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OLM 20141222B The Prime Factors
Posted By: kruidenbuiltje
Date: Monday, 22 December 2014, at 9:11 p.m.
In Response To: OLM 20141222B The Prime Factors (Jason Lee)
What has to happen to make blue win?
1. White has to leave a shot
2. We have to hit
3. We have to contain
4. We have to bearoff quicker

1. If we choose not to run off the backchecker now, we will probably have to keep our backman there for one more move.
The most probable white structure (2 off the 4point) after the next white move leaves a blot with {63,53,43,D3,31}=11/36
There are better and worse stuctures, but let's take this as an average.

2. 11/36

3. After a hit white has some semiescape rolls:{16,26,25,26}, with 2 containing backmen half of the white escapes will succeed.
That's 4/36 chance each try, I guess white will get 3 tries, the total chance of success = 1  (32/36)^3 = 30%.
So the containing chance = 70%.

4. When we hit white will probably have 7 checkers off, giving blue about a 40% chance to win. But we might pick up a second checker.
Say we do this half the time, and giving us a 90% winchance, the average chance of bearingoff quicker is 65%.

Conclusion:
Winchance = 11/36 x 11/36 x 70% x 65% = 121/1296 x 45,5% = 4,2%
At equal score we should compare this to 8,4% gammons.
Now we come to the gammonrace:
After 16/9 we may waste 2 pips extra but we should add a little waste for the situation where white throws a 123combi and we fan.
Let's say 3 pips, that's about 6% gammons.
I think staying is still correct.

Answer: 16/9

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