Share a suit6083.3346.9400.58152.47947.231
No shared suit1216.6746.4960.53852.96646.765

How often this matchup comes up

A9o against 22 is made up of 72 specific-card matchups in one seat order, 0.0044% of the 1,624,350 ordered deals, and 144 counting both seat orders, 0.0089%.

A worked example

Say each player puts $100 in before the flop, making a $200 pot. On average 22 takes back $105.70 of it, which is $5.70 more than it put in, and A9o takes back $94.30, $5.70 less than it put in.

In 1,000 deals of exactly this matchup, expect about 525 won outright by 22, about 469 won outright by A9o and about 6 split.

The same matchup from the other side

The mirror image, 22 against A9o, is 52.85% to 47.15%, and its address redirects to this page.

As9h against 2d2c 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 72 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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