AKo vs 33: preflop equity

AKo

46.63%

Wins 46.35%, ties 0.56%

53.37%

Wins 53.09%, ties 0.56%

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

AKo against 33: the numbers

Exact preflop results for AKo against 33, in percent
Hand	Wins	Ties	Loses	Equity
AKo	46.346	0.557	53.097	46.625
33	53.097	0.557	46.346	53.375

AKo and 33 are an offsuit hand and a pocket pair, in that order. One hand holds a pair and the other holds two cards that both outrank it, which keeps the equity closer than most people expect.

With only 6.74 points between them, the board decides this matchup far more than the cards in hand. About 0.56% of boards chop the pot, which is why equity sits slightly above the win figure for both hands.

By strength against a random hand, AKo holds place 12 of 169 and 33 holds place 66.

Boards behind the percentages: 123,285,888 counted in all
Hand	Boards won, about	Boards tied, about	Boards lost, about
AKo	57,138,000	687,000	65,461,000
33	65,461,000	687,000	57,138,000

72 specific deals times 1,712,304 boards gives the exact total. The won, tied and lost counts are approximations from the five-decimal percentages, rounded to the nearest thousand.

AKo 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)
AKo	0.874	2.158	1.883	1.145
33	1.145	1.883	2.158	0.874

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, 33 peaks at 79.55% on low rainbow flops (nine high or lower) and bottoms out at 47.26% on rainbow flops topped by a ten or better. AKo is ahead on rainbow flops topped by a ten or better, even though it trails 33 when every flop is counted.

AKo against 33 by flop texture, in percent
Flop	Share of flops	AKo wins	Ties	33 wins	AKo equity
Rainbow, ten or higher	24.717	52.640	0.208	47.152	52.744
Rainbow, nine or lower	6.314	19.800	1.297	78.903	20.448
Two-tone	46.485	46.316	0.411	53.273	46.522
Monotone	5.151	48.301	2.281	49.418	49.441
Paired	17.333	46.540	0.665	52.795	46.872

Rainbow flops have three suits, two-tone flops repeat one suit, monotone flops are all one suit, and paired flops repeat a rank.

Compared with a random hand

Compared with a random opponent, this matchup shifts AKo from 65.32% by -18.69 points and 33 from 53.69% by -0.32 points.

AKo 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
AKo, all flops	46.625	65.320	-18.695	0.71379
AKo, rainbow, ten or higher	52.744	65.320	-12.576	0.80747
AKo, rainbow, nine or lower	20.448	65.320	-44.872	0.31304
AKo, two-tone	46.522	65.320	-18.798	0.71222
AKo, monotone	49.441	65.320	-15.879	0.75690
AKo, paired	46.872	65.320	-18.448	0.71758
33, all flops	53.375	53.693	-0.318	0.99408
33, rainbow, ten or higher	47.256	53.693	-6.437	0.88011
33, rainbow, nine or lower	79.552	53.693	+25.859	1.48161
33, two-tone	53.478	53.693	-0.215	0.99600
33, monotone	50.559	53.693	-3.134	0.94163
33, paired	53.128	53.693	-0.565	0.98948

Does a shared suit matter?

The suit split reads 53.30% for 33 with a shared suit and 53.77% without one. 33 does better with no shared suit, by 0.47 points.

AKo against 33 by suit overlap, in percent
Deals	Specific deals	Share of deals	AKo wins	Ties	33 wins	AKo equity
Share a suit	60	83.33	46.420	0.568	53.012	46.704
No shared suit	12	16.67	45.977	0.503	53.520	46.228

How often this matchup comes up

Out of 1,624,350 ways to deal two seats two cards each, 72 are AKo in one seat and 33 in the other (0.0044%); with the seats swapped too, 144 (0.0089%).

A worked example

Say each player puts $100 in before the flop, making a $200 pot. On average 33 takes back $106.74 of it, which is $6.74 more than it put in, and AKo takes back $93.26, $6.74 less than it put in.

Over a long run, 1,000 deals split into about 531 for 33, 463 for AKo and 6 tied.

The same matchup from the other side

33 versus AKo is this same page seen from the other hand: 53.37% for 33, 46.63% for AKo.

Open the calculator with AsKh against 3d3c already entered, a deal with no shared suit, and change any card to try your own hand. The matchups after it each swap one hand for a nearby one in the ranking.

How this was computed

The figures are counted, not estimated: 1,712,304 boards for every suit pattern of the 72 specific deals, with both seven-card hands compared each time. Equity gives half a win for a tie. For the flop rows, a board is counted once under each of the ten flops inside it.

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

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