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soft21: Theory of Blackjack, Chapter 15
Hi,
I've been struggling to fully understand the 'Interactive Approximation' mechanism described in chapter 15 of TOBJ, and I'm hoping someone might be able to assist me.
There are a few things I am unsure about, but my first bit of confusion comes right at the start, in the 6-card example; I don't understand how the figures for P12, P13 and P23 are arrived at.
Given the formula -
Pkl = (N/2)M + ((N-2)/2)Mkl - ((N-1)/2)(Mk+Ml)
and the various M values, I get different results to the ones given.
E.g.,
M=516, M1=768, M2=636, M12=1080
therefore,
P12 = 3*516 + 2*1080 - 2.5 * (768+636) = 198
[but the given figure is 190]
I've been putting together some software to generate approximate dealer probabilities in the way that is described in this chapter. I get reasonable answers when doing it the simple, 'Method A', way; but my attempt at the two-card-removal, 'Method B' approach is way off.
The fact that I don't really understand the theoretical basis behind this approach, and can't quite make sense of the introductory example leaves me rather clueless at this point. :-)
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