For money, it looks like a clear cash. Between one-checker and two-checker closeouts, it's hard to imagine that Blue can squeeze out twice as many gammons as losses (with the 5-number crack initiating many of them), even factoring in ownership of the cube. That is, it's wrong to play on.
At the score (-3-6), Blue needs to be more conservative and White more aggressive than for money, so the remaining theoretical redouble issue is whether Blue is good enough to double.
For the take point, I use 10.5% at -6-1c. For the redoubling window: Blue risks 57.5% (his chances at -3-4) to gain 10.5% (winning instead of -1-6c), so the now-or-never window opens at 57.5/67.5 = 85.2%. As Blue's decision is not now or never, he should probably redouble somewhat higher, say 87+%(?), but of course lower than the drop point of 89.5%.
Roughly speaking, let's say after Blue's 31 21 11 (ignoring 33 followed by 31 21 11), he breaks the 9pt (ignoring that 11 can be played better), White wins 90% if she rolls a 6 (optimistic for White) and that otherwise Blue hits and remakes the six-prime 95% of the time (optimistic for Blue) and otherwise loses. The first part gives White (5/36 x 11/36 x 90%) = 55/1296 = 3.8%, and the second part gives White 1241/1296 x 5% = 4.8%, for 8.6% so far. The third part is (accepting Stick's figure) 2.5% wins after close-out -- White gets 91.4% of that, which is 2.3%.
That sums to 10.9% so far, already over the 10.5% take point. The chance of a prime-rolling accident in the majority (leap) variations seems like enough to move it past (100 - 87+) = 13-%, so... while I'm going by crude approximations, I'm guessing that theoretically this is a borderline no-redouble, and the take is trivial.
Be that as it may, in the practical realm I recommend redoubling now because I think most humans would pass a situation that is so conceptually hopeless-looking, agonizing to play (and even potentially ridicule-prone), and Blue may not get another chance to invoke a cube error; after he leaps, he has surely lost his market so a future Opp cube error can come only after he cracks now or has an accident later but re-reaches a redouble anyway.
Alternate problem: Convert White's 1pt spare to an 11pt blot, shown below. Now what is the right cube action for (a) money, and (b) the given score of -3-6?
Nack
P.S. Ignore the dice. (Not sure what I'm doing wrong; when I try to set up a position without dice, Gnu crashes.)
| 87 | |
|---|---|
| |
| Blue on roll. Cube action? | 138 |
Position ID: 2+aMAAjYtg2AAw Match ID: UYnkABAAIAAA | |
