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last roll situation
Posted By: scotty
Date: Sunday, 6 July 2014, at 1:01 p.m.
I'm struggling to understand the basics of match equity, and how to apply it to make cube decisions. It appears to me that the leader at 2a 3a can offer the cube in a last roll situation when he has less than 50% chance of winning the game. Is this correct? It certainly seems counterintuitive until one begins to delve into the problem. Please consider the following situation:
Match score is 2a 3a. Leader has 2 checkers remaining to bear off, on 4pt and 3pt. Trailer has one checker remaining on his 1 pt. The leader is on roll. The cube is at 1. We'll use Kit Woolseys MET.
The leader has 17 shots which bear off both men and win the game.
If the leader doubles and wins, the leader wins the match, and MWC = 100. If the leader doesn't cube and wins, he will lead 20 Crawford and MWC= 75%.
If the leader doubles and loses, he will trail 21 Crowford and MWC = 30%. If the leader doesn't cube and loses the score will be tied 11, and MWC = 50.
So the leader is risking 20% to gain 25% by offering the cube.
The leader has 17/36 chances to gain 25% and 19/36 chances to lose 20%.
The leader's MWC increases by 25*(17/36)  20*(19/36) = 1.25 %. Therefore, the leader is better off on average by offering the cube. Cube action= double/take. If the cube was at 2, this would be no redouble/take
Is this analysis flawed? Can the leader really offer the cube with only 17 winning rolls? Is there a simpler way to look at these decisions? Any and all help is greatly appreciated.

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