To outwit is to beat someone or defeat them because you are smarter or more clever.(verb)
If you beat your opponent at a game of strategy because you are more adept and more clever at the game, this is an example of when you outwit your opponent.
See outwit in Webster's New World College Dictionary
See outwit in American Heritage Dictionary 4
transitive verb out·wit·ted, out·wit·ting, out·wits
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