I hoped with help of you guys to shed some light on the cube-efficiency riddle of problem 44, but I have made things only muddier. So forget the above posts, it's better they are deleted. I should have prepared myself well, considering the number of viewers here, but I spent also a lot of energy on the other thread, and it was unwise of me to go on while I am tired.
It's about this position:
White - Pips 76
Black - Pips 50
Black to Play 4-3
Code:
18/14 8/5 Eq.: +0,511
0,616 0,002 0,000 - 0,384 0,012 0,000 CL +0,221 CF +0,511
18/15 8/4 Eq.: +0,353 ( -0,159)
0,586 0,002 0,000 - 0,414 0,015 0,000 CL +0,159 CF +0,353
The difference has to do with the cube, but it has to be found out how. White has some flexibility, so at black's next turn the situation will look something like this:
Being curious how the placement of the black checker impacts the cube decisions, I show the rollouts for the checker from the 16 to the 13-point, ignoring the checker in the innerboard by moving it to 3:
White - Pips 66
Black - Pips 40
16-point
Code:
Cube analysis
Rollout cubeless equity +0,267
Cubeful equities:
1. Double, take +0,432
2. Double, pass +1,000 ( +0,568)
3. No double +0,421 ( -0,010)
Proper cube action: Redouble, take
15-point
Code:
Cube analysis
Rollout cubeless equity +0,313
Cubeful equities:
1. Double, take +0,537
2. Double, pass +1,000 ( +0,463)
3. No double +0,442 ( -0,095)
Proper cube action: Redouble, take
14-point
Code:
Cube analysis
Rollout cubeless equity +0,411
Cubeful equities:
1. Double, take +0,746
2. Double, pass +1,000 ( +0,254)
3. No double +0,542 ( -0,204)
Proper cube action: Redouble, take
13-point
Code:
Cube analysis
Rollout cubeless equity +0,524
Cubeful equities:
1. Double, take +0,971
2. Double, pass +1,000 ( +0,029)
3. No double +0,646 ( -0,326)
Proper cube action: Redouble, take
There is a sharper drop in “take strength” from 15 to 14, which is continued from 14 to 13. It's a difference of more than 0,2.
From the 14-point black can jump additionally with 63 and 54. If he doesn't manage to jump, with the same dice he will get 1 pip closer to white's blot, though this will differ one shot at most.
So I am dumbfounded by the plunge in take-ability, and hope someone can help.