Code:
Cube analysis
Rollout cubeless equity +0,667
Cubeful equities:
1. Double, pass +1,000
2. Double, take +1,133 ( +0,133)
3. No double +0,916 ( -0,084)
Proper cube action: Double, pass
Ideally we use as little memory as possible, and amplify the reference positions we know with our deductive reasoning. From Kit Woolsey's book we can infer the directive that
if white has a two-point holding game and black has no rear checkers left but the 13-point, it is virtually always a pass for white
The following two statements lead to the right cube analysis:
A)If black gets the rear checker into white's outfield while white is on the bar the above directive is practically fulfilled.
B)If black covers the 1-point, he will very likely be able to move the rear checker ahead, which also means that above directive is practically fulfilled.
ad A) black gets the rear checker into the outfield with 16, 26, 52, 53, 55, which gives 9 possibilities (=25%). If he does get his rear checker out white's only hope is to throw a 1:
white doesn't hit with 25:
Code:
Cube analysis
Rollout cubeless equity +0,617
Cubeful equities:
1. Double, pass +1,000
2. Double, take +1,060 ( +0,060)
3. No double +0,946 ( -0,054)
Proper cube action: Double, pass
white hits with 15:
Code:
Cube analysis
Rollout cubeless equity +0,512
Cubeful equities:
1. Double, take +0,772
2. Double, pass +1,000 ( +0,228)
3. No double +0,659 ( -0,113)
Proper cube action: Double, take
ad B) black covers with 4's, 31, 22, 33 or 66, which gives 16 possibilities (=45%)
The chance that white doesn't throw a 1 is 70%, multiplied by the probability that black gets his rear checker out: 70% times 25% = 17% (A). The chance that black covers immediately is 45% (B). If we do A + B then at least 17 plus 45 is about 60% of black's numbers leads to a pass for white. Of the remaining 40% certainly no half of it that will lead to a win for white, so I think the pass is very clear.
In response to Kamba, as we can directly infer from the directive, putting two extra checkers on the midpoint turns out to be of no significance:
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Code:
Cube analysis
Rollout cubeless equity +0,669
Cubeful equities:
1. Double, pass +1,000
2. Double, take +1,114 ( +0,114)
3. No double +0,895 ( -0,105)
Proper cube action: Double, pass
Putting the builder out of direct range leads also to a pass:
Code:
Cube analysis
Rollout cubeless equity +0,632
Cubeful equities:
1. Double, pass +1,000
2. Double, take +1,080 ( +0,080)
3. No double +0,911 ( -0,089)
Proper cube action: Double, pass
Black has only 6 shots that will cover, which is 16%. However, the chance that white will not enter is 45%, after which he will be in direct range (=about 60%). So the chance that black will cover is 16 + 45% times 60% = 16 + 27 = 43%. A + B = 17 + 43, so will give about the same number of passes as in the original position. The difference is that white has somewhat more opportunity to hit the 1-point blot.
3-point board for white:
Code:
Cube analysis
Rollout cubeless equity +0,463
Cubeful equities:
1. No double +0,689
2. Double, pass +1,000 ( +0,311)
3. Double, take +0,679 ( -0,011)
Proper cube action: No double, take
This might be doubled, but it is a huge take. This is rather difficult to infer. If white hits, he will become a serious contender. The chance that white hits is the chance that black doesn't cover multiplied by the chance that white hits: (100 – 45)% times 30% = 18%. Black might fail to cover a second time: 55% times 55% times 30% = 10%. Let's make an estimate (and please correct me) that with a 3-board half of those 30% hits will lead to victory, than he has got 15% wins. Of the remaining 70% that white enters on the 2-point white should at least be able to win 10%, which adds up to the necessary 25% to take. Ofcourse in reality it will be more, but at least this calculation leads to the right decision.