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Shot Time! Extra Checker off? or Extra Gammon Chances?

Posted By: Daniel Murphy
Date: Wednesday, 22 August 2012, at 2:32 a.m.

In Response To: Shot Time! Extra Checker off? or Extra Gammon Chances? (ah_clem)

** It doesn't seem that you win many more gammons with the hit.

Why not? 25% of the time (which is how often White enters without hitting) you gain 1/2 a roll because Blue puts White back 4 pips. About 24% of the time, Blue gains 1 and 1/2 rolls because White fans once. About 20% of the time, Blue gains at least 2 and 1/2 rolls because White fans 2 or more times.

That should add up to serious extra gammon chances, especially compared to the nonhitting play, where gammon chances appear to be almost none. After 6/off 1/off, Blue would have 12 checkers left and most 5's lose a turn, so say about 6 rolls to bear off; meanwhile White should be off the gammon in a little less than three rolls on average, since White only needs 23 pips to get off the gammon and many of his smaller rolls (all the aces) hit.

** And by giving white the chance to stick around and possibly get a shot you're lowering your winning chances.

Blue will get hit more often after 6/5* 6/off, but not much more often. The extra chance of getting hit exactly two rolls from now is only 16/36 * 3/36 * 11/36 = 1.1% (that's a fan, followed by Blue rolling 66 55 or 44, followed by a hit). Further shots are very unlikely.

So I'd say the extra gammon from 6/5* 6/off are big. On the other hand, 6/off 1/off should win quite a few more games --

** Meanwhile, if you are hit your winning chances are ~7% with 2 off and 11% with 3 off.

Are those cubeless numbers? If Blue wins about 7% cubeless with 2 checkers off, he wins 0% cubeful, not 7%, because White has the cube, Blue's take point on a 4-cube is about 9%, and White should immediately double Blue out if White hits. What if Blue has 3 off and White hits? Well, if White redoubles immediately, Blue gets his 11%, if that number is accurate. But since White has 2 checkers to bring around, and he's about 2% shy of Blue's take point, he can afford to wait and see what he bearoff looks like, and he should be able to reduce Blue's wins quite a bit below 11% by redoubling Blue out.

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