AJs vs 33: preflop equity

AJs

49.85%

Wins 49.57%, ties 0.56%

50.15%

Wins 49.87%, ties 0.56%

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

AJs against 33: the numbers

Exact preflop results for AJs against 33, in percent
Hand	Wins	Ties	Loses	Equity
AJs	49.567	0.562	49.871	49.848
33	49.871	0.562	49.567	50.152

One side is a suited hand, the other is 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 0.30 points between them, the board decides this matchup far more than the cards in hand. Of every 100 boards, about 0.56 are split pots, and the equity figures already include them.

For context, AJs sits at number 11 of 169 starting hands and 33 at number 66 when each is run against a random hand.

Boards behind the percentages: 41,095,296 counted in all
Hand	Boards won, about	Boards tied, about	Boards lost, about
AJs	20,370,000	231,000	20,495,000
33	20,495,000	231,000	20,370,000

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.

AJs 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)
AJs	0.994	2.017	2.005	1.006
33	1.006	2.005	2.017	0.994

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

If you know the kind of flop that came, the numbers shift: 33 holds 76.05% on low rainbow flops (nine high or lower) and 45.01% on rainbow flops topped by a ten or better. Watch for rainbow flops topped by a ten or better and two-tone flops: on those flops AJs holds the better equity.

AJs against 33 by flop texture, in percent
Flop	Share of flops	AJs wins	Ties	33 wins	AJs equity
Rainbow, ten or higher	24.595	54.893	0.195	44.912	54.991
Rainbow, nine or lower	6.314	23.408	1.095	75.497	23.955
Two-tone	46.545	50.654	0.348	48.998	50.828
Monotone	5.212	48.257	3.185	48.558	49.850
Paired	17.334	49.016	0.673	50.311	49.352

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

Compared with a random opponent, this matchup shifts AJs from 65.39% by -15.54 points and 33 from 53.69% by -3.54 points.

AJs 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
AJs, all flops	49.848	65.393	-15.545	0.76228
AJs, rainbow, ten or higher	54.991	65.393	-10.402	0.84093
AJs, rainbow, nine or lower	23.955	65.393	-41.438	0.36632
AJs, two-tone	50.828	65.393	-14.565	0.77727
AJs, monotone	49.850	65.393	-15.543	0.76231
AJs, paired	49.352	65.393	-16.041	0.75470
33, all flops	50.152	53.693	-3.541	0.93405
33, rainbow, ten or higher	45.009	53.693	-8.684	0.83827
33, rainbow, nine or lower	76.045	53.693	+22.352	1.41629
33, two-tone	49.172	53.693	-4.521	0.91580
33, monotone	50.150	53.693	-3.543	0.93401
33, paired	50.648	53.693	-3.045	0.94329

Does a shared suit matter?

The suit split reads 50.33% for 33 with a shared suit and 49.97% without one. 33 does better with a shared suit, by 0.36 points.

AJs against 33 by suit overlap, in percent
Deals	Specific deals	Share of deals	AJs wins	Ties	33 wins	AJs equity
Share a suit	12	50.00	49.372	0.592	50.036	49.668
No shared suit	12	50.00	49.763	0.532	49.705	50.029

How often this matchup comes up

This page stands for 24 specific-card matchups (0.0015% of 1,624,350 ordered deals), or 48 once you count the seats both ways (0.0030%).

A worked example

Try it with money: two players each put in $100 and the whole board runs out every possible way. 33 averages $100.30 from the $200, up $0.30; AJs averages $99.70, down $0.30.

Run 1,000 deals and the tally comes out near 499 for 33, 496 for AJs and 5 ties.

The same matchup from the other side

33 against AJs adds nothing new: it is 50.15% for 33 and 49.85% for AJs, the same figures reversed.

Open the calculator with AsJs against 3h3d 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

This is an exact count with no sampling. For the 24 ways to deal one AJs and one 33 without reusing a card, grouped by suit pattern, every one of the 1,712,304 possible boards is dealt and both seven-card hands are compared. A tie counts as half a win in the equity column, and each board is counted once under each of its ten three-card flops.

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

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