What would be the right play here and why?

I'm only an intermediate players, but here's how I would look at it.

Basically 21/15 18/15 doesn't seem to do anything and 21-15 13-10 looks crazy, so I would narrow it down to 21/18 8/2 and 13/10*, 13/7.

How do you evaluate the resulting positions.. The safe play doesn't seem all that safe after the next roll, and White is going to have a pretty strong board very soon, so this seems like a slight advantage for White.

After playing two down, White hits on 22, 25, 43, 46, 45, and 55 in which case I'll be in trouble if I don't make the 21 point on my next roll, and on 21, 41, 51, 42, 44, he'll hit on his 4 point in which case I'll be in trouble if I don't hit back right away. So it looks like about a third of the time I'll be screwed after the next exchange. What's the upside to playing two down? Okay on 17 rolls he dances or enters without hitting, after which I guess I would be a moderate favourite due to the chance of making a 4-point board. So about half the time I'm a decent favourite, a third of the time I'm a big underdog, and the rest of the time when I get hit and roll a four it's probably about even.

All in all it seems close to me and I'm not sure what the right play is. In the heat of the moment I probably make the safe play, but the more I think about it, the more appealing the risky play starts to look.

You're ahead 22 after the roll so you don't particularly need to hit. I would make the 15. It advances your rearmost checkers which is the general technique for disengaging. In particular, it gets the man from 21 out of that scary place. While you're leaving a man behind on the 18, one of the opposing points is stripped, he has another blot in your outfield to worry about, and you are outboarding him 3:2.

I didn't like the look of this play because it seems like it will be difficult to bring home the 15 and 13 points anyway, so I didn't think it would be worth the risk of exposing the blot on the 18. But maybe it's okay.

Why 21/15 13/10* looks crazy? Even if White finds a hit, she'll usually break one of her very valuable point (5 or 13) AND she'll expose to quite many returns AND she will do it while outboarded 3:2.

Now that you point out the rationale I can see the arguments for it. I guess I was afraid of variations where 2-3 of the men get sent back, but when I actually look at it, I see that that is a fairly unlikely possibility. So perhaps it's worth it.

I guess another argument in favour of the 21/16 13/10 play over my play of 2 down is that it doesn't really leave any super-crushing rolls for my opponent next time.

Whereas after 13/10 13/7, 44 and especially 22 are disastrous for me.

Small difference in number of crushers is a minor consideration.

I think connectivity is very very important here, and for that reason I wouldn't consider 2 down at all.

I think its a choice between 21/15 18/15 and 21/15 13/10*.

For those who are interested, I set this up in XGmobile.