I’ll talk about money games here to make my question simpler. Often when playing against XG I notice I miss lots of opportunities for small early doubles (like 0.03-0.05 errors or less). I understand that doubling in these situations is more profitable than not doubling, but I’m wondering in what sense it’s better than the possibility of holding off and waiting for a more efficient double. Of course those aren’t guaranteed and things could turn around and we don’t get a better opportunity, but it seems totally plausible to me that p(we get a more efficient double opportunity)*EV(we get a more efficient double opportunity) could sometimes greater than EV(we make a small double now).

Basically, my question is — is it really the case that the most profitable strategy in a money game is to double the first time XG says the EV of double/take exceeds the EV of no double/take (even if it’s just by a tiny amount)?

Yes.

If what you could gain by waiting were more profitable than doubling now, then xG would, by definition, tell you to wait! So, for that reason, it is, once again by definition, correct to double.

Makes sense -- I keep forgetting that the "no double" evaluation doesn't mean "never double", just that you will hold off and use the cube appropriately after this turn. This was also the root cause of another question I posted a while ago. Thanks!