Game of chance made our detailed missive (8)
I believe the answer is:
'game of chance' is the definition.
(roulette is a kind of game of chance)
'made our detailed missive' is the wordplay.
'made' is an anagram indicator.
'detailed' means to remove the last letter (the word must be end-less or 'de-tailed').
'missive' becomes 'letter' (synonyms).
'letter' with its last letter removed is 'lette'.
'our' is an anagram of 'rou'.
(Other definitions for roulette that I've seen before include "gambling business" , "Spinning-wheel game" , "Wheel for the gambler" , "sort of gambling" , "risky venture" .)