late 14c., jupartie , ioparde, etc., "danger, risk;" earlier "a cunning plan, a stratagem" (c. 1300), from or based on Old French jeu parti "a lost game," more correctly "a divided game, game with even chances" (hence "uncertainty"). The sense perhaps developed in Anglo-French.
This is from jeu "a game" (from Latin iocus "jest;" see joke (n.)) + parti, past participle of partir "to divide, separate" (10c.), from Latin partire/partiri "to share, part, distribute, divide," from pars "a part, piece, a share" (from PIE root *pere- (2) "to grant, allot"). Jeopardous "in peril" (mid-15c.) is now obsolete.
word-forming element used to make verbs, Middle English -isen, from Old French -iser/-izer, from Late Latin -izare, from Greek -izein, a verb-forming element denoting the doing of the noun or adjective to which it is attached.
The variation of -ize and -ise began in Old French and Middle English, perhaps aided by a few words (such as surprise, see below) where the ending is French or Latin, not Greek. With the classical revival, English partially reverted to the correct Greek -z- spelling from late 16c. But the 1694 edition of the authoritative French Academy dictionary standardized the spellings as -s-, which influenced English.
In Britain, despite the opposition to it (at least formerly) of OED, Encyclopaedia Britannica, the Times of London, and Fowler, -ise remains dominant. Fowler thinks this is to avoid the difficulty of remembering the short list of common words not from Greek which must be spelled with an -s- (such as advertise, devise, surprise). American English has always favored -ize. The spelling variation involves about 200 English verbs.