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Cube decision at -3 -5
Posted By: Chuck Bower In Response To: Cube decision at -3 -5 (Neil Robins)
Date: Saturday, 27 November 2010, at 5:27 p.m.
Step 1: find White's takepoint.
Pass for 25%; take and win for 50%, take and lose simple for 15%. Take and lose gammon for 0%. What %-age of White's losses will be gammons? I'll guess 50%. Now prorating the losses, we find if White takes and loses he will have 7.5% MWC.
Thus taking risks (25 - 7.5)% = 17.5% out of the available (50 - 7.5)% = 42.5%. The worthless-cube takepoint is 17.5/42.5 = 35/85 ~ 35/(6/7) = 35*7/6 ~41% cubeless game winning chances (cgwc).
Suppose White turns the game around. What is his cashpoint (= Blue's takepoint)? Pass for 50% MWC. Take and win for 100%. Take and lose simply for 25%. Take and lose a gammon for 0%. Here I'll guess 20% of Blue's losses will be gammons, leading to prorated losses being worth 20% MWC. Thus facing a 4-cube Blue will be risking (50-20)% out of an available (100-20%) so the takepoint will be 30/80 or 3/8.
If White were able to use the cube with perfect efficiency then he doesn't need 41% cgwc to take this, but rather (1 - 3/8) of that, or about 25% cgwc. The true takepoint is somewhere between these two extremes, with a 70% efficient cube meaning about 30% "realistic cube" takepoint.
After all that we need to ask "can White win 30% (cubeless) of the upcoming games if he takes?" His primary gameplan is twofold: force Blue to break up the pretty prime AND trap at least one of Blue's checkers behind his own (partial) prime. The secondary gameplan is to maintain enough timing to play an acepoint (misnomer for '24-point') game as a fallback.
Very crudely, let's say that all of Blue's nine blocked rolls (which force him to break the prime) give White 40% cgwc. That's 10% wins there. If the other 75% of games evolve into perfectly timed acepoint games (and noting White can often stay forever since bg's are no more meaningful that gammons) then 25% wins there gives 3/16 or 18.75% more wins. Now we're up to almost 29% wins.
Looks very close to me. That makes the double automatic. The take could well come down to the skills of the players, particularly White (I think) who is probably going to have the tougher decisions, particularly if this turns into a last ditch effort. (I guess that means that if I'm White I should pass. :) Bot vs. bot, I think it's a take.
One last note: if the second spare on the 6-point were merely back two spaces to the 8-point, White's chances go up considerably. So if this is a pass at the 1 or 2 % level I'm thinking that would shift it to a take.
D & (close?) T.
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