Pascal's rationalisation of religion

Great Expectations:
This is an application of the idea of expectation! Blaise Pascal (1623-1662) gave an interesting argument to show that a rational person should believe in the existence of God. Pascal said that we have to make a wager whether to believe or not to believe. He suggests that we are playing a game with two strategies, believe and not believe, with payoffs as follows:

	God does not exist	God does exist
Probability	p	(1-p)
Believe	-u	$\nu$
Do not believe	0	-x

Here -u represents the cost to you of passing up some worldly pleasures as a consequence of believing that God exists. If you do not believe, and God is a vengeful God, you will lose x. If God does exist, and you believe that God exists, then the payoff is $\nu$. Now to determine the strategy that is best, you should compare the two expected values

$$-pu+(1-p)\nu\qquad{\rm {and}}\qquad p0+(1-p)(-x),$$

and choose the larger of the two. In general, the choice will depend on the value of p. But Pascal assumed that the value of $\nu$ is infinite, and so the strategy of believing is best no matter what probability you assign for the existence of God. Whether Pascal is correct in assigning

$$\nu=\infty$$

is, of course, hardly a matter for mere mathematicians!!!