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Betting on Thirteens

Answering the "Many Gods" objection to Pascal's Wager. (Part 2)

Dice showing a roll of thirteen. This is the second of two responses to the "Many Gods" objection to Pascal's wager. The first part pointed out that the wager as it was originally penned cannot be a false dichotomy because there can logically be no third option between at least one god existing and no gods existing. Choosing which god or gods to believe in then depends on arguments separate from the wager itself.

The second possible riposte is a little bolder. This shows that the wager can still apply directly to an individual god, such as the Christian Trinity, even if other gods could be out there. First, let's give our anomaly a friend and try our hand at Gambling.

Mathematicians struggle with Infinities at the best of times, though they do know that any Casino that offered an infinite payout would soon be broke. Instead we'll say that you put down a fiver to play, and you get £50 if you win. Our gamble is simple: roll two dice, and you win if it's a seven. The odds of throwing seven on two fair dice is well known to be 1 in 6, so a bit of basic probability theory suggests you can expect to make an average of £3.33 each go for playing this game. In other words, success is sufficiently probable and the payout sufficiently large that this is actually a good gamble.

Now suppose that the Casino next door offers a similar game, but these guys tell you that you get the prize if you throw a twelve. Throwing a twelve is much less likely however, the odds of such a score are 1 in 36. In that Casino, you can expect to lose £3.61 each try if you play the game. It really doesn't matter if there are ten or a hundred Casinos offering this game on the "throw a twelve" mode; you just ignore them and go back to the first place.

Now imagine that the next door Casino offered a prize on throwing a nine, which has much more respectable odds of 1 in 9. Here you can expect to make a profit playing the game, but only to the tune of 55 pence per throw. While this is much better than any Casino you'll find in Las Vegas, it would still be outright daft to come here when you can make your fortune six times faster down the street. Again, you ignore it and go back to the first place.

Finally, what if a Casino tried to tell you that they'll offer the same game and all you have to do is roll thirteen? These are normal, cubical dice numbered one to six. The odds of rolling thirteen on two normal dice is precisely zero. It doesn't matter how big the pot is, every time you bet in this gambling house you can guarantee you give them your fiver for nothing! You'd unavoidably be better giving it to charity; at least then you get the nice feeling of having helped someone.

What does all this have to do with Pascal and the false dilemma charge? Atheists will often assume, quite incorrectly, that every religion is effectively the same. They imagine that even were it feasible that some god exists, the chance of picking the right one is stretched evenly across hundreds of thousands of different religions until it's imperceptible. They also often incorrectly assume that the reward is always the same eternity of paradise but for the sake of simplicity I'll let that one go.

Because the religions are not in fact all the same, because each has different evidence supporting it and different problems inherent in it, the odds that each is correct are certainly not spread evenly. Betting on Islam may make sense according to Pascal's logic, certainly the promised reward is noteworthy and some of their arguments make a measure of sense. Nevertheless (and again I'd make this judgement based on external arguments) that gamble may be seen as the betting on nines house. It's good, but not sufficiently good.
Betting on Zeus is just asking to fail; like going to the throw a twelve house it is far more likely to be false than to be true. Certainly Zeus, neither timeless nor omnipotent, wouldn't be consistent with many of the positive arguments for God's existence.
Betting on the Flying Spaghetti monster is even dafter. Indeed betting on any of the "gods" that people make up in order to fill out the number of possible deities is as foolish as going to the "throw a thirteen" casino. Even their own proponents acknowledge that they have no evidence for such a god, do not believe in such a god, and invented it for the sole purpose of attracting mockery. Anything that can be asserted without evidence can be similarly dismissed, and even if they array in their millions these invented deities contribute nothing to the wager.
Finally, just as our first betting house offers genuinely attractive odds irrespective of what the others were doing, one religion which does have a large body of supporting evidence and a guarantee of God's favour becomes the clear favourite in terms of Pascal's wager. Defending the position that this religion is Christianity is beyond the scope of this analysis but well within the coverage of a decent Christian apologist.

One thing is sure however; Pascal's wager is not destroyed by its opponents merely spitting out fictional deities at a rate that would turn a machine gun green with envy.