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your getting ~15 to 1 when you raise and he 3bets.

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After we raise and establish that he has the case A, can we make up the deficit in implied odds?

If the Q does fall, there is only 2 possible combos of AQ (which we can discount) out there and villian is drawing to 7 outs 99% of the time.

This means villian has only 15% equity if we make our hand on the turn. We have 85% of all money from there on in.

I think a conservative estimate would be ~5BB implied earnings. Hero owns 4.2BB or 8.4sb.

8.4sb + 15sb = 23.4sb requiring 22.5:1.

But then there are the time he slows down on the turn to aggression because he fears his kicker is no good but then go nuts when he fills up on the river.

I think the marginal +EV you might have by making the call is negated by the times he flips over A5.

I think it's close but I think folding is better.

This hand/situation coming up so rarely + you hitting your 2 outs on the turn so rarely + 15% chance of taking a severe beating when you hit = fold.