Re: Getting "Exact" Indeces trhough Simulation

From Stanford Wong's BJ21

Posted by Pete Moss on 21 Nov 1997, at 1:32 p.m., in response to Getting "Exact" Indeces trhough Simulation, posted by MathProf on 20 Nov 1997, at 4:33 a.m.

I've been trying to thing of a better word than "exact". So far, nothing.

You don't really need a regression (smoothing) of the overall data. You are only interested in finding one tc that optimizes a yes/no decision. How closely you can fit a curve to the EV (or other score function) at tc's far removed from the decision point doesn't matter.

I recently posted "Moss's Algebraic Approximation", which is an analytical rather than simulation method, but the principles are the same. It is an improvement over similar methods I have seen, but it shares several defects with them:

1. The tc to EV function is modeled as a straight line. That assumption can break down badly for tc's that are very unlikely (very high or very low indices).

2. The score function is universal -- it penalizes a bad fit at points where the fit is of no interest for purposes of the problem being solved -- points far removed from the index.

3. The residual error score of the fit is tacitly least-squares. An information-theoretic or cross-entropy fit would be more appropriate.

Despite these problems, the method works rather well for tc's that are not too extreme. The index it calculates for taking insurance using Hi/Lo at single deck indicates the right decision in every possible situation except when the running count is +1 and exactly 37 cards remain unseen.

Having dissed regression, I'll now have to come up with a better alternative. I have a better analytical method than the linear least-squares fit, but I've been reluctant to describe it on the web because it is rather involved. For simulation, I think some simple interpolation method would work well. More later.

Pete

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