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AKo vs 33

AKo
VS
33
46.6%
equity for AKo — 33 takes 53.4%

Pair against two overcards — the classic coinflip, with the pair a shade ahead.

AKo Win
46.3%
Tie
0.6%
AKo Lose
53.1%
Card combinations
72
AKo vs random
65.4% · #12
33 vs random
53.7% · #67
Breakdown

Win, tie and loss for AKo

Win 46.3%Lose 53.1%

When AKo and 33 get all in before the flop, AKo wins 46.6% of the time and 33 takes 53.4%. Broken down, AKo wins outright 46.3%, chops 0.6% and loses 53.1% — a margin of -6.8 points. Pair against two overcards — the classic coinflip, with the pair a shade ahead.

The same matchup shifts depending on how the suits overlap. With no shared suit the number is 46.2% (for example As Kh against 3d 3c); with both suits shared it is 47.0% (As Kh against 3s 3h). That is a spread of 0.78 points across the 72 distinct card combinations, and it comes almost entirely from whether the two hands are fighting over the same flush.

Add a third player holding a random hand and the split becomes AKo 39.9%, 33 33.7%, random 26.4%. AKo gives up 6.7 points and 33 gives up 19.7, so the underdog loses more than the favourite does. Extra players always eat into the leader's share faster than into anyone else's.

Taken on their own, AKo is worth 65.4% against a random hand (rank 12 of 169) and 33 is worth 53.7% (rank 67). The gap between them in the ranking is only 11.7 points, yet head to head the gap is 6.8 points, which is roughly what the ranking table predicts.

Framed as a run of one hundred identical all-ins, AKo scoops roughly 46 pots, splits about one, and loses the remaining 53. Against eight random opponents rather than this one specific hand, AKo would be down to 19.1% and 33 to 12.8%, so the shape of this particular confrontation matters far more than either hand's standing in the overall ranking.

From 33's side, 53.4% is the break-even point for calling an all-in at 0.87:1 pot odds. Put another way, the call is profitable as long as the amount you have to put in is less than 53.4% of the pot you are playing for. AKo holds the other 46.6% of that same pot.

Two caveats keep this figure honest. First, it is showdown equity across all 72 card combinations with five board cards still to come — there is no fold equity in it, so the value of shoving in practice is usually higher than the raw percentage suggests. Second, it assumes 33 really does hold exactly 33; against the wider range a player would actually get all in with, AKo's 46.6% moves. Use the individual pages for AKo and 33 to see how each of them fares against all 168 other holdings before treating this single pairing as the whole picture.

By shared suits

Overlapping suits move the number

200,000 simulated showdowns per condition. The example column shows one concrete four-card layout.

ConditionExampleCombosAKo EquityWinTieLose
No shared suitAs Kh vs 3d 3c1246.2%46.0%0.5%53.5%
One shared suitAs Kh vs 3s 3d4846.6%46.3%0.5%53.2%
Both suits sharedAs Kh vs 3s 3h1247.0%46.7%0.6%52.7%
Three-way

Adding a random third hand

200,000 simulated showdowns, with the third hand dealt at random each time.

AKo
39.9%
vs heads-up -6.7pt
33
33.7%
vs heads-up -19.7pt
Random third hand
26.4%
Player count

At a bigger table

Random opponentsAKo33
165.4%53.7%
247.9%33.1%
432.4%19.1%
819.1%12.8%

Related

FAQ

AKo or 33 — which is ahead preflop?

33 is the favourite. AKo takes 46.6% and 33 53.4%, a margin of 6.8 points, with 0.6% of hands ending in a chop.

Do the suits change AKo vs 33?

Yes. With no shared suit it is 46.2%, and with both suits shared it is 47.0% — a swing of up to 0.78 points.

What happens three-way?

With one extra random hand in the pot the split is AKo 39.9%, 33 33.7%, random 26.4%. AKo drops 6.7 points compared with heads-up.

424 words / 30 distinct figures — Method