OK, so the 100bb number doesn't directly come up in this calculation, then.

The ESS at the time you begin the analysis, i.e. the turn, is what matters.

Whatever money is already in the pot is dead money and it doesn't matter how it got there, it is not yours. If we want to consider the value of that money, then we need to start at a time before that money got there. When we analyze your hand from the turn, we're saying, maybe what we did to get to this point was perfect, maybe it was junk, I don't care. I only care about how to make the best decision from here going forward, given what information I now have.

This may mean that we're solving for the EV in a situation and no matter how much EV we can get from this line, we lost so much getting to this spot that the whole line from blinds to showdown is -EV. That's OK. We still know that, given where we started, we made the best of it.

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So in either or both of your scenarios above, tell me how much the ESS is at the start of our analysis. I.e. what is the ESS at the point where you are about to make the semi-bluff?

Then plug that number into the EV calculation and solve for x again.

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IMPORTANT NOTE: I've gotten a bit tripped up in exactly what x is. I stated in my first post that x is the % that Villain calls OTT. We keep talking about how much Villain folds, so I may have said some backwards things about that greater than or less than sign and whether it means that Villain need to fold more or less than that number.

To be perfectly clear: x is the rate of Villain's calls OTT... and not the rate of Villain's folds OTT.