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a bit of algebra -- does this make sense?

Posted By: Timothy Chow
Date: Wednesday, 30 March 2011, at 8:37 p.m.

In Response To: a bit of algebra -- does this make sense? (Chuck Bower)

E(o) should be defined as the average equity for all the other rolls, but yes, this is correct. Here's a way to give the argument without writing down formulas. You're splitting the possible outcomes into two (disjoint) cases, A and B. The current equity is going to be the weighted average of the average equities in the two cases (weighted by the probability that the case will occur). Then your observation is that if the current equity equals the average equity in case A, then it must also equal the average equity in case B.

Not sure how this is useful, though. The main reason I personally would study positions with resets would be to find positions where the equity is undefined. If the reset has the form "dance, dance" and the position looks like a double from either side, then the cube value could get exponentially high, creating a divergent series when you try to compute the equity. I don't see how your observation is useful in analyzing this sort of situation, though.

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