Rough tough stuff, Paul! Thanks for posting.
In Position 4, we can ballpark White's winning chances by noting that most of his wins come when he rolls 55 or 66 at least once in the next two rolls. The probability of this happening is 2/36 + 2/36 - 4/1296, which is a little less than 1/9, or about 11%. But almost 30% of the time, you'll bear off in two rolls so he'll lose anyway. So now White is down to 8%. There are some other ways White can win, e.g., by rolling 65 or 64 first and then 44 or 33, but it should be clear that White can't be much above the critical 9% needed to take, so doubling should be at worst a small error.
If, however, we keep White's pip count the same but arrange for 44 to work as well, as in the diagram below, then the take is easy and the double is questionable.
| White | 18 |
|---|---|
| |
| Blue | 8 |
| GNUBg Id: KRAAYAcAAAAAAA:UQkgASAAMAAA XGID=-BC------------a-----aa-a-:1:1:1:00:6:2:0:9:16 | |
In Position 6, I was confused at first because White's raw take point is somewhere around 23%, which is lower than 25%, so I thought Blue should be more cautious with the cube when there aren't many gammons to be won. However, what I forgot was that White has essentially no recube vig, so Blue should be slightly more aggressive with the cube even in a straight race. Also, Blue does win some gammons here.