this problem involves both "running vs staying", and whether to try for another checker or commit to containing one already hit:
The decision to try for a second checker or commit to containing the one you already have is often difficult. This position permits you to commit to containment by running, 23/14, or stay back while making the useful 3 point. making the 3 point is correct by a comfortable margin.
The first piece of information we can discover is that this decision is not about racing per se. If it were, then if the roll were 5-4, with the same number of pips, the decision would be close to the same, but it’s not. A 5-4 allows you to make the better 4 point, but at the expense of an indirect shot and a weaker resulting builder distribution. But both plays are edged out by the game plan of radically committing to containment with 6/1 9/5
Similarly, if the reason for making the point had only to do with the race, then if the blot were on the 21 point instead and the roll were 5-3, you’d probably make the 3 point despite the indirect shots, or at least it would be close. However, running to the midpoint is clear, even though several other options are available that allow you to try again for a second checker. With 5-2, though, which can’t run cleanly but can make the 4 point very nicely, running becomes a triple-whoppin’ blunder!
It’s a principle which arises often: When you have a play that runs your last man cleanly, it’s often time to say “Pips, schmips” and commit to containment of a single checker, even if you’re down in the race. When “you can run, but you can’t hide”, that is, the run isn’t clean till your blot is missed in the outfield, it’s good to look for something better, particularly if racing isn’t necessarily a winning game plan even if you succeed in breaking contact.
There is a principle that Kit Woolsey has made famous, which advises: “When behind in the race, don’t race.”
In this case, both ideas lead to the same play. The alternative to running makes a good point for the board or prime you will need to contain either one or two checkers, without taking excessive risk of being contained yourself. These considerations make the point-making 9/3, 6/3 a clear winner.
One of the most dangerous positions in backgammon is that of the out-timed and rapidly deteriorating position. Take a look at this position. Black to play 5-1.
These stretched positions usually arise when one side (Black in this case) has built a great front position quickly, but at the cost of leaving one or more stragglers disconnected from the main force
Most players in this situation assume that they must have done something wrong to get here. Perhaps they built an inner board point when they should have run, or brought down a builder instead of making an anchor. Sometimes that's true, but often these positions just happen. Black may have correctly pursued an all-out attack, and White just happened to anchor at the last minute. No need for recriminations—the point is, what to do next?
To save these crumbling positions, you have to make the most of your assets. In this case, you have two assets: you're ahead in the race by a ton, and right now your board is stronger than White's. To use these assets, you've got to force a conclusion to the game (at least this phase of it) right now.
Come up to the edge with bar/20, and make the only reasonable ace, 9/8
You can't punt with bar/24 and 9/4. That play isn't even safe, and you have to roll a four almost immediately just to get to the edge of White's prime.
Could White crush you if he rolls a 4-3 next, pointing on you? Sure. But guess what? If you stay back and he rolls 4-3, you're crushed anyway. Don't guard against rolls that beat you no matter how you play.
True, there's some delicious duplication involved here — White needs 4s and 3s to hit your new blots, the same numbers that hit on the 20-point. But that's just a bonus. You'd make this play even if there were no duplication involved, because you've got to get your back checker out immediately. There's no time left to pray for a good roll. 51 actually is a pretty good shot (6-1 or 6-2 would be much worse), so make the most of it and see who survives the next roll.