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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!

`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:
`

`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).
`
At 4-cube, my MWC4 = Ps + Pg + Pbg

`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).
`

`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...
`

`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. :)
`

`Where am I wrong? [I am unable to believe it could be gnubg who is wrong
``here...] Could someone please help me understand that?
`
Thanks,
Petr Kadlec
-- -----------------------------------------------------------

`If everything seems to be going well, you obviously don't know what the
``hell is going on.
`

**[Bug-gnubg] Match math mysteries**,
*Petr Kadlec* **<=**