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OLM 20140405A  The Prime Factors
Posted By: kruidenbuiltje
Date: Sunday, 6 April 2014, at 12:00 p.m.
In Response To: OLM 20140405A  The Prime Factors (Jason Lee)
Sylvester's Law states that a player with 2 out of 3 advantages on position, race and threat has a double.
Applied to the problem this would mean a plus in position, and a minus in race. So if we were to give blue a plus in threat, he would score +1 on the Sylvesterscale, so No Double.
I guess the Sylvester's Law is applicable in general middle game positions, but this position is far too specific.
The combination of entry from the bar and primes will sometimes give bad entry's. And since blue has a rather threatening prime and great outfield control, he has several good/very threatening entry's.

Blue has 4/36 fans,
but his entry's with a 1 or 4 can be used to slot the 5th prime point.
An entry with a 3 can be used to create a broken 5prime (creating more future badentrys or forced wastemoves for white).
Entry's + 5 or 6 give triple outfield coverage against no extra risk.
The only left entry is D2, blue can use this to shift the 8point to the 4point (since this has some risk involved, I will not call this a good entry).
So blue has 25/36 good entry's.

How about the white entry's? Because of the blue prime, white has more entryworries.
His entry's with a 3 or 5: {35,25,15,D3} = 7/36 are bad.
The entry's with a 6 are good for jumping the prime.
The entry's with a 1,2 or 4 will not create problems.
So white has 25/36 good/reasonable entry's.

But the white entry's are not as good as blue's since they do not contain a threat, except maybe the entry's +6, which threaten to escape a checker.
Positions where both sides have equal chance of a good number are Double/Take. The blue numbers are qualitively better, but this is compensated by white's enormous raceadvantage.
So I say Double/Take.

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