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| XGID=--A-BaC-CBB--Ba--a-bbcbab-:1:-1:1:64:5:6:0:7:10 | |||||
| Blue to play 64 | |||||
What’s the play if you don’t hit?
The best non-hitting play looks like O = 13/9 6/2. Anything else leaves a direct shot, fails to cover the 2pt, or else buries a dilly builder down on the 2pt.
If Blue makes play O, White will have 2 numbers that hit (62), 8 numbers that turn this into a non-contact position (66, 65, 64, 63), and 6 more that run out to his 14pt or 13pt (61, 52, 42). That’s 10 numbers that would make White a prohibitive favorite, and 6 more that would (almost) turn this into a one-roll proposition. Out of these latter 6, if we give Blue 2 hits, then White becomes a prohibitive favorite in the other 4. That bumps the total of number of “winning” rolls for White in this estimate to 14, roughly 39%.
If Blue attacks, J = 9/5*, 8/2, White will hit a return shot with 15 rolls (any 5, plus 41, 32). Four of those are jokers that also let White close his board (65, 52). The rest of the time, Blue will be on the bar with a 30% chance to hit the blot in White’s board, and White’s runner, at least for the moment, will still be behind Blue’s four-point block. The 4 jokers are 11%, and if we say that the other 11 hits demand an immediate return hit, then the compound chance that White hits and leaves a blot that Blue misses is (11/36)*(25/36) = 30% of 70% = 21%. That means White becomes a prohibitive favorite 32% of the time.
Given that this is DMP, and also that containing White’s runner is critical, the choice seems clear.
Mike