Pascal's Wager Revisited

To people who are familiar with Pascal's Wager I won't repeat it. Those who are unfamiliar with it can read up about it here. I want to share three of the main criticisms of it in what follows.

There is the evidential objection, the many gods objection, and the gambler’s objection.

The evidential objection concerns how much evidence Christianity should have before I must take seriously the claims of Christianity. Keep in mind that the only brands of Christianity that make the wager a strong argument are the ones that promise an everlasting conscious torment in a fiery hell. Other brands of Christianity don't even apply, those affirming annihilation, or universal salvation, since there is not much to fear if one is wrong. In any case, I judge that conservative Christianity has about a .00001% probability of being correct, or 1 in 100,000. This is something I think one can conclude from the arguments in my book. Given that I might be wrong in this judgment, since I've been wrong before, I'll up it to a .0001% probability, or 1 in 10,000. This probability has nothing to do with how many other religions and gods there are. It's a probability based solely on the merits of the evidence and arguments themselves.

Keep in mind what this means. It means unless there is a religion with a greater amount of probability then there is a .0001% chance this life is all there is. It means that there is a 99.999% probability that Christianity is delusional and that Pascal’s Wager is an argument akin to someone crying "wolf," or someone else yelling "the sky is falling." Why should I place that bet even if the payout is an infinite amount? If the bet was some money, wouldn't I be throwing money away? Sure, people are not being unreasonable by placing a bet on these odds, but what reason would we say that a non-gambler should bet based on these odds?

And what are we to bet? According to the Christian faith I must bet it all, my whole life. I must die daily. I must take up my cross and follow Jesus. I must be totally committed and have total faith. That’s what I’m called upon to do, daily, even to the point of guarding my very thoughts. I must sacrifice that which I think about and I should not lust, hate, covet, nor entertain any doubts.

I can understand betting a few dollars to win the lottery even though there is a 1 in 80 million chance to win. But I would never consider betting everything I own based on those odds, even if the payout was 800 trillion dollars, nor would I want to bet my whole life on a 1 to 10,000 chance of eternal bliss.

Still, I'll admit Pascal's wager has a good deal of force, the evidential objection alone notwithstanding, since the payout is an infinite amount with an eternal bliss if correct.

The many gods objection almost eliminates the force of Pascal's wager, I think, since now we have many religions and many gods all clamoring for our obedience; Muslims, Mormons, Jehovah's Witnesses, and so on, and so forth. One religion claims that if you don't follow its god you will fry in hell, while another one makes the same claim. Since many gods are threatening us with hell if we don't believe, then Pascal's Wager cannot help us to decide between them. All of them offer an infinite payout, too. All of them demand belief and obedience. Whom should we believe? Whom should we obey? Pascal’s Wager does not answer this objection on its own terms. We still must judge which religious viewpoint has the most probability and such judgments are based on the accidents of birth, as I’ve argued.

The third objection is what I call the the gambler’s objection. Anyone who plays the very popular poker game called Texas Hold'em , for instance, knows what I’m talking about when I say there is a distinction to be made between the actual odds and the pot odds. Actual odds are the mathematical odds of our hand winning the pot. Pot odds concern the relationship of the money in the pot to the actual odds of our having the winning hand. If, say, in order to bet on our hand we only need to bet $5 more to win a pot of $200 (or a ratio of 1:40, which is known as the pot odds), then that’s a good bet even if the actual mathematical odds of winning the hand are not that great. If, on the other hand, we must place a bet of $50 to win the same pot of $200 (or a ratio of 1:4 pot odds) the bet is a bad one unless the actual odds of winning the hand are much greater.

Let’s say you need a particular winning card to be drawn, which could be a spade (for a flush), or an Ace, or a King, and you calculate the odds of one of those cards being drawn are about 1 in 3. Let’s say there are five players and you must decide whether or not to bet $4 on a pot that has $36 in it. That’s 36 divided by 4 equals 9; or 9 to 1 pot odds. At that point you must ask yourself whether you should place that $4 bet. The actual odds are against you 1 to 3, but the pot odds are in your favor 9 to 1. Because of the pot odds you should bet the $4, and here’s why: If you faced this same situation seventy-five times and bet $4 each time for a total of $300, and you won one time out of three bets (the actual odds), your gain would be about $900 because of the pot odds.

Now let’s consider the actual odds and the pot odds when it comes to Pascal’s Wager. The actual odds for the Christian faith, as I calculate them, are 1 in 10,000, being generous. The payout is an infinite amount; an eternal bliss (the pot odds). With the pot odds so extremely high I should always make the bet, it’s argued. But here’s the problem. Pot odds only come into play if the gambler plays a certain number of hands. If the actual odds for a winning hand in Texas Hold’em are 1 in 3, it does not matter what the pot odds are if he must bet everything he has, and if this is his last hand! Pot odds only matter when the gambler can play a number of hands and when he’s not betting it all. It’s the number of hands along with the size of the bet that make the pot odds what they are.

How many times can a gambling religious seeker go “all in” on a bet that has a chance of winning the eternal bliss pot, when the odds are 1 in 10,000? He can only do this one time! There are no second chances. The poker game will be over for him no matter what the result is. The actual odds are extremely low for his bet. With those odds he will undoubtedly lose everything he has on this one bet! It’s only if this religious gambler can make 10,000 lifetime wagers and that he has something leftover to bet each time that would make the pot odds worth the bet!

Given the actual odds as I calculate them, I would have to sacrifice 10,000 lifetimes for the pot odds of an infinite bliss in heaven to be worth the bet. Not just one life. 10,000 lifetimes. But I will not have 10,000 lifetimes to make that bet worth it! So I must bet on the actual odds, and I do.

For this reason gamblers who play Texas Hold’em do not bet everything they’ve got unless they are pretty sure they have a winning hand, with the actual odds being over 50% or more, preferably 60% to 90%, depending on several other factors. Since I calculate the odds at much less than this and because I must bet on the actual odds, going "all in" on a bet like this is simply a bad bet.

Hence Pascal’s wager fails…badly.

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