| |
BGonline.org Forums
Much Debated Cube Action from Charlotte
Posted By: John O'Hagan In Response To: Much Debated Cube Action from Charlotte (Bill Riles)
Date: Monday, 19 January 2009, at 6:56 p.m.
Assuming no gammons for either side, my OTB estimate is that Green's redoubling window opens at 31%. This is not entirely correct since both sides have some gammon chances. White gets some when 1)Green hits without covering and White rolls a 6 or 2)Green fails to hit and can't run off the gammon. Green's gammons are much smaller in number since they only occur around 3% of the time when he rolls one of his 4 hit-and-cover numbers. I would give White about 2.5 gammons in 36 and Green about 0.1 in 36. The net effect of these gammons is to lower Green's minimum dbling point.
Thinking about wins, losses, and gammons, my estimates for this position are: Green single wins 12.2/36. Green gammon wins 0.1/36. White single wins 21.2/36. White gammon wins 2.5/36. So ~ 1% of our wins are gammons as are ~10% of our losses. The loss from redoubling is therefore 90% of our equity from down 1-4 Crawford (I use 18% for this score) or 16.2%.
How about the gain from recubing? If we don't double and win this game, 99% of the time we'll be ahead 7-6 to 9 with 60% ME and 1% of the time we'll win a gammon and the match with 100% ME. This comes to 60.4% ME if we win and don't recube. If we do recube and win, our ME is 100%. The gain from redoubling is therefore 39.6%.
Loss/Loss + Gain is therefore 16.2/16.2 + 39.6 which is about 29%. The doubling window is from 29% to 60%. Our chances are about 12.3/36 which is over 34%, so we are in the window. The probllem with redoubling when you're just barely in the window (which we are here) is that cube ownership only has to be worth a little bit to make not redoubling correct.
If we don't redouble now, our chances of winning the game go up in any variation. If we hit and cover, we'll be 100% vs. 97% if we've already recubed. Hit without covering + fan also becomes 100% vs. about 90% if we recube now. Hit without covering, White gets a 6, we'll win maybe 12% vs. around 10% if we cube now. Fail to hit and we'll win maybe 6% vs. 5% or so if we cube now. Not sending the cube over now means we win more but our ME is lower when we do win (60% vs. 100%) but it's higher when we lose (18% vs. 0%). Using these figures, our chances if we don't recube now are: 13.25/36 single wins (with 60% ME), 0.1/36 gammon wins (100%ME), 20.4 single losses (18% ME), and 2.25 gammon losses with 0% ME (assuming that the ability to recube the oppt out saves a couple of games that would have been gammon losses if we had been forced to play them out to conclusion). Adding these up gives a total of 11.72 wins in 36 matches which is less than the 12.3/36 we get by recubing.
So (unless I've made some arithmetical error), it looks like redoubling is correct. Taking a roll will give you more wins in this game but it reduces your chances of winning the match.
| |
BGonline.org Forums is maintained by Stick with WebBBS 5.12.