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It's Getting Better All The Time
Posted By: kruidenbuiltje
Date: Tuesday, 20 August 2013, at 8:56 p.m.
In Response To: It's Getting Better All The Time (David Rennie)
1)
Question 1, will the blue front position break?
Blue has 11 pips to spare before he has to throw a 5 or 6
{D4,43,4x,41,D3,3x,31,D2x,x1,D1} = 16/36
average pips = (16+14+8+10+12+6+4+4+2+4)/16 = 5 pips
So 11 pips to spare equals 3,2 moves to throw a 5 or 6.
Chance that this doesn't happen = 16/36 ^ 3,2 = 7,5%.
Blue might break later because the other 2 checkers won't escape,
so the result is somewhat higher.
Answer: The blue front position will break in say about 10%.
Question 2, will white enter and jump the 5prime?
Let's give white 4 moves to succeed
Possible sequences: {61,x,x,x}, {1 except 61,6 except 61,x,x}, x = anything
The first sequence has 4 permutations
The second sequence has 6 permutations
chance for first sequence = 1/18 x 4 permutations = 4/18
Chance for second sequence = 9/36 x 9/36 = 1/16 x 6 permutations = 6/16
So the chance of white escaping within 4 moves = about 60% (4/18 + 6/16)
Not all white escapes are wins, say blue hits 1/3rd this makes 40% chance for white of crossing the outfield.
So white gets 10% (blue breaks) + 40% of the rest = 46%
So blue has 54% chance of winning and he has some gammonchances (for instance after hitting the other white blot or the escapee)
Blue should double, white should take.
2) 8 free pips = 2,6 moves before a 5 or 6
16/36 ^ 2,6 = 12,1%, so white has 5% more chance
3) 7 free pips .. 16/36 ^2,4 = 14,3%, so white has 7% more chance (vs. position 1)
2) and 3) are No Double
4) Blue's (Gammon)chances are higher, TGTD or maybe DP

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