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[QUOTE="c0rnBr34d, post: 5948821, member: 394557"]
Another glaring error in estimation and down the rabbit hole I go.  So from the logic above correcting for probabilities.  If each V has a 33% chance of having an Ace based on the range combo counts above the probability of neither of them having an Ace is about 44% instead of the 67% I used above.  Similarly to how if you have two coin flips the percentage chance that neither of them will be heads is not 100% but 25% instead (1-1/2)*(1-1/2)=(1/2)(1/2)=1/4=25%.  So even if we think 45% of each of their ranges are Ax which is much higher than reality in my opinion then the probability of neither of them having an Ace is (1-.45)*(1-.45)=(.55)(.55)=30.25%.

Going back to our EV calculation even if we only get our bet through 30% of the time we are profitable here:  (27BB * .30) - (10 BB * .70) = 8.1675 - 7 = +1.1675 BB on average.

And that's when 45% of both players continuing ranges contain and Ace and they never fold to the cbet.  The more I think about it the more I like the cbet against standard ranges.  The more narrow the ranges get the more I like checking.  For example if BTN 4B and somehow we just called then I like the check.  The top of ranges are Ace heavy and ranges like QQ+, AK (83% Ax) or JJ+, KQs+, AQ+ (64% Ax) and when we block the high pairs we want them to have it makes it even more likely that they have an Ace.  I do not think this is the case here though with a small out of position 3 bet.
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