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Pascal's wager is an argument that frames belief in God as a decision under uncertainty: since reason cannot settle whether God exists, one should weigh the stakes, and because the possible gain from believing is taken to be infinite while the cost is finite, the prudent bet is to believe. Advanced by Pascal, an early architect of probability theory, in his Pensées (1670) and dissected in Hájek's 2003 Waging war on Pascal's wager, it is widely read as the first explicit use of decision-theoretic reasoning (expectations over uncertain states) rather than a proof. The referent is a decision-under-uncertainty argument assessed by its expected-utility structure and its objections, such as the 'many gods' reply and the problem of infinite utilities, and it marks where the mathematics of gambling first crossed into metaphysics.[1]
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