Position 474

 How should White play 52 here:

This position is from a class of problems that I call “which hit?”. You are in a great position where you get to choose which hit you want to make.

First, you consider bar/23 13/8*:

This brings another builder to bear on your open 4 and 2 points, but even if you end up hitting loose there, you do not have a close builder to cover with.

It is good to slot your 8 point, but the downside of this play is that Black can hit you from the bar with 62 and 44.

Because you are so far behind in the race, your 9 and 10 points have value as blocking points, and this move  take a builder past those points.

Consider bar/20 13/11*

You now have 3 builders for your 10, 9 and 8 points. Your 9 and 10 points are valuable because they will block Black’s rear most checker directly if Black enters on your 4 point. Even just making your 11, 10 or nine points has value because Black can no longer hit you on those points and when they run, you can hit them from there.

If Black moves a checker to their 10 or 9 points, then the checker on your 20 point is an additional builder to hit them with a direct shot.

This is the correct play.