A9s is dominated so it is worst by default.
33 is the next worst as it's up against 5 discrete overcards.
AQo is second best as it is missing an out and has to improve to beat the threes.
J7s is best as it can improve by hitting either card. I am betting for the sake of this puzzleit's suited-ness pushes it right over the edge to beat out the prettier AQo. Not to mention the miniscule boost it gets from being (barely) connectable.
That said... that's just the math. I would rather PLAY the AQ.
I'd always rather have a pair than not. Not sure how 33 isn't in first when it is the favorite vs any of the other hands. Pretty easy, 33, AQ, A9, J7. If you think otherwise, play a big pot with AQ and watch your stomach sink when the board is 2, 7, 9.
## isn't in first because it is not a favorite against all three hands. Lets take a look at what Poker stove has to say:
A9 18.475%
33 26.090%
AQ 27.692%
J7 27.743%
I had a feeling the A9 may be low but I didn't think it was the worst.
Yes, I agree that its not the favorite against all three, I don't believe that was the question. If you were matching those hands up individually, 33 is certainly the favorite.
Now that I actually looked, 33 is the clear favorite against A9 and AQ but is a dog against J7. I thought that was interesting.
The revealed wsop percents include folded cards from other players as well as the 4 live hands.
It's a useless question in a vacuum.
just some fun