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501 Essential Backgammon Problems #360

Posted By: Taper_Mike
Date: Sunday, 29 December 2013, at 7:32 p.m.

In Response To: 501 Essential Backgammon Problems #360 (Igor)

 White is Player 2 score: 0 pip: 22 Unlimited GameJacoby pip: 118 score: 0 Blue is Player 1
XGID=-BBA-CBB-------------dABf-:1:1:1:32:0:0:1:0:10
Blue to play 32

### Cover or Run?

Blue needs 52 pips plus half a roll to save the gammon. At 8 pips per roll, he will need 7 rolls to accomplish that. Unfortunately, White needs only 10 crossovers to win. He will probably be off in 6 rolls or less. Saving the gammon is going to be difficult. Against that backdrop, Blue needs to find a play for this 32.

The first decision is whether to split off the 23pt in an effort to shake loose a blot when White rolls a 2. I think now is the time. Otherwise, White can play all his numbers safely on his next turn.

Next is the choice whether to cover inside or not. Moving 5/3 wastes two valuable pips that could be used to race. White will leave a blot whenever he rolls 23, 24, 25, or 26. Blue will be 30% to hit. The compound probability that White leaves a blot that Blue hits is (8/36)*(11/36) = 88/1296 = 6.8%. Is Blue’s chance of saving the gammon so low that he should cater to his 6.8% chance of hitting?

I am not sure!

My first instinct was to make the 4pt. Now that I have computed the 6.8% figure, however, I am going to take the extra crossover.

U (Up) = 23/18

Mike

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