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BGonline.org Forums
Recube vig
Posted By: Timothy Chow In Response To: Recube vig (Ray Kershaw)
Date: Thursday, 14 January 2010, at 3:48 a.m.
Ray Kershaw asks if it is possible to have a position where the equities are in the following order: ND > DP > DT.
This situation is sometimes described as "Too good to redouble, take." It's a take because DP > DT, and so if the opponent is doubled then the correct response is to take. However, the person on roll is wrong to double, because ND has the highest equity. It seems that most people say that it's "too good to redouble" (rather than "no double") because the equity of ND is greater than the equity of DP. (As a side note, this probably means I need to introduce another color into my idea of a stoplight chart to represent "too good to redouble, take." At the time, I assumed that this would just be called "no double.")
I'm told that the above scenario can occur in match play, though so far I haven't located an explicit example. Searching around, I've found a couple of supposed examples on the web, but when I plug them into GNU, they always come out saying either "No double, take" or "Too good to redouble, pass" and I haven't found a position yet that causes GNU to say "Too good to redouble, take." (And GNU does have the option "Too good to redouble, take" in its source code.") So I too would be interested in seeing an explicit example.
I'm also told that the above scenario cannot occur in money play. Thinking about it briefly, I couldn't see how to prove this. I then learned that Douglas Zare included a proof (assuming equities exist) in his 25 December 2002 article ("Giving Gifts") on Gammon Village. I haven't inspected his proof but it is undoubtedly correct.
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