Imagined odds of perfect finish (7)
I believe the answer is:
pretend
'imagined' is the definition.
(I've seen this before)
'odds of perfect finish' is the wordplay.
'odds of' indicates alternate letters (the letters in odd-numbered positions are used).
'finish' becomes 'end' (come to an end).
The alternating letters of 'perfect' are 'pret'.
'pret'+'end'='PRETEND'
(Other definitions for pretend that I've seen before include "Simulate - make up" , "keep up appearances" , "Profess falsely" , "make a false claim" , "Simulate, feign" .)