White is trailing 1-3 in a match to 5. Should White double? Should Blue take if doubled?

I'd say double pass.

There's some simple math that can be applied at this score to incorporate gammons into the take point. You take the chance Blue gets gammoned and add it to 20% and that's the take point. So if Blue gets gammoned 15%, he needs 35% to take.

White has to cube partly because when he loses he gets gammoned a lot anyways, so doubling often doesn't hurt him when he loses and if he hits right away, he definitely wants the cube on 2.

The take/pass is really unclear to me and I could be way off, but I'm going to guess Blue gets gammoned 15-20% and doesn't quite win enough to take given that White hits 20/36 and then Blue has a really tough game. Yet Blue has a ton of work still left to do when White dances. So double/pass.

White's double looks clear because it kills Black's gammons while creating gammons for White that win the match. But if White dances on the first roll then I'd much rather be Blue, so I take.

I agree the double is easier to find than the take/pass decision. It’s a 0.110 double.

The take/pass decision may surprise you. It’s a take. But it’s a huge take — dropping is a 0.575 blunder!

I thought it was an interesting problem since it’s so hard to evaluate the take/drop decision, which usually makes me think they’re at least close, but dropping is a mega blunder.

Here are the win percentages:
White: W 56.1% (G 11.6%, B 0.5%)
Blue: W 43.9% (G 25.9%, B 0.6%)

is there a thread that explains this terminology, most of my games were vs arabic speakers so i never learned any lingo in any language

Nice to see you on the BG forum rickroll. This site is a little dated but has a thorough glossary.

Here are some terms from this thread --

Gammon
A completed game of backgammon in which the losing player has not borne off any checkers. A gammon is also called a double game because the winner receives twice the value of the doubling cube.

Take Point
The minimum game winning chances at which it is correct for a player to accept a double; the point at which a player is equally well off accepting a double or refusing a double; a player's drop point.

Dance
[From the action a player makes as he first reaches to enter his checker then pulls his arm back when he notices the numbers are blocked.] To throw numbers which fail to enter a checker from the bar.

Crunch
The forced evacuation of desirable points (2) due to the lack of alternate plays; in particular, a position in which you are forced to bury checkers deep within your home board.

"Killing gammons" isn't on there, but the idea is that (in the position I screenshotted) he only needs 2 points to win, so if I double to 2 he doesn't benefit from winning a gammon (which would give him 4 points, overkill since he only needs 2). On the other hand I need 4 points to win, so with the cube on 2 a gammon (again, 4 points) would be very good for me.

The numbers associated with an error (e.g., 0.110) are a measure of how bad the error is. It's related to how many points of EV your move gives up compared to the best one (though in matches it's a little bit more complicated). The higher the number the worse the error. 0.110 is a pretty bad error (a blunder), and 0.575 is an enormous blunder.

awesome, tyvm