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How did Blaise Pascal apply ideas similar to game theory in Pascal’s wager?

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French philosopher Blaise Pascal — Blaise Pascal Blaise Pascal, oil painting by an anonymous artist, c. 1650; in the Musée Carnavalet–Histoire de Paris, Paris. Pascal laid the foundation for probability theory.

In his Pensées, Blaise Pascal applied elements of game theory to argue that belief in the Christian God is a rational choice. He framed the decision to believe as a wager, where one must weigh the potential gains and losses of two possibilities: God exists or God does not exist.1

Pascal analyzed the outcomes as follows:
* If you believe and God exists: You gain infinite happiness.1
* If you do not believe and God exists: You suffer infinite loss.1
* If you believe and God does not exist: You incur only finite disadvantages from a life of Christian living.1
* If you do not believe and God does not exist: You receive finite pleasure from a life unhindered by Christian morality.1

By comparing these outcomes, Pascal concluded that the potential for infinite gain outweighs any finite cost, making the wager for belief the only logical choice. This approach reflects his broader work in the theory of probabilities, where he utilized mathematical expectation to solve problems involving uncertainty.1234