AKs vs 33: preflop equity

AKs against 33: the numbers

Here a suited hand (AKs) meets a pocket pair (33). 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 1.58 points between them, the board decides this matchup far more than the cards in hand. About 0.58% of boards chop the pot, which is why equity sits slightly above the win figure for both hands.

Ranked by equity against a random hand, AKs is number 8 of the 169 starting hands and 33 is number 66.

The total is exact: 24 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.

The last column is the break-even price: the pot odds a call needs to offer, as a ratio of pot to call.

Who is ahead on which flops

Split by what the flop looks like, 33 peaks at 76.87% on low rainbow flops (nine high or lower) and bottoms out at 45.79% on rainbow flops topped by a ten or better. AKs takes over on rainbow flops topped by a ten or better and two-tone flops, so the favorite before the flop is the underdog on those boards.

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

The table below sets each hand against its own random-hand baseline: a change of -17.84 points for AKs, from 67.05%, and -2.90 for 33, from 53.69%.

Does a shared suit matter?

Suit overlap shows up in the numbers. With a suit in common 33 has 50.98% equity, and with none in common it has 50.61%. 33 does better with a shared suit, by 0.37 points.

How often this matchup comes up

AKs against 33 is made up of 24 specific-card matchups in one seat order, 0.0015% of the 1,624,350 ordered deals, and 48 counting both seat orders, 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 $101.58 from the $200, up $1.58; AKs averages $98.42, down $1.58.

A thousand deals look like this: 33 takes 505, AKs takes 489, 6 are ties.

The same matchup from the other side

33 against AKs adds nothing new: it is 50.79% for 33 and 49.21% for AKs, the same figures reversed.

Keep exploring

AsKs against 3h3d 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 AsKs against 3h3d in the equity calculator
• AKs combos
• 33 combos
• AKs vs T8s
• AKs vs T9o
• 77 vs 33
• All hand matchups