Ignoring the odds, mind began producing plan (4)
I believe the answer is:
idea
'plan' is the definition.
(thesaurus)
'ignoring the odds mind began' is the wordplay.
'ignoring the odds' means one should take alternating letters (letters in odd-numbered positions are removed).
'mind'+'began'='mindbegan'
The alternate letters of 'mindbegan' are 'IDEA'.
'producing' is the link.
(Other definitions for idea that I've seen before include "It comes to mind" , "Something imagined in the mind" , "Thought; concept" , "Theory" , "Flash of inspiration?" .)