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BGonline.org Forums
OLM Sa 05/15/10
Posted By: Chuck Bower In Response To: OLM Sa 05/15/10 (Jason Lee)
Date: Sunday, 16 May 2010, at 5:10 p.m.
16/10 is forced.
The ace is either 16/15 or 10/9. Everyone either knows or can count that the difference in getting hit when four away is one more compared to three away. If that were the only factor then 16/15 would be clear. What are the other factors?
4-4 is a likely (but not sure) game winner for opp, even when it doesn't hit. This can't be said for 3-3, although 3-3 isn't a loser roll for opp when it misses. Also, some of opp's sixes can be a problem and adding 6-3 to to the mix slightly favors staying back. (It matters only 2/36 * 11/36 = 1.7% of the time compared to 1/36 = 2.8% of the time we get hit with the extra shot. Counting 4-4 as only half a hit from above, it looks close.)
Another pair of swing sequences are opp's 5-3 and 5-4 rolls. One hits either way but in the non-hitting situations 5-4 moves past our last checker if we play 16/15, but 5-3 either blots or forces opp to hold the midpoint if we stay on the 16-point. (It's hard for me to quantify the effects of this OtF = "over the forum".)
Finally there is a tertiary consideration in that if we get missed and opp holds the midpoint, only {2-1, 1-1, 3-3} = 4 rolls leave a repeat shot after 16/15 compared to {1-1, 2-1, 3-1, 2-2, 4-4} = 7 rolls after 10/9. Those two scenarios occur (respectively and approximately) 8/36 * 4/36 * 12/36 = 0.85% (note the leading zero :) compared to 12/36 * 7/36 * 12/36 = 2.2% of the time. (Surprisingly this seems to be a bigger factor than the extra shot we get when opp rolls 6-3 after our 10/9.)
Looks very close, but I think I've talked myself into minimizing shots:
16/10, 16/15.
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