True as true, ignoring the odds (7)
I believe the answer is:
sincere
'true' is the definition.
(synonyms)
'as true ignoring the odds' is the wordplay.
'as' becomes 'since' (both can mean 'because').
'ignoring the odds' means one should take alternating letters (letters in odd-numbered positions are removed).
The alternating letters of 'true' are 're'.
'since'+'re'='SINCERE'
(Other definitions for sincere that I've seen before include "like informal correspondents?" , "Free from deception" , "Genuine and honest" , "Unaffected" , "Genuine; deceit-free" .)