Hypothetical Hand--Math & Probability Question

[LondonBroil]

Suppose your playing any limit and get dealt AA. 4 callers to you, you raise, blinds fold, 4 callers call.

Flop comes AKQ rainbow. Checked to you, you bet, all 4 call.

Turn is a small rag completing the rainbow. 1st player bets, call, call, call, you raise, 1st player 3-bets, call, call, call. Action on you and all 4 callers flip up 10J. Do you...

A. Fold
B. Call
C. Raise

and why?

[nathanielt]

raise, you've seen 22 cards out of 52, leaving 30 cards unseen. With 10 outs, you have a 1 in 3 chance of hitting, and are getting paid 4 to 1 on every bet.

[slavic]

Your odds a ~3.6 to 1 so you make .40 for every dollar you put in. Cap it if they will.

[slavic]

Correction odds change since we know the other hole cards. ~2.9 to 1 so capping is even more correct in fact it's almost criminal not to.

[Homer]

You're getting 4:1 on the cap, so the question is whether your odds of filling on the river are better than 4:1. In this situation, there are 38 unknown cards, of which 10 fill you up. Hence, you are 2.8:1 against filling on the river, making this an easy cap.

Rather than going through this computation you could reason that without knowing any of your opponent's cards, you are 3.6:1 against filling on the river. Since you know your opponents' hole cards, and none of them lower your outs, your odds will be even better.

-- Homer