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AQo vs 44

AQo
VS
44
46.4%
equity for AQo — 44 takes 53.6%

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

AQo Win
46.1%
Tie
0.5%
AQo Lose
53.4%
Card combinations
72
AQo vs random
64.4% · #14
44 vs random
57.0% · #48
Breakdown

Win, tie and loss for AQo

Win 46.1%Lose 53.4%

When AQo and 44 get all in before the flop, AQo wins 46.4% of the time and 44 takes 53.6%. Broken down, AQo wins outright 46.1%, chops 0.5% and loses 53.4% — a margin of -7.2 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 46.1% (for example As Qh against 4d 4c); with both suits shared it is 46.7% (As Qh against 4s 4h). That is a spread of 0.61 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 AQo 38.9%, 44 35.9%, random 25.2%. AQo gives up 7.5 points and 44 gives up 17.7, 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, AQo is worth 64.4% against a random hand (rank 14 of 169) and 44 is worth 57.0% (rank 48). The gap between them in the ranking is only 7.4 points, yet head to head the gap is 7.2 points, which is roughly what the ranking table predicts.

Framed as a run of one hundred identical all-ins, AQo scoops roughly 46 pots, splits about one, and loses the remaining 53. Against eight random opponents rather than this one specific hand, AQo would be down to 17.5% and 44 to 13.1%, so the shape of this particular confrontation matters far more than either hand's standing in the overall ranking.

From 44's side, 53.6% 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 53.6% of the pot you are playing for. AQo holds the other 46.4% 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 44 really does hold exactly 44; against the wider range a player would actually get all in with, AQo's 46.4% moves. Use the individual pages for AQo and 44 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.

ConditionExampleCombosAQo EquityWinTieLose
No shared suitAs Qh vs 4d 4c1246.1%45.9%0.4%53.7%
One shared suitAs Qh vs 4s 4d4846.4%46.1%0.5%53.4%
Both suits sharedAs Qh vs 4s 4h1246.7%46.4%0.6%53.0%
Three-way

Adding a random third hand

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

AQo
38.9%
vs heads-up -7.5pt
44
35.9%
vs heads-up -17.7pt
Random third hand
25.2%
Player count

At a bigger table

Random opponentsAQo44
164.4%57.0%
246.9%37.0%
430.3%20.7%
817.5%13.1%

Related

FAQ

AQo or 44 — which is ahead preflop?

44 is the favourite. AQo takes 46.4% and 44 53.6%, a margin of 7.2 points, with 0.5% of hands ending in a chop.

Do the suits change AQo vs 44?

Yes. With no shared suit it is 46.1%, and with both suits shared it is 46.7% — a swing of up to 0.61 points.

What happens three-way?

With one extra random hand in the pot the split is AQo 38.9%, 44 35.9%, random 25.2%. AQo drops 7.5 points compared with heads-up.

424 words / 29 distinct figures — Method