Here is the position, with the cube in the centre.



I chose not to hit, reasoning that White has a huge number of return shots, and even if he misses my position is still not so great.

However this turned out to be a huge blunder according to gnu:



However the equity calculations seem strange to me. If I calculate from the hitting play my equity should be .433 - .567 + .168 - .267 = -.233

And the not hitting play should be .349 - .651 +.056 - .110 = -.356. So still a bad move but not a 22% blunder.

I'm thinking it has something to do with being able to pass the double after a lot of White's hitting sequences and being forced to take the double in the 7-point holding game if I don't hit. Is this right?

(410 messages from you and you seem very interesting.
Ideas for you : getting XG and book "theory of backgammon" from Dirk Schiemann.)

2 kind of equities: cubeless and cubeful. With XG, you can get both (on XG you have to let a mouse on a certain move to get the associated ecl (equity cubeless)).
It happens both moves has same ECL but different equities (==cubeful equities, which matters and the end). However, it's more the exception than the rule.

Usually the difference between two moves in equity cubeful are greater than differences in ECL. If you are favorite, the best move gives you better ECL and closer to an efficient double.
If you are underdog, the best move reduces probability to give efficient double to opponent.