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Match Play. Red trails 1-4 to 7. Should Red redouble? If redoubled, should White take?
A problem that lends itself to direct calculation.
Red will win this position 5/36 (when he rolls 22, 33, 44, 55 or 66) plus 31/36 x 11/36.
5/36 = 13.9 and 31/36 x 11/36 = 341/1296 = 26.5. the total is 40.4% so for working purposes let’s use 40%.
If Red doesn’t redouble then 40% of the time he will win and trail 3-4 (40% winning chances from match equity tables). That gives 40% x 40% = 16%. 60% of the time he will lose and trail 1-6 (10% winning chances). 60% x 10% = 6%. Total winning chances = 16% + 6% = 22%
If Red does redouble then 40% of the time, he will lead 5-4 (60% winning chances). 40% x 60% = 24%
Ergo, by a small margin (2%) Red increases his winning chances by redoubling.
An XG rollout confirms that Red should redouble but it is very, very close. Obviously White must take the redouble.
d/d. the cube is useless to White