Cap for the chap going into the bookie's (6)

I believe the answer is:

better

I'm a little stuck... Click here to teach me more about this clue!

'cap' is the definition.
(I've seen this before)

I cannot understand how the rest of the clue works.

(Other definitions for better that I've seen before include "M ore appropriate" , "'Discretion is the . . . . . . part of valour'" , "More appropriate; gambler" , "Improve upon" , "punter" .)

I've seen this clue in the Evening Standard.

Want a hint initially instead of a full solution? Install my app