AQo hand - turn decision (playalong)

[Dave G.]

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You are getting 6.5:1 when its back to you. This could be a weaker ace, but not likely. It's more likely to be two pair, a set or a flopped flush. Without a further read on villain I'm not going to assume he's tricky enough to bluff-raise.

My instincts say to call down. We can improve to a hand that can win if we are behind two pair or something, and without knowing much about villain, I'm not ready to fold top pair just yet. I expect to pay off most of the time.

I'd like to break this down mathematically though, so here goes. If villain has a set or a flush you are drawing dead. In terms of probability, the chance that villain was dealt 2 spades is roughly 4.3%. The chance that he was dealt a pocket pair that is now a set is about 0.8%. The chance that he has two pair is about 1.7%, and the chance that he has a random ace with an unpaired kicker is about 3.4%. However, this is villains least likely holding, so we can halve this value to 1.7% to try for a more accurate estimation.

It is reasonable to conclude that villain wouldn't be playing this way with much else, unless he's a complete donk. So if we conclude that these are villains only possible holdings at this point and weight the probabilities accordingly, we end up with: 50.5% chance of a flush, 9.5% chance of a set, 20% chance of two pair and 20% chance of a lone ace.

~60% of the time we are drawing dead.
20% of the time we are good.
20% of the time we have 9 outs to a better two pair, which corresponds to a 17.3% chance of improving.

It will cost us 2BB to show down from here. So the EV of calling this down is:

(-2)*0.6 + (-2)*(0.2)*(0.827) + (7.75)*0.2 + (7.75)*(0.2*0.173) = +0.28 EV.

It's pretty close, and given the inaccuracies involved in estimating his likely holdings, I'd err on the side of calling down here. (And hopefully the math is done correctly too...)
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[NAU_Player]

[ QUOTE ]
In white:<font color="#FFFFFF">
You are getting 6.5:1 when its back to you. This could be a weaker ace, but not likely. It's more likely to be two pair, a set or a flopped flush. Without a further read on villain I'm not going to assume he's tricky enough to bluff-raise.

My instincts say to call down. We can improve to a hand that can win if we are behind two pair or something, and without knowing much about villain, I'm not ready to fold top pair just yet. I expect to pay off most of the time.

I'd like to break this down mathematically though, so here goes. If villain has a set or a flush you are drawing dead. In terms of probability, the chance that villain was dealt 2 spades is roughly 4.3%. The chance that he was dealt a pocket pair that is now a set is about 0.8%. The chance that he has two pair is about 1.7%, and the chance that he has a random ace with an unpaired kicker is about 3.4%. However, this is villains least likely holding, so we can halve this value to 1.7% to try for a more accurate estimation.

It is reasonable to conclude that villain wouldn't be playing this way with much else, unless he's a complete donk. So if we conclude that these are villains only possible holdings at this point and weight the probabilities accordingly, we end up with: 50.5% chance of a flush, 9.5% chance of a set, 20% chance of two pair and 20% chance of a lone ace.

~60% of the time we are drawing dead.
20% of the time we are good.
20% of the time we have 9 outs to a better two pair, which corresponds to a 17.3% chance of improving.

It will cost us 2BB to show down from here. So the EV of calling this down is:

(-2)*0.6 + (-2)*(0.2)*(0.827) + (7.75)*0.2 + (7.75)*(0.2*0.173) = +0.28 EV.

It's pretty close, and given the inaccuracies involved in estimating his likely holdings, I'd err on the side of calling down here. (And hopefully the math is done correctly too...)
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potd. good job

[MrWookie47]

Your math is correct, but I could pretty easily see a villain with a pair and one spade raising here. That does nothing but help the case for calling down.