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Why the big difference in equity between paths?

Posted By: Daniel Murphy
Date: Wednesday, 18 August 2010, at 6:41 p.m.

In Response To: Why the big difference in equity between paths? (Chuck Bower)

Here (using XG) the Double path wins 2% more total games and 4% more gammons. Why?

Does it? Because as you know, Chuck, Jason's rollout result does NOT tell us that D/T wins 2% more games and 4% more gammons. The D/T breakdown should be fairly accurate. The ND isn't necessarily so.

For an obvious example, imagine a position with 60% wins, 40% gammons and 40% losses with NO CHANGE in that breakdown with any of the 1296 upcoming sequences -- and imagine that the evaluations this roll and next are accurate. The position is a double/pass now and will always be a double/pass next roll.

A rollout will say:

  • D/T W 60% G 40% L 40%
  • ND W 60% G 40% L 40%

But, obviously, ND now does not lead to W 60% G 40% L 40%. It leads to W 100% G 0% L 0%. After ND, all sequences lead to D/P, and the bot "helpfully" (?) tells us what it thinks the game breakdown would be if the double were taken.

In the OLM position, I'd suppose that D/T leads to a lot more than 4% more gammons than ND (since after ND now Side-on-roll will be cashing some of those possible gammons next roll) and fewer single wins, (for the same reason, and also for having given opponent cube access).

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