Turns I botched, including three in game of ill repute (9)

I believe the answer is:

notorious

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

'of ill repute' is the definition.
(both can mean infamous)

I cannot understand how the rest of the clue works.

(Other definitions for notorious that I've seen before include "Hitchcock film" , "Scandalous" , "having a terrible reputation?" , "Famous for bad deeds" , "Infamous" .)

I've seen this clue in The Guardian.

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