Recently, I posted the position below.
| White | 23 |
|---|---|
| |
| Blue | 139 |
| GNUBg Id: bwAQADYbWBVAAA:UYkYAAAAAAAA XGID=--BB-BB---a-BAAAA------bdA:1:1:1:61:0:0:0:0:10 | |
Having studied it further, I now present my best attempt to explain how one might arrive at the best play OTB. The key idea is, look at White's best and worst rolls after each play.
Let's look at the worst rolls first. After any of the three plays, 11 will be blocked, as will the four rolls that are blocked by Blue's two outside points. In addition, there are two rolls in each case that are particularly bad for White.
After 14/13: 21 is blocked.
After 15/14: 31 exposes another blot.
After 16/15: 41 exposes another blot.
This information alone gives us a tentative ranking of 15/14 being best, followed by 16/15, followed by 14/13.
Now look at White's best rolls. These are the rolls that let White scoot past without giving Blue a shot.
After 14/13: 64 44.
After 15/14: 65 55.
After 16/15: 66 65 64 44.
So 15/14 is confirmed as being the preferred play.
Of course we haven't looked at all the rolls in between. In this case, I think it happens that they all average out to being roughly the same story in all three cases. White has two rolls that hit both outfield blots. Otherwise, Blue typically gets a direct shot and loses a gammon if he misses.
It may not always be the case (in similar positions) that one can get away with just looking at the best and worst rolls. However, going through all the rolls for all three plays, keeping them all in your head, and balancing them against each other is probably infeasible for most players OTB with a clock running. Enumerating the best and worst rolls, though, is just about feasible, and I think is the best strategy for evaluating the alternatives in a limited amount of time.