ATo vs 33: preflop equity

ATo

47.68%

Wins 47.42%, ties 0.52%

52.32%

Wins 52.06%, ties 0.52%

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

ATo against 33: the numbers

Exact preflop results for ATo against 33, in percent
Hand	Wins	Ties	Loses	Equity
ATo	47.419	0.517	52.064	47.677
33	52.064	0.517	47.419	52.323

The first hand is an offsuit hand; the second 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.

33 leads by less than 5 points of equity, so the result of any one deal is close to a toss-up. Ties are 0.52% of the outcomes here; each tied board gives both hands half the pot.

Ranked by equity against a random hand, ATo is number 19 of the 169 starting hands and 33 is number 66.

Boards behind the percentages: 123,285,888 counted in all
Hand	Boards won, about	Boards tied, about	Boards lost, about
ATo	58,461,000	637,000	64,188,000
33	64,188,000	637,000	58,461,000

The total is exact: 72 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.

ATo 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)
ATo	0.911	2.109	1.921	1.097
33	1.097	1.921	2.109	0.911

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

The flop changes the picture. 33 does best on low rainbow flops (nine high or lower), at 77.02%, and worst on rainbow flops topped by a ten or better, at 46.36%. Rainbow flops topped by a ten or better and monotone flops favor ATo, the hand that is behind overall.

ATo against 33 by flop texture, in percent
Flop	Share of flops	ATo wins	Ties	33 wins	ATo equity
Rainbow, ten or higher	24.717	53.521	0.242	46.237	53.642
Rainbow, nine or lower	6.314	22.531	0.897	76.572	22.979
Two-tone	46.485	47.523	0.360	52.117	47.703
Monotone	5.151	49.166	2.246	48.588	50.289
Paired	17.333	46.982	0.677	52.341	47.321

A rainbow flop shows three suits, a two-tone flop repeats one suit, a monotone flop is a single suit, and a paired flop repeats a rank.

Compared with a random hand

Relative to a random opponent, ATo changes by -15.04 points (baseline 62.72%) and 33 by -1.37 points (baseline 53.69%).

ATo 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
ATo, all flops	47.677	62.722	-15.045	0.76013
ATo, rainbow, ten or higher	53.642	62.722	-9.080	0.85523
ATo, rainbow, nine or lower	22.979	62.722	-39.743	0.36636
ATo, two-tone	47.703	62.722	-15.019	0.76055
ATo, monotone	50.289	62.722	-12.433	0.80178
ATo, paired	47.321	62.722	-15.401	0.75446
33, all flops	52.323	53.693	-1.370	0.97448
33, rainbow, ten or higher	46.358	53.693	-7.335	0.86339
33, rainbow, nine or lower	77.021	53.693	+23.328	1.43447
33, two-tone	52.297	53.693	-1.396	0.97400
33, monotone	49.711	53.693	-3.982	0.92584
33, paired	52.679	53.693	-1.014	0.98111

Does a shared suit matter?

Of the deals of this matchup, 60 share a suit (33 at 52.24%) and 12 do not (52.73%). 33 does better with no shared suit, by 0.49 points.

ATo against 33 by suit overlap, in percent
Deals	Specific deals	Share of deals	ATo wins	Ties	33 wins	ATo equity
Share a suit	60	83.33	47.495	0.528	51.977	47.759
No shared suit	12	16.67	47.035	0.462	52.503	47.266

How often this matchup comes up

You will meet this exact matchup 0.0089% of the time in a random heads-up deal: 144 of 1,624,350, counting either seat order.

A worked example

Say each player puts $100 in before the flop, making a $200 pot. On average 33 takes back $104.64 of it, which is $4.64 more than it put in, and ATo takes back $95.36, $4.64 less than it put in.

Think in thousands: about 521 of 1,000 go to 33, about 474 go to ATo, and about 5 are chopped.

The same matchup from the other side

Read it from the other side: 33 against ATo is the same matchup with the numbers swapped, so 33 holds 52.32% and ATo holds 47.68%. That address sends you back to this page.

AsTh against 3d3c is a ready-made deal for the calculator, with no suit in common between the hands. The neighboring matchups below replace one hand with another of similar strength.

How this was computed

We counted every case. Each suit pattern of the 72 specific ATo against 33 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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