Are there any good cube reference positions for the problem of containing two checkers?
Here's why I'm asking. A couple of months ago, I walked in on a chouettes game that had just ended. Unfortunately I don't remember the exact position, but it was something like this.
| team | 63 |
|---|---|
| |
| box | 160 |
| Position Id: dwYAEBI7MhMZAA Match Id: UQkAAAAAAAAA | |
The box (Blue) offered a redouble and everyone on the team dropped. I thought it was a take (but of course I wasn't in the game at that point) and they all thought I was crazy. Later analysis by gnubg suggested that taking is right by a large margin. (Had I been in the game, I would probably have been offered extras. Had I accepted extras, I would have lost the game with 70% probability, despite the take being correct. This, by the way, is why I posted a couple of weeks ago about a different way to do extras in chouettes. But I digress.)
Is there a way to reason one's way to the correct solution in such problems? Obviously, knowing the reference positions for containing a single checker is a necessary starting point. I'm familiar with some of these from studying the Backgammon Encyclopedia and, in this particular position, judged that the chances of escaping one checker before getting a hopeless one-checker-back position were pretty good. But, it would be nice to have some more explicit guidelines. What are the critical parameters? Presumably: number of checkers off, number of points made in both home boards. What else?