The Most Rational Bet

Imagine that you're a contestant on a game show and that the game consists of placing a sealed box in front of you and being told that the box contains either $1,000,000 or $1. There's a 50/50 chance of either. You have to guess which it is, and if you choose correctly you get to keep whatever it is that you guessed. Suppose further that refusing to guess at all is the same as guessing $1.

Those are the terms of the game. What would you do? Would you play? Which option would you choose?

Suppose you were told that the odds were not 50/50 but rather 100 to 1 that there was $1 in the box. Which option would you choose then?

The reasonable thing to do, of course, is to guess that there's a fortune in the box regardless of the odds. If you're right you gain $1,000,000, and if you're wrong you lose almost nothing. If, on the other hand, you bet that there's $1 in the box and you're right you gain very little, but if you're wrong you lose out on a fortune. To bet on the $1 seems irrational and foolish.

This is, broadly, the argument proposed by the brilliant French physicist and philosopher Blaise Pascal in the 17th century that's come to be known as Pascal's Wager. In Pascal's version the choice is between believing God exists and committing one's life to Him or declining to believe He exists. As with the box and the fortune, Pascal says that if you believe and you're wrong you lose relatively little, but if you believe and you're right you gain an immeasurable benefit.

By "believe" Pascal doesn't intend a simple intellectual assent but rather he means a placing of one's trust in the one in whom he believes. Nor is Pascal offering this argument as a "proof" that God exists. Nor does he assume that one can simply choose to believe or even should choose to believe as a result of a calculation of the benefits and liabilities. What he's saying is that belief, if one has it, makes perfect sense.

In other words, the skeptic who declares theistic belief to be irrational is simply wrong. The theist has everything to gain and relatively little to lose. The skeptic has relatively little to gain and everything to lose, so whose position, Pascal might ask, is the more rational?

This argument has triggered a lot of reaction, much of it negative. There are a number of objections to it, and although most of them are pretty weak, some of them are not. Susan Rinnard a philosopher at Harvard, did a video on Pascal's argument which does a pretty good job in just a few minutes of explaining the Wager and which offers a version of the argument that avoids some of the pitfalls of the original:

For those interested in reading an excellent treatment of the Wager with responses to the major objections Michael Rota's book Taking Pascal's Wager is one of the best resources out there. It's certainly much better than most of the stuff one finds on Pascal's Wager on YouTube.