Run one's eyes over report into what's prevalent in the betting industry (4)

I believe the answer is:

luck

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

'run' is the definition.
Although both the answer and definition are singular nouns, I can't understand how they can define each other.

I don't understand the rest of the clue.

Can you help me to learn more?

(Other definitions for luck that I've seen before include "Good or bad fortune" , "See 1" , "'Fortune, fate (4)'" , "''The devil''s children has the devil's ....'" , "Chance, fate, fortune" .)

I've seen this clue in the Irish Times.

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