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Pascal’s Wager and Game Theory

Despite its academic origins, game theory can be seen all throughout the world. It’s in love, war, employment, and nearly every aspect of our lives. It shouldn’t come as a surprise then that religion – even as one of the most nonsecular subjects – too can be viewed within the scope of game theory. Pascal’s Wager states that any rational person should behave as if God exists, even if they consider the probability of his existence to be infinitesimally small.

Pascal came to this conclusion with a simple set of assumptions. Clearly, God either exists or he doesn’t. If God exists and a person believes, he/she stands to receive an infinite reward in the form of eternal salvation. If God exists and a person does not believe,  he/she stands to serve an infinite punishment in the fiery pits of hell. However, if God does not exist, then the payoff/cost for either believing or not believing is some finite amount, far overshadowed by the infinite reward/punishment associated with the existence of God. For any nonzero probability of p of God existing, the expected payoff for believing in God will be infinitely larger than the payoff for not believing in God. Why exactly believing is a dominant strategy becomes far more clear when looking at a 2×2 matrix and considering Nash equilibria.

Let’s consider a simplified case where believing / not believing in God in a world where God does not exist share the same utility to a person. For example, not believing in God in a world where God does not exist might provide one with 200 units of pleasure associated with not having to go to mass / follow religious traditions. And believing in God in a world where God exists might provide one with 200 units of pleasure associated with being part of a larger organization and having a more positive outlook toward the afterlife.


Person                                  God Exists             God Does Not Exist

Believe                                   INFINITY                  200

Do NOT Believe                       -INFINITY                  200


Believing in God is a dominant strategy for a logical actor as regardless of the state of God’s existence, belief provides the maximum payoff. Learning about Pascal’s Wager has shown me that game theory and the consideration of payoffs play an impactful role all throughout our daily lives. We are constantly considering payoffs and looking to maximize our payoffs, even in topics as far off from economics and game theory as religion.



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September 2015