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Daily Quiz 4/17
Posted By: kruidenbuiltje In Response To: Daily Quiz 4/17 (Daily Quiz)
Date: Wednesday, 2 May 2012, at 5:18 p.m.
Daily Quiz 17 april 2012
Number 1
Quite a nice puzzle this one, I see 4 variations, from safe to bold they are: 1) 5/4/1; 2)5x2/1; 3) 5x2 1off; 4) 3off 1off.
Variation 1: 5/4/1. White is then on the move and needs to throw 19 pips to get off the gammon, according to the Keith count blue then has a wastage of 11 pips and thus needs 22 pips to win. But this is more a sort of a 4-move position. That means 33 pips, here we see that blue having an odd number of checkers matters a lot. When we use the EPC blue has the equivalent of 29 pips, this is reasonable, since blue’s low doubles play better than white’s. If we translate it into a race (19-29) white would score a percentage of about 90%, that means 10% gammons. The risk of this play depends whether white should stick around. If he would stay every 61,51,41,31,21 gives a shot, that is 10/36 x 11/36 = 110/1296 = 8% hits, but since blue is still a big favourite because of his, by then, 9 checkers off, it would be better for white to run. So the risk of variation 1) is negligible.
Variation 2: 5x2/1. This variation has a risk comparable with variation 1. But here the gains increase. If white enters the next move the gammon-race is 21-29, about 86%, thus 14% gammons, but a fan would lower the blue pipcount to 22, bringing the race to 21-22, about 72%, thus 28% gammons. A weighed average would give about 16% gammons.
Variation 3: 5x2 1off. With only 6 checkers to go blue has now created a 3-move position. When white enters right away (without hitting) the race is 21-22, thus 28% gammons, a fan will cause a race: 21-15, about 54% gammons, and then there are the hits nullifying the gammon-chances. White will very probably not win (as we have calculated in an earlier daily quiz, a lot has to happen for that). The weighed average of gammons is: 11/36 x 0 (the hits) + 4/36 x 54% (the fans) + 21/36 x 28% (the rest) = 22% gammons.
Variation 4: 3off 1off. It is easy to see that the risk in this variation will not pay off, since the reward is as high as in variation 3 (a 3-move position).
Answer: 5x2 1off
Number 2
The question here seems to be whether blue should play the normal 13/11 here with the 2, or should blue take the opportunity to split safely with 24/22. Since the 11-point doesn’t fit in a prime with the 5-point the value of the 11-point is decreased. With his 10-point made white has a few more chances to make either the 4-point (62,64), the 5-point (51,53) or the bar-point (63), so there is extra reason to split now. Also the risk of 24x14 is somewhat duplicated as the same throw makes the 4-point for white.
Answer: 6/5 24/22
Number 3
White needs 9 crossovers to avoid the gammon, that is 5 moves. Taking 2 off brings blue in a possible 5-move situation as well, and the risk of being hit after 6/5(2) 1off (2) is {54,64,43}=6/36 x 11/36 = 66/1296 = 5%, and a hit doesn’t mean that blue will lose, so the losing risk is only a few percent. I think the two valuable crossovers will pay off.
Answer: 6/5(2) 1off(2)
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