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Explain Jacoby paradox

Posted By: ah_clem
Date: Monday, 10 December 2012, at 3:06 p.m.

In Response To: Explain Jacoby paradox (leobueno)

Here's my understanding if it:

Suppose blue fails to bear off right away. In the first position, White wins with 29 shakes; in the second she wins with 32 shakes. In either case it's a pass for blue assuming white has access to the cube. By turning the cube, blue gives her access to the cube, leaving either 7 or 4 shakes that lose for white on the table.

Being cubed out with only four shakes that could win it is not so bad, but passing with 7 shakes to win is giving up too much. So in the first position blue should hang on to the cube so that he might get a second roll to win it if he fails on the first roll. In the second position, his chances of getting a second roll are so small that it's not worth hanging on to the cube.

Another way to say it is that white's cube vig is higher in the first position than the second - when she gets to use the cube she cashes a position that's 29/36 (~80%). In the second position, she cashes with vs 32/36 (~89%), which isn't as much of a gain. Blue doesn't want to give up all that cube vig, so it's a hold in the first position and a cube in the second.

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