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Winning percentages with one man closed out

Posted By: Chuck Bower
Date: Thursday, 7 October 2010, at 8:12 p.m.

In Response To: Winning percentages with one man closed out (David)

Here's one that's not terribly difficult, but you need to remember a couple key ones. (I'm using the table on p. 97 of Woolsey's Cube Reference Positions. All numbers are cubeless, and from the point-of-view of the person with the (perfect) closed board.)

5 off -- 79% cGWC (cubeless Game Winning Chance)

11 off -- 24% cGWC.

Now there are 11-5 = 6 intervals between these values and 79%-24% = 55% cGWC difference. It's pretty close to linear, so each increment is 55%/6 = 9%.

Outside this range and you have to do a bit more memorization.

12 off -- 17%;

13-off -- 20% (because you can pick up the lone checker that isn't on the bar);

14-off -- 8% (a number everyone should remember who's ever heard the sob stories that go like "I had all my checkers off except one, about to backgammon my opponent, and I still lost! What are the chances of THAT??" :(

With 4, 3, 2, 1, 0 off the difference (from 21%) goes {6, 5, 4, 2, 2}%.

And 3% gammons if closed-out player has none off.

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