A9s vs 55: preflop equity

If 55 and A9s get all the chips in before the flop, 55 owns 52.50% of the pot in the long run and A9s owns 47.50%.

A9s

47.50%

Wins 47.26%, ties 0.48%

55

52.50%

Wins 52.26%, ties 0.48%

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

A9s against 55: the numbers

Exact preflop results for A9s against 55, in percent
HandWinsTiesLosesEquity
A9s47.2620.47652.26247.500
5552.2620.47647.26252.500

A9s, a suited hand, plays 55, a pocket pair. A pair against two higher cards is the classic race: the pair is usually a small favorite or close to even, and each overcard that pairs is a way to take the lead.

With only 5.00 points between them, the board decides this matchup far more than the cards in hand. A split pot comes up on 0.48% of boards, so the wins and the equity differ by half of that.

For context, A9s sits at number 18 of 169 starting hands and 55 at number 27 when each is run against a random hand.

Boards behind the percentages: 41,095,296 counted in all
HandBoards won, aboutBoards tied, aboutBoards lost, about
A9s19,422,000196,00021,477,000
5521,477,000196,00019,422,000

Exact total: 24 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.

A9s against 55 read as odds
HandEquity as odds (to 1)Wins one deal inLoses one deal inPot odds needed to call (to 1)
A9s0.9052.1161.9131.105
551.1051.9132.1160.905

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 55's equity moves by 10.06 points, from 51.09% on two-tone flops to 61.15% on low rainbow flops (nine high or lower). 55 stays ahead on all five textures.

A9s against 55 by flop texture, in percent
FlopShare of flopsA9s winsTies55 winsA9s equity
Rainbow, ten or higher25.22048.1890.24751.56448.313
Rainbow, nine or lower5.68938.4850.72260.79338.846
Two-tone46.54548.7540.31050.93648.909
Monotone5.21246.8762.60250.52248.177
Paired17.33444.9030.53654.56145.171

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

Compared with a random opponent, this matchup shifts A9s from 62.78% by -15.28 points and 55 from 60.33% by -7.83 points.

A9s and 55 here compared with each against a random hand, in percent
CaseEquity hereAgainst a random handChange in pointsTimes the random-hand equity
A9s, all flops47.50062.781-15.2810.75660
A9s, rainbow, ten or higher48.31362.781-14.4680.76955
A9s, rainbow, nine or lower38.84662.781-23.9350.61875
A9s, two-tone48.90962.781-13.8720.77904
A9s, monotone48.17762.781-14.6040.76738
A9s, paired45.17162.781-17.6100.71950
55, all flops52.50060.325-7.8250.87029
55, rainbow, ten or higher51.68760.325-8.6380.85681
55, rainbow, nine or lower61.15460.325+0.8291.01374
55, two-tone51.09160.325-9.2340.84693
55, monotone51.82360.325-8.5020.85906
55, paired54.82960.325-5.4960.90889

Does a shared suit matter?

The suit split reads 52.69% for 55 with a shared suit and 52.31% without one. 55 does better with a shared suit, by 0.38 points.

A9s against 55 by suit overlap, in percent
DealsSpecific dealsShare of dealsA9s winsTies55 winsA9s equity
Share a suit1250.0047.0550.51752.42847.314
No shared suit1250.0047.4680.43652.09647.686

How often this matchup comes up

Counting specific cards, A9s against 55 appears in 24 of the 1,624,350 ordered heads-up deals (0.0015%), and in 48 when the seats are swapped too (0.0030%).

A worked example

Worked example: both players commit $100, so $200 sits in the middle. Over every board, 55's average share is $105.00 (a gain of $5.00) and A9s' is $95.00 (a loss of $5.00).

Per 1,000 deals: 55 wins about 523, A9s wins about 472, and about 5 end in a split pot.

The same matchup from the other side

Swap the hands and you get 55 with 52.50% against A9s with 47.50%. We keep one page per matchup, with the better-ranked hand first.

Try As9s against 5h5d 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 24 deals of A9s against 55 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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