Sozzled, heading off for chancy game (5)
I believe the answer is:
lotto
'chancy game' is the definition.
'lotto' can be an answer for 'game' (the UK National Lottery). I'm not sure about the 'chancy' bit.
'sozzled heading off' is the wordplay.
'sozzled' becomes 'blotto' (synonyms).
'heading off' means to remove the first letter.
'blotto' with its first letter taken away is 'LOTTO'.
'for' is the link.
Can you help me to learn more?
(Other definitions for lotto that I've seen before include "chancy business" , "Housey-housey, bingo" , "Children's game; lottery" , "form of gambling" , "house" .)