Game Theory & Pascal’s Wager

Pascal’s argument (written in the 1600’s) went like this: Suppose you concede that you don’t know whether or not God exists and therefore assign a 50 percent chance to either proposition How should you weight these odds when decided whether to lead a pious life? If you act piously and God exists, Pascal argued, your gain – eternal happiness - is infinite. If, on the other hand, God does not exist, your loss, or negative return, is small – the sacrifices of piety. To weigh these possible gains and losses, Pascal proposed, you multiply the probability of each possible outcomes by its payoff and add them all up, forming a kind of average or expected payoff. 

In other words, the mathematical expectation of your return on piety is one-half infinity (your gain if God exists) minus one-half a small number (your loss if he does not exist). Pascal knew enough about infinity to know that the answer to this calculation is infinite, and thus the expected return on piety is infinitely positive. Every reasonable person, Pascal concluded, should therefore follow the laws of God. Today this argument is know as Pascal’s wager. 

Pascal’s wager is often considered the founding of the mathematical discipline of game theory, the quantitative study of optimal decision strategies in games.

Leonard Mlodinow, The Drunkard's Walk: How Randomness Rules Our Lives

So Much Straw

It is said that on 6 December 1273, while he was celebrating mass, a great change came over Thomas Aquinas. At the age of 49, his Summa Theologica ("Summary of Theology" – nearly 1300 pages) unfinished, he stopped writing. To his faithful secretary and companion Reginald of Pipersno, he said, ‘Reginald, I can do no more; such things have been revealed to me that all that I have written seems to me as so much straw. Now, I await the end of my life of my works.’ Aquinas died three months later.

All our talk about God is halting, partial, hopelessly inadequate. This does not mean we should not hold firm beliefs about God or do the best job we can as philosophers and theologians. It simply means that no matter how much skill or effort we bring to the job, God always remains in part a mystery. The gap between God and our ideas about God was, we believe, salvifically narrowed by God’s revelatory initiative, but not closed.

Like Aquinas, all Christians can see that human talk about God ultimately comes to an end. It’s best efforts are like straw.

Stephen T. Davis, Logic and the Nature of God