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Dropping the free double

Posted By: Maik Stiebler
Date: Sunday, 9 December 2018, at 7:57 a.m.

In Response To: Dropping the free double (Michael)

Does this answer the OP?

Yes. Dropping the "free take" (at 1away:odd away) is basically giving up a winnable game in exchange for the right to use the "free drop" (at 1a:even away) later. So, OP is basically the question, "What's the value of the right to use the free drop when n->inf". My answer, if expressed in a slightly obfuscated way in my original response, is basically: The value is that you get to wait until 31P 54 happens and then get to restore the position to the normal starting position.

I derived the equation b*b*b*x=0.365*a*b*b*x+0.200*a*b*x+0.008*a*x in my original response (still based on the faulty assumption that 31P 62S is the critical line). Maybe it is more instructive to look at the following equivalent:

1/a=(0.365 + 0.200/b + 0.008/b^2)/b,

where the left hand side represents the sacrifice at 1a:odd a (you improve opponent's game winning chance from a to 1) and the right hand side represents the gain of using the free drop at a later 1a: even a (the dividend is the MWC in an unspecified unit if you take after 31 62, the divisor [b] is the value of the starting position in the same unit).

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