Thursday, December 10, 2009

Interesting Double Dillema



Here is an interesting situation that can often arise when beginners play in tournaments.
To understand this imagine as if your tournament life is on the line and you are up against a Giant of Backgammon. Why of course its only a 7 point match and if luck is on your side than hey...you could have a story to tell your grandkids (not another granpa bg story)
The question is.. what is the cube action here?



is mid 1700's FIBS player

score: 0
pip: 102
7 point match
pip: 47
score: 2

is Backgammon Giant XGID=-ECbCBA-A----a--a--bb-cbb-:1:-1:-1:00:2:0:0:7:10 on roll, cube action?
I'll leave this up before
I comment on it and reveal what I would have done.



For money this is a clear BEAVER. Black has a 52% chance of wining with about 9.5% gammon. White has the other 48% with about 4.5% gammon. For match play. This situation comes down to the match equity tables. Using the ExtremeGammon MET and rolling it out over 5000 times.. the result is NO DOUBLE/TAKE Black wins 50.5% with 12% gammons White wins 49.5% with 4.63% gammons Redoubling is shown as a -.069 error All of this however assumes opponents of equal ability. If we know that the player on roll is considerably worse (150-200 Elo points) than the Giant with the blots exposed, the situation changes considerably. Gone is the 23.6% from going down 4-0 and there is no 50% at 2-2... If we take the FIBS rating conservaively and apply the Trice/Jacobs MET tables for a rating difference of 100 points: Black will be 18.3% down 4-0, and 43.9% tied 2-2. This means that it favors black to play a few games as possible and here is a perfect opportunity. By doubling black with either be down 6-0 or up 4-2.. of course if black pulls off the gammon win he'll win it all. Whites reredouble will be a very slim window as black can take down to 7.7%. At -100 Elo points Blacks double is only a -.02 error.. Im not going to manually extrapolate the rest now but there is a 5% swing here for 100 points.. at 150 it will be correct to double. The paradox is that the worse player will not know any of this.... unless that player is you or me and we have a grasp.... but what if knowing this only makes us -100 to the Giant?...

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