Betting with the devil

[Theophylact]

A nice paper on Infinite Decision Theory, with (among other things) application to Pascal's Wager. It also contains a reference to a problem I've never seen before:

You are in hell and facing an eternity of torment, but the devil offers you a way out, which you can take once and only once at any time from now on. Today, if you ask him to, the devil will toss a fair coin once and if it comes up heads you are free (but if tails then you face eternal torment with no possibility of reprieve). You don’t have to play today, though, because tomorrow the devil will make the deal slightly more favourable to you (and you know this): he’ll toss the coin twice but just one head will free you. The day after, the offer will improve further: 3 tosses with just one head needed. And so on (4 tosses, 5 tosses, ….1000 tosses …) for the rest of time if needed. So, given that the devil will give you better odds on every day after this one, but that you want to escape from hell some time, when should you accept his offer?

[iNeb]

What if he uses one of the tricked two tails coins? I mean he is the devil!

[gjimene2]

on day 666

[IC]

Originally posted by Theophylact
A nice paper on Infinite Decision Theory, with (among other things) application to Pascal's Wager. It also contains a reference to a problem I've never seen before:

As you should NEVER deal with the devil, the answer is obvious.

Never.

[ShawnD1]

I would wait 100 days.

Luckily I'm good with numbers here to figure out my odds. The equation to figure out my odds of leaving is ugly so I'll try to figure that out later. The odds of me staying in hell look like this:
100C100 * (1/2)^100
The odds of me staying in hell would be 7.8886 x 10^-31

Beat that, Satan



*edit*
Ok I MIGHT have figured out my odds of getting out of hell. Technically it should be 1 - my above answer but I think the ugly way looks neater .



Freedom from hell never looked so good

[no1_vern]

Pascals wager goes like this:


-wager--------------------God exists------God does not exist
Wager for God---------Gain all--------Status quo
Wager against God---Misery----------Status quo

Wagering for God superdominates wagering against God: the worst
outcome associated with wagering for God (status quo) is at least as
good as the best outcome associated with wagering against God (status
quo); and if God exists, the result of wagering for God is strictly
better that the result of wagering against God. (The fact that the
result is much better does not matter yet.) Pascal draws the
conclusion at this point that rationality requires you to wager for
God.

[no1_vern]

Remember that as the sample size gets larger, the percentage of each event will get closer and closer to the expectation. If we were flipping a coin, the expectation is 50% 'heads' and 50% 'tails'. In a sample of 10 tosses, we'd expect 5 heads and 5 tails, but may well have 7 heads and 3 tails. However, as our sample size grows, we'll get closer and closer to 50%, BUT the actual number which one side leads the other will increase. At 1,000,000 tosses, we may be at 49.75% heads and 50.25% tails, but tails has actually come up 50,000 more times than heads!!

Are you sure you would take the bet if you looked at the numbers like this? You may have a streak of 30,000 tails before it EVER comes up heads.

BTW Ive never seen this either, makes you think, though.

[IC]

Proselytizing off topic thread crap deleted.
IC, this is not your captive audience.
The community forum is not your pulpit.
YGPM.

surreal
Moderator

[ShawnD1]

Originally posted by no1_vern
Are you sure you would take the bet if you looked at the numbers like this? You may have a streak of 30,000 tails before it EVER comes up heads.

Probability of 30,000 tails with 0 heads in the first 30,000 throws:
(1/2)^30000
= 0

The number is so close to 0 that my calculator (Ti-83+) actually says the number is 0. The event will absolutely never happen.

[no1_vern]

NEVER? I disagree. Highly improbable, yes.

EACH toss is a has a 1 in 2 chance of coming up tails. The odds of this result NEVER CHANGES. While its highly improbable, I wouldnt bet(not a gambling man-with my soul at least) on/against a 30,000 tails streak, it is possible. It is a fact that "streaks" happen. Ask any statitician, In fact ask any gambler.
Fro example there was an article a while back on a group of students who as a class project "tossed" a coin and kept track. There were several groups each group was to toss the coin 1,000 times. In one group they had a streak of tails that lasted 226 tosses(the longest heads streak was 130). Impossible? NO mearly statistics.

It is of course YOUR soul in this example, but...