Ok, your assumptions about the winning chances when jumping the prime seem reasonable, so let's go with them.
43.3% of the time we jump the prime, and, given your assumptions, we'll then have an EV of 0.85 * 4 + 0.10 * 2 - 0.05 * 2 = 3.5
We would be indifferent to doubling if our EV x when playing on and not jumping the prime brings the overall EV to 2.
0.433 * 3.5 + 0.567 * x = 2
=> x = 0.855
So our equity must be 0.855 in case we don't jump the prime to make us indifferent. If it is better, we play on for a gammon. If it is less, we double to take the 2 points down.
A GNU rollout says that if we play on, we'll win 61% with 48% being gammon wins. We have already covered 43.3% x 85% = 36.8% of the gammon wins with jumping the prime. This leaves 11.2% gammons if we don't jump. We also have covered 43.3% x 10% = 4.33% of the normal wins if we jump.
Of our losses, we have already accounted for 43.3% x 5% = 2.2% when we jump the prime. This leaves us 36.8% losses if we don't jump. GNU says we'll lose a gammon 8.6% of the time and I assume strongly that all of them happen if we don't jump.
So if we don't jump, we win 61% - 36.8% - 4.33% = 19.87% with 11.2% being gammons. We lose 28.2% normal games and 8.6% gammons.
Our EV here is 0.0767 * 2 + 0.112 * 4 - 2 * 0.282 - 4 * 0.086 = -0.307
So overall we have: 0.433 * 3.5 + 0.567 * (-0.307) = 1.34
This result is roughly equal to what GNU says (note that the GNU result is normalized to 1 point, and that the above analysis doesn't take backgammon wins into account)
Code:
1. Double, Pass => +1.00
2. Double, Take => +1.035 (+0.035)
3. Double, Pass => +0.745 (-0.255)
Correct cube action: Redouble, Pass
And a caveat - I suck at pen and paper maths... so there might well be errors in my analysis...