Suppose that my opponent is 1 away post-Crawford, and I have an even score (so my opponent has a 'mandatory take' at least for early doubles). A common trick is to hold off doubling until my opponent's position is truly awful, a ploy that can both lower your PR (more decisions) and generate a potentially large error from your opponent.

Suppose that someone is playing the trick on you. When you should take? I seem to remember reading somewhere that this involves comparing a win probability with a gammon probability (take if chance you win > chance you are gammoned?), but I can't really remember the details.

Relatedly, if you are the 'trickster', when should send the double?

Not doubling an optional double doesn't lower your PR in XG. Not sure about Gnu.

The 3-away 1-away math is something close to: if you get gammoned at a higher percentage than you win, then pass, otherwise take. 5-away or longer, you can take deeper, but I don't exactly remember the details. At 5-away, it might be something like "multiply the gammon % by 2/3 and then if that's higher than your win % then pass".

The trickster should double if he has any potential market losing sequences.

I should have searched for this before posting, but here's the math:

https://www.bkgm.com/articles/GOL/May00/matt.htm

It's funny, this article is where I originally learned this stuff 23 years ago, and I recently told a friend that "you can actually take deeper when your opponent is 5-away than 3-away." But that friend... I just realized he's the author of this article!

@grinder Thanks for the information: I didn't know that it depends on the score (e.g. 3A1A vs 5A1A).

Re PR: I'm sure you are right about optional doubles, but often these won't be optional doubles. Instead, they might be absolutely tiny doubles which cost you 0.0001 equity or so each time you fail to make them. For this reason, I do think that the strategy can lower your PR provided you aren't going to play anything too close to a 0.