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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 bear-off quicker

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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 4-point) 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.

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2. 11/36

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3. After a hit white has some semi-escape 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%.

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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% win-chance, the average chance of bearing-off quicker is 65%.

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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 gammon-race:

After 16/9 we may waste 2 pips extra but we should add a little waste for the situation where white throws a 1-2-3-combi and we fan.

Let's say 3 pips, that's about 6% gammons.

I think staying is still correct.

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Answer: 16/9

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