Not any announcer ignoring the odds (4)
I believe the answer is:
none
'not any' is the definition.
(I've seen this before)
'announcer ignoring the odds' is the wordplay.
'ignoring the odds' indicates alternate letters (letters in odd-numbered positions are removed).
The alternating letters of 'announcer' are 'NONE'.
(Other definitions for none that I've seen before include "service for monks" , "Not a sausage" , "What's left after taking all" , "Not a single person" , "Bugger all" .)