A2s vs 97s: preflop equity

Over all 1,712,304 boards that can follow this deal, A2s finishes with 55.53% of the pot and 97s with 44.47%.

A2s

55.53%

Wins 55.27%, ties 0.52%

97s

44.47%

Wins 44.21%, ties 0.52%

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

A2s against 97s: the numbers

Exact preflop results for A2s against 97s, in percent
HandWinsTiesLosesEquity
A2s55.2670.51744.21655.525
97s44.2160.51755.26744.475

Each side holds one of the suited hands: A2s and 97s. Neither hand shares a rank with the other, so this is a contest of high cards, connection and suits.

That is a modest edge, the kind that shows up over many hands and is easy to miss in one. A split pot comes up on 0.52% of boards, so the wins and the equity differ by half of that.

A2s ranks number 46 of 169 starting hands, and 97s ranks number 94, by equity against a random hand.

Boards behind the percentages: 27,396,864 counted in all
HandBoards won, aboutBoards tied, aboutBoards lost, about
A2s15,141,000142,00012,114,000
97s12,114,000142,00015,141,000

The total is exact: 16 specific deals times 1,712,304 boards. The three counts are approximate, worked out from the percentages to five decimals and rounded to the nearest thousand.

A2s against 97s read as odds
HandEquity as odds (to 1)Wins one deal inLoses one deal inPot odds needed to call (to 1)
A2s1.2481.8092.2620.801
97s0.8012.2621.8091.248

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

Paired flops are the best for A2s (61.42%); low rainbow flops (nine high or lower) are the worst (36.40%). Watch for low rainbow flops (nine high or lower): on those flops 97s holds the better equity.

A2s against 97s by flop texture, in percent
FlopShare of flopsA2s winsTies97s winsA2s equity
Rainbow, ten or higher25.22058.4810.22141.29858.591
Rainbow, nine or lower5.68936.0670.66063.27336.397
Two-tone46.72754.1460.27445.58054.283
Monotone5.27351.7013.43344.86653.418
Paired17.09161.0790.67338.24861.415

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

Start from the random-hand figures, 57.38% for A2s and 49.12% for 97s. This opponent changes them by -1.85 and -4.65 points.

A2s and 97s here compared with each against a random hand, in percent
CaseEquity hereAgainst a random handChange in pointsTimes the random-hand equity
A2s, all flops55.52557.379-1.8540.96769
A2s, rainbow, ten or higher58.59157.379+1.2121.02112
A2s, rainbow, nine or lower36.39757.379-20.9820.63433
A2s, two-tone54.28357.379-3.0960.94604
A2s, monotone53.41857.379-3.9610.93097
A2s, paired61.41557.379+4.0361.07034
97s, all flops44.47549.118-4.6430.90547
97s, rainbow, ten or higher41.40949.118-7.7090.84305
97s, rainbow, nine or lower63.60349.118+14.4851.29490
97s, two-tone45.71749.118-3.4010.93076
97s, monotone46.58249.118-2.5360.94837
97s, paired38.58549.118-10.5330.78556

Does a shared suit matter?

Does suit overlap move the numbers? A2s has 57.21% when the hands share a suit and 54.97% when they do not. A2s does better with a shared suit, by 2.24 points.

A2s against 97s by suit overlap, in percent
DealsSpecific dealsShare of dealsA2s winsTies97s winsA2s equity
Share a suit425.0056.9060.60042.49457.206
No shared suit1275.0054.7200.49044.79054.965

How often this matchup comes up

A2s against 97s is made up of 16 specific-card matchups in one seat order, 0.0010% of the 1,624,350 ordered deals, and 32 counting both seat orders, 0.0020%.

A worked example

A $100 all-in from each player makes a $200 pot, and the exact equity says A2s gets $111.06 of it on average and 97s gets $88.94.

Run 1,000 deals and the tally comes out near 553 for A2s, 442 for 97s and 5 ties.

The same matchup from the other side

If you came looking for 97s against A2s, the numbers are the same with the hands swapped: 44.47% and 55.53%.

The calculator link fills in As2s against 9h7h, 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

We counted every case. Each suit pattern of the 16 specific A2s against 97s deals meets all 1,712,304 boards, and the better five-card hand wins; a split pot is half a win each. The flop table reads each board under all ten of its three-card flops.

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

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