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And Variant

Posted By: Daniel Murphy
Date: Sunday, 4 March 2012, at 2:33 p.m.

In Response To: And Variant (Stick)

With White's board closed, I'll try to count White's hits on his first or second turn:

 Play 1st Roll Blotters 1st/2nd Hits 6/1* 2/1 Hit 12/36 -- 33.3% Fan 16/36 0/36 Anchor 8/36 1/36 0.2% 6/1* 6/5 Hit 11/36 -- 30.5% Fan 9/36 8/36 1.7% Anchor 9/36 0/36 Others 7/36 0/36 Play 1st Roll Blotters 1st/2nd Hits 5/0 2/1* Hit 11/36 -- 33.3% Fan 16/36 13/36 5.5% Anchor 9/36 2/36 0.4%

6/1* 6/5 is rather safe. White gets more hits on his second roll, but not enough to make for fewer hits on his first roll. So 6/1* 6/5 should be best at DMP. But gammons count at 3a3a. 6/1* 2/1 increases fanning numbers from 9/36 to 16/36 and also gets 16*7/1296 = 8.6% ways to put a second checker on the bar in a safe position. Extra gammons should easily be worth ~1.3% more hits.

So 6/1* 6/5 at DMP, 6/1* 2/1 at 3a3a.

In the original position, hits don't all win (either, since Blue will has 3 or 4 off but I've ignored that!). At 3a3a, this should mean that 6/1* 2/1 is even better, since the cost of being hit is smaller. At DMP the open point may make a difference for best play. Suppose Blue still wins 40% of the time after being hit. Then

6/1* 2/1 -> 66.48% (missed) + 13.48% (hit and win) = 79.88% wins

6/1* 6/5 -> 67.76% (missed) + 12.89% (hit and win) = 80.65% wins

a difference of 0.7% instead of 1.28%.

So, I'd play 6/1* 6/5 over the board at DMP, and 6/1* 2/1 at 3a3a. But at DMP there's plenty of room for error from my having rounded, ignored future hits, estimate wins after a hit with the open 5 point and ignored wins after a closeout.

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