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## [Bug-gnubg] Match math mysteries

 From: Petr Kadlec Subject: [Bug-gnubg] Match math mysteries Date: Sun, 14 Dec 2003 18:13:36 +0100

```Hi all!

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When recently discussing a match with a friend (with help of gnubg's analysis), I figured something which seems strange to me: Situation: we are playing a match and I am trailing at 3-away, 2-away. During the game, the opponent doubles and I take. BUT NOW: What should I do? After some (painful...) thinking, I believe I have a compulsory double, since when I lose the game, I lose the match, but if I win with 2-cube, I will still be 1 point away, but with a 4-cube whoever wins the game, wins the match; so that I have nothing to lose. More exactly (at least I will try, I am _really_ not good at bg theory), I see it this way:
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At 2-cube, my MWC2 = Ps * C + Pg + Pbg, where Ps,Pg,Pbg are probabilities of single/gammon/backgammon win, C is MWC when leading 1-away, 2-away (which is, I believe, 0.7 according to Woolsey MET).
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At 4-cube, my MWC4 = Ps + Pg + Pbg

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As C < 1, always MWC4 > MWC2, so that I should double, no matter of my winning chances (except the situation Ps=Pg=Pb=0, but that is obviously uninteresting).
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Now you may ask, where I see any problem? The problem is that according to gnubg analysis, the situation is "Optional double, take". OPTIONAL? HOW SO? I have tried more positions, and even when gnubg says the position is "double, take", the difference between this and "no double" is very small. I would expect the difference to be equal to (1 - C) * Ps, for C = 0.7 it is 0.3 * Ps. For example, in position 3N0BAIB77wEAAA, gnubg reports P(win)=0.227, with double/take MWC (correctly) equal to that, but no-double MWC is reported to be also equal to 22.67%, although I would expect it to be 0.7 times smaller (ca 16%). But a rollout result is the same -- no difference...
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I tried to look to the source to find some explanation, but when something I believed to be a MWC was sent to eq2mwc, I gave up. :)
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Where am I wrong? [I am unable to believe it could be gnubg who is wrong here...] Could someone please help me understand that?
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Thanks,
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