Crossword Genius

In desperation, pays to card's limit (2,4,4,3)

Ross

I believe the answer is:

at ones wits end

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'in desperation' is the definition.
I know nothing about this answer so I can't tell whether it can be defined by this definition.

'pays to card's limit' is the wordplay.
'pays' becomes 'atones' (as in to pay someone back).
'to card's' becomes 'wits' ('wit' can be a synonym of 'card').
'limit' becomes 'end' (I've seen this in another clue).
'atones'+'wits'+'end'='AT ONES WITS END'

Can you help me to learn more?

(Other definitions for at ones wits end that I've seen before include "In a state of desperation" , "Unable to see a way forward when in trouble" , "Not knowing what to do next" , "Desperate" , "at a loss" .)

I've seen this clue in The Times.
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