AJo vs 33: preflop equity

AJo against 33: the numbers

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.

With only 5.34 points between them, the board decides this matchup far more than the cards in hand. A split pot comes up on 0.53% of boards, so the wins and the equity differ by half of that.

For context, AJo sits at number 15 of 169 starting hands and 33 at number 66 when each is run against a random hand.

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.

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

Split by what the flop looks like, 33 peaks at 78.69% on low rainbow flops (nine high or lower) and bottoms out at 46.45% on rainbow flops topped by a ten or better. The lead reverses on rainbow flops topped by a ten or better and monotone flops: there AJo is the favorite even though 33 is ahead overall.

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

How much does the opponent matter? Compared with its random-hand 63.56%, AJo changes by -16.23 points, and 33, from 53.69%, by -1.02.

Does a shared suit matter?

The suit split reads 52.59% for 33 with a shared suit and 53.08% without one. 33 does better with no shared suit, by 0.49 points.

How often this matchup comes up

How often does it happen? 72 of the 1,624,350 ordered deals (0.0044%) are AJo against 33, and 144 (0.0089%) if either hand may sit in either seat.

A worked example

Say each player puts $100 in before the flop, making a $200 pot. On average 33 takes back $105.34 of it, which is $5.34 more than it put in, and AJo takes back $94.66, $5.34 less than it put in.

In 1,000 deals of exactly this matchup, expect about 524 won outright by 33, about 471 won outright by AJo and about 5 split.

The same matchup from the other side

33 versus AJo is this same page seen from the other hand: 52.67% for 33, 47.33% for AJo.

Keep exploring

AsJh 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.

• Open AsJh against 3d3c in the equity calculator
• AJo combos
• 33 combos
• AJo vs T8s
• AJo vs T9o
• KQs vs 33
• All hand matchups