To tell someone's fortune; to predict or divine what will happen to someone in the future.
From 'fortune' plus the verbal suffix '-ize', which comes from Greek '-izein'. The '-ize' suffix productively creates verbs meaning 'to make, become, or practice' something, making this a regular formation from the 15th century onward.
English loves the '-ize' suffix so much that we can almost turn any noun into a verb—companies 'strategize', people 'socialize'—but 'fortunize' is rare because 'fortune-tell' already existed, showing how language develops competing forms for the same idea.
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