You wake up one morning in hell and see the Devil in front of you. He says to you, "Yes, you're dead. Yes, you're in hell. But there's hope for you. We can play a little game. If you win, you go to heaven for all eternity. If you lose the game, you stay in hell forever. Your only choice is when you decide to play the game. If you play the game today, you have a 1/2 chance of winning. If you play tomorrow, you have a 2/3 chance of winning....the day after that, a 3/4 chance of winning, and so on, and so on, with each day progressively increasing your chances of winning."


Remove all the theological problems from this and work within the confines of the mind experiment as it stands. Assume that the Devil will keep his word and assume that if you win the game, you will indeed go to heaven.

When is the most rational time to play the game?

After a very long bout of torture.......if it were possible, after an infite amount of time but since that isn't possible, after such a time that the chances are close enough to 100% so as to effectively be considered 100%

That's not the traditional answer, but hold off a second and let's hear some more answers.

What if it's not a game of chance?

When you reach the point that the risk/reward quotient is sufficiently tipped in favor of taking the chance of being in Hell forever.

Here are the options:

1) stay in Hell forever by not playing
2) deciding when the risk/reward is worth it

Option 1 is really not an option since that option is incorporated within option 2 should you lose.

So what do you do? You put up with the fires and pain of Hell as long as you can to increae your odds of going to Heaven.

math

From the math point of view, the risk/reward calculation is infinity/infinity, which is an undefined and therefore meaningless term.

I don't see that

Today, there is a 50% chance, tomorrow it is 66%, the next day is 75% and so on. Mathmatically, your odds improve.

Refuse to play it. Entering into a gambit with the devil is morally reprehensible, it's gambling, and God's divine judgement places you in Hell, so face it. (yes, I comprehend you're dismissing all theological elements of the question, but I don't think it's a relevant idea without them)

I don't know what Max has up his sleave, so I don't know if this radically changes the outcome, but what if you were hellbound, and it was God that gave you the challenge? Let's say that he suspended his Natural Law to allow for such a gamble, and told you so, so your conscience would be clear.

Max, does this change it too much?

FJ

If that is the case, let us say...ah, it's a sticky one. You're never going to get a certain chance, so I suppose, assuming the game is fair (if God himself made the challenge, it would be), then I'd say...hmm, I dunno.

I don't think the devil has the authority to release anyone from hell. That's within God's purview, and not the devil's. But let's ignore that theological problem.

The devil is likely to cheat at the game, making sure you lose any, but let's ignore that theological problem.

But let's do the math.

Today: 1/2 50%
Day 2: 2/3 66.6666%
Day 3: 3/4 75%
Day 4: 4/5 80%
Day 5: 5/6 84%
Day 6: 7/8 87.5%
Day 7: 9/10 90%
Day 8: 10/11 91%
Day 9: 11/12 91.666%
Day 10: 12/13 92.07%

So around day 7 or 8 is the optimal time. Each day past that you're getting less of a chance, so is it worth one day of hell to get an extra 0.6%?
The law of diminishing returns.

All the normal understandings go out the window when infinite values enter the calculation.

Assume that the value of staying in Hell forever is infinitely negative while the value of entering Heaven is infinitely positive (surely there's no argument with either of those). Then the expected value of playing the game on day i is (i / (i + 1)) * [positive infinity] + (1 / (i + 1)) * [negative infinity]. But the value of any positive number times positive infinity is still positive infinity, and the value of any positive number times negative infinity is still negative infinity. The equation therefore reduces to [positive infinity] + [negative infinity] = [positive infinity] - [positive infinity], and (unlike with "normal" numbers) infinity - infinity doesn't equal 0, but is indeterminate.

Why?

The set of positive integers (1, 2, 3, 4, 5 . . . . ) is of infinite magnitude.

* If I subtract from that the equally infinite set of prime numbers, I still have an infinite number of elements left, so in this case, infinity - infinity = infinity.

* If I subtract the set from itself, then there are no elements left, and infinity - infinity = 0.

* If I subtract the set (2, 3, 4, 5 . . . . ) from it, then infinity - infinity = 1, and more generally if I omit the first n positive integers, then infinity - infinity = n.

So there is no way to evaluate the original equation because there is no point at which I can say that a 6% (or whatever) chance of being in Hell forever is an acceptable risk in light of a 94% (or whatever_ chance of being in Heaven forever.

I would take the 50% offer if getting out of hell is the goal. Why would I want to stay in there at all? The longer I stay in there, the longer he has the pleasure of my company. I think that's the game.

Siggy

What if there really is no real time in Hell?

by this, I mean a day could be like a hundred or a thousand yeras. Tomorrow could techinically never come. And, you can't trust Satan anyway, so why try? I can't assume that Satan will keep his word. That in itself is a fallacy.

Hmmm............ Does the devil experience pleasure?

I'm with Siggy. You play the game right away. If you are one of the Elect, you can't lose, and your chances are 100% from the get-go.

Only my elbow.





Any theological concerns regarding the validity of the thought-experiment ought to be discarded. The original designer of this experiment used hell and heaven simply in order to incorporate the concepts of infinite-value and infinite disvalue.

It's a paradox.

Spending one more day in hell (finite cost) to increase your chances of obtaining heaven (infinite reward) will always be worth it. Even if the increase in chance in infinitesmal (like .000007 per day after 1 year, iirc), the most rational decision is to wait that one more day.

But what about the hope issue? Let's say we play the game on day one and take our 50% chance. If we win, great. If we lose, then we're stuck in hell without ever having the hope of getting out. Each day you stay there and increase your chances, you still maintain the hope that some day you can leave. How much should this hope enter into the equation?

Wouldn't the atmosphere reduce the level of hope? Hell is the absence of the Face of God, so hope would wither and die very quickly. What will you win if you've lost your soul for even one day? If you wait, you're experiencing the full effects of Hell.

Siggy

I got it right.

Hope plays a large part, IMO. You put up with Hell as long as possible in the hope that you will be able to leave. Your hope increases as your odds increase.

That's right. Another reason not to trust the devil.