AJo vs A2s: preflop equity

Before any board card is dealt, AJo holds 68.39% equity against A2s, which leaves A2s with 31.61%.

AJo

68.39%

Wins 64.49%, ties 7.80%

A2s

31.61%

Wins 27.71%, ties 7.80%

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

AJo against A2s: the numbers

Exact preflop results for AJo against A2s, in percent
HandWinsTiesLosesEquity
AJo64.4907.80227.70868.391
A2s27.7087.80264.49031.609

AJo is an offsuit hand and A2s is a suited hand. Sharing a rank is the signature of a dominated hand, since the weaker hand is usually out-kicked when the shared rank shows up.

A lead of 36.78 points is large but not decisive: A2s still takes about 277 of every 1,000 deals. Ties are 7.80% of the outcomes here; each tied board gives both hands half the pot.

In the ranking of all 169 starting hands, AJo is number 15 and A2s is number 46.

Boards behind the percentages: 61,642,944 counted in all
HandBoards won, aboutBoards tied, aboutBoards lost, about
AJo39,754,0004,809,00017,080,000
A2s17,080,0004,809,00039,754,000

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.

AJo against A2s read as odds
HandEquity as odds (to 1)Wins one deal inLoses one deal inPot odds needed to call (to 1)
AJo2.1641.5513.6090.462
A2s0.4623.6091.5512.164

In the last column, a pot-to-call ratio at or above the figure makes a call break even or better at this equity.

Who is ahead on which flops

Across the five flop textures AJo's equity moves by 18.85 points, from 56.62% on low rainbow flops (nine high or lower) to 75.47% on rainbow flops topped by a ten or better. AJo stays ahead on all five textures, but the swing between them is large, so how the flop looks matters a great deal.

AJo against A2s by flop texture, in percent
FlopShare of flopsAJo winsTiesA2s winsAJo equity
Rainbow, ten or higher23.90572.6125.71521.67375.469
Rainbow, nine or lower7.04254.3424.54541.11356.615
Two-tone46.52764.8835.17229.94567.469
Monotone5.19260.5636.08733.35063.606
Paired17.33457.53319.57322.89467.319

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, 63.56% for AJo and 57.38% for A2s. This opponent changes them by +4.83 and -25.77 points.

AJo and A2s here compared with each against a random hand, in percent
CaseEquity hereAgainst a random handChange in pointsTimes the random-hand equity
AJo, all flops68.39163.563+4.8281.07596
AJo, rainbow, ten or higher75.46963.563+11.9061.18731
AJo, rainbow, nine or lower56.61563.563-6.9480.89069
AJo, two-tone67.46963.563+3.9061.06145
AJo, monotone63.60663.563+0.0431.00068
AJo, paired67.31963.563+3.7561.05909
A2s, all flops31.60957.379-25.7700.55088
A2s, rainbow, ten or higher24.53157.379-32.8480.42753
A2s, rainbow, nine or lower43.38557.379-13.9940.75611
A2s, two-tone32.53157.379-24.8480.56695
A2s, monotone36.39457.379-20.9850.63427
A2s, paired32.68157.379-24.6980.56956

Does a shared suit matter?

Split by suits, the deals give AJo 69.21% when the hands overlap in a suit and 67.98% when they do not. AJo does better with a shared suit, by 1.23 points.

AJo against A2s by suit overlap, in percent
DealsSpecific dealsShare of dealsAJo winsTiesA2s winsAJo equity
Share a suit1233.3365.2567.91126.83369.211
No shared suit2466.6764.1077.74728.14667.981

How often this matchup comes up

AJo against A2s is made up of 36 specific-card matchups in one seat order, 0.0022% of the 1,624,350 ordered deals, and 72 counting both seat orders, 0.0044%.

A worked example

Worked example: both players commit $100, so $200 sits in the middle. Over every board, AJo's average share is $136.78 (a gain of $36.78) and A2s' is $63.22 (a loss of $36.78).

Scaled to 1,000 deals, that is roughly 645 wins for AJo, 277 for A2s and 78 chopped pots.

The same matchup from the other side

The reversed view, A2s against AJo, shows 31.61% for A2s and 68.39% for AJo. It is the same count, so it redirects here.

The calculator link fills in AsJh against Ad2d, 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

Nothing here is simulated. The 36 deals of AJo against A2s 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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