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Notes -
Pascal's wager is terrible because infinite rewards break game theory.
Suppose I ask you to give me $10 and in exchange I will reward you with $10000. Should you take this wager? To answer this question you could estimate the probability p that I'm telling the truth and calculate the expected value of the wager: 10000p - 10(1-p). If it is positive you should pay, if it isn't you shouldn't. It's unlikely that you will be able to prove that p=0 but it also doesn't matter, as long as you estimate it to be low enough that all you need to know.
But suppose I promise you an infinite reward for your $10. The condition is now ∞p - 10(1-p) > 0 which is always true if p > 0. So, as long as you can't call me a liar certainly you have to enter the wager. What's worse this is independent of the entry price. As long as I ask for a finite price, no matter how large, you have to pay it.
What does this mean? Either we should reject all wagers that involve infinite rewards (because otherwise we would have to take all of them) or, if we choose not to, we are lucky that there are multiple incompatible religion. Because taking one religion's wager means rejecting many other and some of the other will have infinite punishments for rejecting them all of the wagers are undecidable and we are free to choose whichever we want or reject all of them.
Rejecting infinite wagers doesn't suffice, you'd still need to worry about graham's-number wagers.
The correct thing would seem to orient yourself around one of the possible infinite rewards—work out what credibly is the best, weigh competing infinite positives and negatives, etc. I'm not sure what the math would entail, but I don't see why they'd all cancel out.
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Also I wanted to point out how bizarre the entry about the wager in the pensées is: it ends with a note that, if this argument (the wager) isn't enough to convince you to believe you should then go to mass every day and the monotonous repetition of the liturgy will make you as stupid as a beast and then you will be able to believe. It seems unexplicably blasphemous to me.
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