As I'd previously thought, Daniel would be the only person to reply to this and smack it right on the head. Don't think of this as a bad thing, I was fairly lost myself when asked this question because I never have to do it. I asked Nack to give me a clear explanation and he thankfully replied. Below is his copy & pasted email: If White does not redouble (correctly holds the cube), he deserves 0.504 x 2 = 1.008. If White (incorrectly) redoubles, he deserves 0.463 x 2 = 0.926.
With the cube on 4, (and not on roll), Green's equity is -.2315 x 4 = -0.926. (Snowie does not allow you to punch this up; I'm inferring it because Green's negative equity has to work out the same as White's positive equity.)
Another way to look at it is if the cube is at a given level, there is a big difference in equity depending upon who owns it:
White's 1-cube value owning the cube is .504. Because the White-own number is more than twice the Green-own number, it's wrong to redouble. But the White-own number is less than twice the neither-own number, so it is right for White to double from the center.
Green should not offer 1 point. (He would be giving a little bit away if Snowie's eval is right). On the other hand, it probably wouldn't matter because in my experience most people would wave it off, wrongly thinking their position is worth more than a point, except perhaps for the rare person who correctly did not double.
What I would be looking to do in this position is to offer that I be paid 2 points to take an extra 4 cube to anyone who thinks I should pass, and then lower my offer to 1.5. From what I have seen that is the direction in which most people will err in this type of situation. Even if they do the math, they can get it wrong: "Let's see... 25 hits win plus double 6s wins half the time, so that's 25.5 - 10.5 = 15, and 15/36 x 4 = 60/36, which is 1.67. Okay, I'll pay 1.5!" What they forget/ignore is that Green still has a chunk of equity after White hits; that's why White's actual (post-double) equity is not even quite 1. - Nack Ballard
Based on Snowie's evaluations:
White's 1-cube value when the cube is in the center is .365. (I punched it up.)
White's 1-cube value when Green owns the cube is only .2315.
                               | Pip: 103 | |
| Pip: 75 |
| Cube action equity | |||
|---|---|---|---|
| 3-Ply | Money equity: | 0.374 | |
| 0.2% 4.7% 67.4% 32.6% 2.3% 0.1% | |||
| 1. | No redouble | 0.504 | |
| 2. | Redouble, take | 0.463 | (-0.040) |
| 3. | Redouble, pass | 1.000 | (+0.496) |
| Proper cube action: No redouble, take | 8% | ||