Intoxicated by initially big game (6)
I believe the answer is:
blotto
'intoxicated' is the definition.
(similar in meaning)
'initially big game' is the wordplay.
'initially big' becomes 'b' (I am not sure about this - if you are sure you should believe this answer much more).
'game' becomes 'lotto' (lotto is a kind of game).
'b'+'lotto'='BLOTTO'
'by' is the link.
Can you help me to learn more?
(Other definitions for blotto that I've seen before include "Cockeyed drunk" , "Plastered, hammered, sloshed" , "Get very drunk" , "Blind drunk" , "Very drunk (informal)" .)