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hope i have the solution
Posted By: scotty
Date: Wednesday, 9 July 2014, at 2:28 a.m.
In Response To: now try this one (Bob Koca)
if blue cubes and misses, does white have a recube?
trailer cubes and wins, score is 0 2 MWC = 100
no cube and wins score is 32 MWC = 40.0530
trailer cubes and loses, score is 4 0 MWC = 0
no cube and loses score is 41C MWC = 18.5640
gain = mwc(cube/win)  mwc(no cube/win) = 59.947
risk = mwc(no cube/lose)  mwc(cube/lose)= 18.5640
with the cube at 2, the bottom of whites window drops to 23% and white will have any easy recube. This example really illustrates the importance of considering how one's actions with the cube affect the decisions of one's opponent! Can blue take white's recube?
Blue must have 50% winning chances to take the recube. However he only has 17/36. If blue cubes, and misses, he will have to drop the recube and leave most of his wins on the table.
MWC if the leader doesn't cube:
the trailers chances of winning with no cube are 30/36 x 19/36 = 44%
Therefore the leaders chances of winning are 56%.
56% of the time, the leader will win one point and lead the match 1a 4a crawford, with MWC = 81.436%.
44% of the time, the leader will lose one point, and lead the match 2a 3a, with MWC = 60%
his weighted average MWC = .56 x 81.4 + .44 x 60 = 72%
MWC if the leader cubes: 1/6 of the time the leader wins 2 points and MWC = 100 5/6 of the time, the leader loses the match and MWC= 0
his net equity expectation if he cubes is 100/6 = 16.7%. He loses 55.3% of his MWC.
I'm not sure how to calculate EMG. I have seen an equation for it somewhere. And i'm not positive that my 'weighed' MWC calculation is valid, but it seems reasonable to me. It appears that this situation is particularly volatile due to blue having substantial winning chance, with most of those wins coming only if the trailer misses. Second, if the leader cubes, he effectively gives up his lead in the match to stake it all on one game, where the trailer has first shot at many of the wins.
I'm sure i would not have seen this over the board. I'll have to figure out the game winning chances where it make sense for the leader to offer the cube at 2a. I've given the cube many times, knowing that it was an auto recube, and have lost matches as a result when my lead in the game turned sour. With the recube available to the trailer, doesn't that effectively mean that the trailers true takepoint is somewhere around 23% at 2a 4a? There are so many interesting question to explore!
Hope i got this one right! Thanks ever so much.

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