Quote from: ah_clem on November 10, 2009, 10:27:18 PM
Maybe I overestimate his winning chances after being hit...
Upon doing some research, it appears that I do overestimate it.
See http://www.bkgm.com/rgb/rgb.cgi?view+946 (http://www.bkgm.com/rgb/rgb.cgi?view+946)
The Spleischft formula says that if O has n checkers borne off and one checker on the bar with X's home board closed out, O's winning chances are 6*(n+1) out of 100 games. (here n must be > 8, there's another foumula for 8 and less). Assuming rkb bears off two checkers next roll and we hit right away and we obtain a closeout, the forumla gives rkb winning chances of 6*(12 +1) == 84%.
Assuming a 1/3 chance to hit, that gives us about a 5% winning chance. Furthermore, since we haven't made our ace point yet, we might be able to send a second checker back by recirculating. So our chances are probably better than 5%.
I'm going to stick with my vote, since looking up formulae is borderline cheating, and also because it seems to be close to the 4% backgammon rate above.