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BGonline.org Forums
Prioritising Contact After the Hit
Posted By: Daniel Murphy In Response To: Prioritising Contact After the Hit (ah_clem)
Date: Friday, 25 May 2012, at 5:13 p.m.
Stick and Neil have already noted that if the question was to slot the 8 point or not, slotting is wrong with Blue holding the cube, and right with White holding the cube. I wanted instead to address this:
Is hitting correct here? Right now, white needs a 1 and then a 6 to escape. If we put her on the bar, she needs a 2 and then either a 5 or a 6. Granted, it's not much of a difference, but I wouldn't hit here.
Rejecting the hit is indeed wise, but I would call that difference "huge." Numbers:
Goal in 1 roll in 1 or 2 rolls in 1, 2 or 3 rolls Chance of rolling a 2 and then either a 5 or 6 11.11% 29.63% 47.29% Chance of rolling a 1 and then a 6 5.55% 17.05% 30.41% That hitting makes it much easier for White to roll well is only part of the difference. The other part is that it makes Blue's job harder. After playing 7/1*(2) Blue has only one way to use his five spare checkers to complete a 6-prime -- by making the 2 point. Best play preserves Blue's chance to make a 6 prime by making the 8 point and then either (1) advance the prime by making the 2 point or (2) if Blue rolls very badly, by then attacking the ace point, in which case, if Blue makes the ace point but still has the 7 or 8 point, White would only escape with either 2-5 or 2-6, but not both 2-5 and 2-6.
To put that another way, if Blue makes the ace point, he has a 4-prime in front of White and 5 spares to complete his prime. If Blue keeps the 7 point, he has a 5-prime and 5 spares to routinely complete and advance his 6-prime and closeout. Nearly always, if Blue slots the 8 point, he'll make the 8, then the 2 and then the 1, or make the 2 and then the 1 without making the 8. Even in Blue's most awkward sequences, he'll have a 4-prime and 7, not 5, spares to work with -- the extra 2 spares being the ones that are dead on the ace point if Blue plays 7/1*(2).
Since 7/1*(2) makes the closeout harder, White not only gets more ways to escape, but is likely to get more rolls to try.
Just showing my work:
Probability of rolling a 2 followed by either a 5 or a 6 One roll: 4/36 0.111111 One or two rolls: 4/36 0.111111 7/36 * 20/36 + 0.108024 25/36 * 4/36 + 0.077160 One, two or three rolls: 4/36 0.111111 7/36 * 20/36 + 0.108024 25/36 * 4/36 + 0.077160 7/36 * 16/36 * 20/36 + 0.048010 25/36 * 7/36 * 20/36 + 0.075017 25/36 * 25/36 * 4/36 + 0.053583
Probability of rolling a 1 followed by a 6 One roll: 2/36 0.055555 One or two rolls: 2/36 0.055555 9/36 * 11/36 + 0.076388 25/36 * 2/36 + 0.038580 One, two or three rolls: 2/36 0.055555 9/36 * 11/36 + 0.076388 25/36 * 2/36 + 0.038580 9/36 * 25/36 * 11/36 + 0.053047 25/36 * 9/36 * 11/36 + 0.053047 25/36 * 25/36 * 2/36 + 0.026791
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