Why did a 17th-century mathematician treat belief in God as a bet?

Because Blaise Pascal thought reason alone could never settle whether God exists, yet everyone has to live one way or the other. So he treated the question like a coin toss you can't refuse to play, and asked what a sensible gambler would do.

His answer, written in notes published after his death as the Pensées, compares outcomes. If you live as a believer and God doesn't exist, you lose only finite things, some pleasures and luxuries. If God does exist, you gain something infinite. "If you gain, you gain all; if you lose, you lose nothing," he wrote. In the language of decision theory, betting on God always has the higher expected value, as long as the chance that God exists isn't zero.

Pascal was the right person to think this way: in 1654, his letters with Pierre de Fermat about gambling problems gave birth to probability theory. That same year, he had an intense religious experience and wrote it down in a note he sewed into his coat. A servant found it only after he died.

Critics have pushed back for centuries. Voltaire said that wanting something to be true is no proof it exists. Diderot pointed out that "an Imam could reason the same way", since many religions could make the same bet. And some doubt that faith adopted for its payoff is genuine faith at all.