# An obvious solution to Pascal's wager : what's this solution formally called?

So here’s a problem similar to Pascal’s wager. At some points in time, when the powerball is a large dollar amount, the Expected Value of a lottery ticket can potentially be positive.

Say each lottery ticket is worth \$1.10, and the time between lottery ticket purchase and payout is 1 month.

A purely rational agent, expecting a 10% 1 month-return, or a 120% annual return - if this was a bot you had programmed to seek optimal investments, it might look at the ROI and invest all of the money it has into lottery tickets.

Say the agent only has 100k and the total amount of lottery tickets purchased is 100 million dollars, and to simplify the math, assume no duplicate tickets.

Then the odds of one of the tickets winning is 1/1000.

So the flaw of the agent is yes, overall, the ROI is positive, but in 999/1000 of the futures the agent is likely to experience, it goes broke.

So this implies a way to not get fooled by Pascal’s wager. Just choose some fraction (I’m not sure how to do this) of the probability distribution. Essentially don’t consider events that have a less than 1% or 0.1% or some arbitrary threshold of likeliness because no matter how bad or good they are, they probably won’t happen to you.

And this is how you could avoid getting mugged by organized religion. A simple analysis of the number of possible (mutually exclusive) religions that exist would indicate that even if “one true religion” exists, backed by a real deity (who is invisible and intangible but is still real), *your *chance of guessing the correct religion is dismally small. Certainly under 1 in 100. So there’s no point in wasting your time and money on one.

Anyways, mathematicians have no doubt proposed this : what’s it called and do they have a better solution?

Doesn’t work because Pascal’s wager assumes infinite payoff for going to Heaven and an infinite negative payoff for going to hell. So the probabilities (unless zero) don’t matter.

However, if there are multiple religions that all give negative infinite payoff for going to appropriate hell then assuming you can only satisfy one religion all choices have a negative infinite term so they are non-comparable by expected values (or expected utilities if it’s utility payoffs that are infinite).

Ok, in this example, I am saying you do :

You consider heaven an infinite reward. (due to discounting it’s finite but that’s besides the point)
100 mutually exclusive religions of significant size.
You believe a true religion exists.
1% chance of going to heaven. (1 in 100)
Since in 99/100 of the futures, you do not go to heaven, and you do not consider events that are less than 1% likely (that’s the fix), you multiply the infinite reward by 0. You do not care it’s infinite because the reward is too unlikely to happen.

So the fix is you simply ignore probabilities that you have a low chance of actually experiencing. Maybe you should consider 1% chances, maybe not, point is you have threshold or some kind of rolloff to zero.

That’s still no solution when talking about infinite happiness versus infinite pain. Saying 1% is so small it may as well not exist is a ludicrous opinion in these circumstances.

We still can’t evaluate unless you tell me what infinity * zero is.

Also discounting won’t make an infinite number finite. Applying a bounded utility function will which is one reason why von Neumann and Morgenstern assumed/derived utility functions to be bounded.

It’s zero. If whatever theory of math you are using doesn’t allow that, then just use my alternate algorithm, which is you simply drop from consideration any very small probability events, where “very small” is up to interpretation/possibly can be solved for. Note that using 1% is an example, you can set the threshold smaller or use some other formulation.

Cool story bro.

It’s not just that. “Solutions” like this miss the point of Pascal’s Wager. The point is that if there is no God or afterlife, you win nothing if you bet right, and you lose nothing if you bet wrong.

This is not correct. Like lottery tickets, religions have a cost. Quite a bit more expensive a cost than a lotto ticket. When Pascal wrote up his wager, some significant fraction of the week was spent observing church practices (I don’t know the details of Catholicism in the 1630s) and the church demanded a tithe of 10% of a person’s income.

Quite an expensive lotto ticket.

Here is a door. There is a 1% chance that there’s a big guy named Bubba behind it that will rape you and then murder you. For a penny, you don’t have to open the door. Since your threshhold is 1% I assume that you’ll be saving your money.

Pascals wager is much more easily combatted by invoking Allah, a god that punishes you for believing in the Christian God.

I didn’t say my threshold was 1%.

You would agree that a threshold exists where you wouldn’t give up a penny for every door you enter, right?

Sure you lose something if you bet wrong; you lose the amount you bet. Which in Pascal’s wager is essentially your entire life. Pascal’s wager is asking you to bet everything you have in the unsupported hope that there’s actually a bet going on.

Consider Nemo’s Wager. That’s the one that says you die and show up at the Gates of Heaven. Should you enter Heaven? Or should you refuse to enter Heaven because there might be some afterlife that’s infinitely better than Heaven - but the only way into this Super Heaven is to refuse to enter Heaven. So by the logic of Nemo’s Wager you should refuse the pleasures of Heaven in order to have a small chance of gaining the infinitely greater pleasures of Super Heaven - even though you have no evidence that Super Heaven exists or that this is the path to getting there.

So how is Nemo’s Wager different than Pascal’s Wager? The logic of Pascal’s Wager is that you should refuse the pleasures of Earth in order to have a small chance of gaining the infinitely greater pleasures of Heaven - even though you have no evidence that Heaven exists or that this is the path to getting there.

You implied that it was 1% or 0.1% or … something else. Do you tell your health insurance company “Please rewrite my policy and lower the premiums. I don’t want to be covered for any of the rare cancers, or any rare diseases at all for that matter. Don’t cover me if my heart attack is on the 3rd Thursday of a month — that won’t happen to me! Or the 2nd Thursday for that matter.”

Google “Kelly’s criterion” or, if you insist, “fuzzy logic”, but let’s have no hard thresholds please.

Start by rejecting any religion which insists it is the “one true religion.” That should reduce the count to well under a 100.

There is no reason to logically privilege any current religion over the others, and there is no reason to favor them over any nonexistent religion, either.

For every current religion, there is just as much evidence for its complete and utter reverse: a hypothetical “opposite day” religion. Whatever you do or think or choose, you are equally likely to be condemned as praised, even if, contrary to common sense, entities that care about such stuff actually exist.

So does: “I was just hedging my bets” get you into the pearly gates?

The whole idea of Pascal’s Wager seems to imply that you can “fool” God into thinking you’ve accepted him into your heart and embraced his ideology.

Uh, cite? Same dude, different name.

We don’t really need to get into a theological discussion of who goes to Jahannam and how long they stay there. The Quran is contradictory on the point and Meccan surahs seem to like Christians and Medinan surahs seem to sentence them to Jahannam. Surah 5:72 for example says

The opinions of individual Muslim scholars vary.

Regardless, in this context, it doesn’t have to be Allah. It can be any ‘anti-God’ who punishes Christians and rewards non-Christians. It changes the math of the equation.

Hmm. Maybe somebody should come up with a religion that says only atheists go to heaven. Just to cover all the bases.

What life? Even if you accept the ridiculous assumption that believing in God means you give up everything, if there is no God, no after life, then once you’re dead it will be as if you never existed. Nothing you did will matter to you. If there is no God, nobody wins and nobody loses.