Monday, August 8, 2011

Pascal's wager part 2

Pascal's wager is often misunderstood, because he never meant it to be taken on its own.  Last time, I mentioned that it's simply a cost-benefit analysis, and doesn't weigh in at all on actual evidence for Christianity.  But to boil the wager down really quick, if you believe in the God of the bible, you risk little (usually seen as a life lived "the way you want to") in order to gain an infinite amount (spending eternity in the presence of God).  If you don't believe in the God of the bible, you risk an infinite amount in order to gain little. But infinites are hard to imagine, so for the sake of argument, let's just say that it's not an infinite amount.  Let's say its a large amount, orders of magnitude more than the "little" that you might give up.  Now, if we're not talking about Christianity, would you take that bet?  Would you put money down on that line?

The way these sort of things work in Vegas, when you encounter a wager that would gain you much when you risk little, that wager is a long-shot.  The bookkeepers in Vegas make sure that type of wager is only possible when you face long odds.  For example, betting on the Cubs to win the World Series.  You can wager only a small amount on that, and if you are correct, you can get a big payoff, because it's such an unlikely occurrence.

Or betting on a horse that faces 1:1200 odds of winning the Kentucky Derby.  But that means if you put a dollar down on that horse, you stand to win a substantial amount if that horse actually won.

Another way to look at is winning the lottery on your first try.  You wager a buck, and get 8 million when you win.  

So, if the Vegas bookies were somehow in charge of such a wager, where you risk little to gain a lot, then you can surmise that wager would be so unlikely, it's not gonna happen.  Those kinds of payoffs only exist on bets whose odds are like winning the lottery.

You get my point.

So, back to Pascal's wager.  Again, let's not think about infinity, but only focus on the payoff being orders of magnitude larger than the risk.  If the odds that the bible is true are even, then that's a pretty good bet!  If the odds that the bible is true is one out of a hundred, that's a pretty good bet!  If the odds were even so low as to be one out of a million, that's still a pretty good bet!

Of course, most people don't think that way, and that's because there's a probabilistic (or maybe economic) fallacy buried somewhere in there.  We'll get to that next time.