The ole' AQ vs. A3 suck out...

[Oriuki]

I'm all in pre-flop with my AQ and get called by A3, flop comes 332 to bust me out of the tourney.

If I'm correct in the other guy being a 3:1 dog, that still gives him a 25% chance to draw out on me over the next 5 cards. That seems really high given that there are only 3 cards in the deck that can help him. Could some explain the math behind that 3:1 calculation?

[Dave B]

he only needs one 3 to take a lead. He has 3 outs (3 3s still in the deck) each out has a 2% prob for each card to come. So-3x2x5= about 30% Consider that you both might hit, str8 and flush possibilities and there you are.

[Sean_in_NJ]

I'm all in pre-flop with my AQ and get called by A3, flop comes 332 to bust me out of the tourney.

If I'm correct in the other guy being a 3:1 dog, that still gives him a 25% chance to draw out on me over the next 5 cards. That seems really high given that there are only 3 cards in the deck that can help him. Could some explain the math behind that 3:1 calculation?

Well, he could also make a low straight or a flush in the suit of his ace. There are a few situations where you would chop, although they're less likely because it would be difficult to counterfeit your Q. Long story longer, it's not just the remaining 3's that will win. I'm not particularly inclined to do all of the math, but that's the general idea.

[Oriuki]

I thought for 3 outs each card had a 6% chance of hitting? That again totals 30% for each of the 5 cards so its moot but I was curious how/where you came up with 2% per card.

A secondary question would be if I held AA and again he had A3, then he needs 2 of the 3 remaining 3's. Would the math then roughly be prob. of hitting one 3 (6%) times the prob of hitting a second 3 (6%) = .0036? So it's a 275:1 dog?

[suitedaces84]

I thought for 3 outs each card had a 6% chance of hitting? That again totals 30% for each of the 5 cards so its moot but I was curious how/where you came up with 2% per card.

A secondary question would be if I held AA and again he had A3, then he needs 2 of the 3 remaining 3's. Would the math then roughly be prob. of hitting one 3 (6%) times the prob of hitting a second 3 (6%) = .0036? So it's a 275:1 dog?

It's not quite that bad due to the straight and flush possibilities. It's something like 20:1. There's a link floating around this site to find the exact values of all these things. There are 48*47*46*45*44 possible boards given only your cards and your oppoents cards, it's practially impossible to figure odds preflop by hand.