Strange, my game (5)
I believe the answer is:
rummy
'game' is the definition.
(I know that rummy is a type of card game)
'strange my' is the wordplay.
'strange' becomes 'rum' (synonyms).
'rum'+'my'='RUMMY'
(Other definitions for rummy that I've seen before include "Card game; strange; like a spirit" , "game of cards" , "Two-pack card game" , "Gin perhaps?" , "Odd; card-game" .)