Devil's Casino
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11 members have voted
You start with $1, What is the probability that you spend eternity in hell?
Quote: AxiomOfChoiceWhy would I want to leave a +EV game? Is there a better game in heaven?
I'm not making any judgements about if heaven or hell is better..
Also, one downside to Fizzbin is you get punched in the face after you win.
Quote: chrisrI'm not making any judgements about if heaven or hell is better..
Also, one downside to Fizzbin is you get punched in the face after you win.
Well that hardly seems fair. Next you're going to tell me that the devil cheats.
Anyway, there is a well-known formula that answers this question. By well-known, I mean that I don't remember it, and I'm too lazy to derive it.
The answer sure as hell isn't 1, though.
Quote: chrisrYou die and go to hell. As punishment for your sins you are forced to play a game the devil made-up called "Fizzbin". The rules are complicated, but there is no strategy. You must always wager exactly $1 and win $1 with p=2/3 and lose $1 with p=1/3. If you lose all of your money you can leave and go to heaven.
You start with $1, What is the probability that you spend eternity in hell?
66.6 % chance you spend eternity in hell is my guess.
For two reasons :
1) after the 1st flip, if you don't lose you're pretty much screwed. If you lose, you are set free. If you win, you have to hit 1/3 twice in a row. And at the devils game, highly unlikely.
2) 66.6 is the devils number, so it seems to fit.
Is there proof of your 1/3 chance to lose and go to heaven? I feel like the devil would just be laughing at you playing a rigged game.
Edit: does the devil offer comps? They would probably be pretty good, though bad for you. Like Jessica alba GOLDEN water boarding you.
Quote: AxiomOfChoiceWhy would I want to leave a +EV game? Is there a better game in heaven?
This is the best post I have read here in months.
Let p be the answer.
p = (1/3) + (2/3)*p^2 = pr(winning on first flip) + pr(not winning on first flip)*pr(having to lose a $1 twice starting with second flip)
3p = 1 + 2*p^2
2*p^2 - 3p + 1 = 0
Using the Quadratic Formula, p=1/2.
http://filmschoolrejects.com/features/exploring-the-twilight-zone-28-a-nice-place-to-visit.php
This is a special case of the Gambler's Ruin problem, with the two possibilities of "infinitely rich" or bust.
Since the chance of winning > 1/2, the chance of busting = 1 - (chance of losing / chance of winning)initial bankroll; in this case, this is 1 - ((1/3) / (2/3))1 = 1/2.
Would have been nice to say why the other quadratic solution doesn't apply.Quote: Wizard1/2
Let p be the answer.
p = (1/3) + (2/3)*p^2 = pr(winning on first flip) + pr(not winning on first flip)*pr(having to lose a $1 twice starting with second flip)
3p = 1 + 2*p^2
2*p^2 - 3p + 1 = 0
Using the Quadratic Formula, p=1/2.
Quote: chrisrThe rules are complicated, but there is no strategy.
I refuse to play any game which I don't know the optimal strategy
I totally agree.Quote: DRichThis is the best post I have read here in months.
I would have to think you refuse A lot of games. So you walk away from something that's positive even without knowing optimal strategy? This is a very, very costly mistake if you like value.Quote: pokerfaceI refuse to play any game which I don't know the optimal strategy
Quote: AxelWolfI would have to think you refuse A lot of games. So you walk away from something that's positive even without knowing optimal strategy? This is a very, very costly mistake if you like value.
I have to say that you are right.
On the other hand, "optimal" is very subjective.
Just use Baccarat as an example, for the educated gamblers, the optimal strategy is to bet banker every hand.
But for many Asians (no offense here), that's the most stupid thing in the world.
I know one of the most popular "optimal" strategies is to bet the same side as the highest bet on the table,
other people think the "optimal" strategy is to bet on the same side as the one who HAS (not bet) most chips on the table.
Quote: chrisrThe rules are complicated
Fizzbin
Each player gets six cards, except for the player on the dealer's right, who gets seven. The second card is turned up, except on Tuesdays. Two jacks is a "Half-Fizzbin," but a third jack is a "Shralk" and is grounds for disqualification. With two jacks, one wants a king and a deuce, except at night, when one wants a queen and a four.
If a king is then dealt, the player would get another card, except when it's dark, in which case he'd have to give it back. The top hand is a "Royal Fizzbin," but the odds of getting one are astronomical, and apparently difficult to be computed exactly.
The last card is called a "Kronk."
Quote: Lemieux66It feels like the Wizard has some work to do!
I'm slow to get jokes, including this one.
Quote: chrisrYou die and go to hell. As punishment for your sins you are forced to play a game the devil made-up called "Fizzbin". The rules are complicated, but there is no strategy. You must always wager exactly $1 and win $1 with p=2/3 and lose $1 with p=1/3. If you lose all of your money you can leave and go to heaven.
You start with $1, What is the probability that you spend eternity in hell?
The key catch phrase is "there is no strategy". So the probability is one, for "obvious" reasons:
Although you can calculate it to be 1/2, the game will play according to the proposed rules, and indeed the probabilities are 2/3 and 1/3, you will still spend eternity in hell. Why ? Because your game host is the devil and decides to keep you forever. As there is no strategy from your part he will just choose all future game results beforehand. You will never be able to prove that you are cheated (you only have one observation of the whole game).
Quote: WizardA bit off topic, but did anybody else see that episode of the Twilight Zone where a pool hustler died and went to, what he thought, was heaven? It speaks to the theme of the devil cheating.
I meant you should write up the perfect strat to the game in hell. You know, just in case. Lol
Quote: WizardA bit off topic, but did anybody else see that episode of the Twilight Zone where a pool hustler died and went to, what he thought, was heaven? It speaks to the theme of the devil cheating.
Great episode though guy was a gangster not pool hustler called A nice Place to Visit. Love Twilight Zone and that was a really deep episode about what does bring us happiness.
I think he wins, then has to play pool forever?
Quote: apocryphal"Is Hell exothermic (gives off heat) or endothermic (absorbs heat)? Support your answer with a proof."
This was an actual question given on a University of Washington chemistry midterm:
Most of the students wrote proofs of their beliefs using Boyle's Law (gas cools off when it expands and heats up when it is compressed) or some variant thereof.
One student, however, wrote the following:
First, we need to know how the mass of Hell is changing in time. So, we need to know the rate that souls are moving into Hell and the rate they are leaving. I think that we can safely assume that once a soul gets to Hell, it will not leave. Therefore, no souls are leaving.
As for how many souls are entering Hell, let's look at the different religions that exist in the world today.Some of these religions state that if you are not a member of their religion, you will go to Hell. Since there are more than one of these religions and since people do not belong to more than one religion, we can project that all people and all souls go to Hell.
With birth and death rates as they are, we can expect the number of souls in Hell to increase exponentially.
Now, we look at the rate of change of the volume in Hell because Boyle's Law states that in order for the temperature and pressure in Hell to stay the same, the volume of Hell has to expand as souls are added.
This gives two possibilities:
(1) If Hell is expanding at a slower rate than the rate at which souls enter Hell, then the temperature and pressure in Hell will increase until all Hell breaks loose.
(2) Of course, if Hell is expanding at a rate faster than the increase of souls in Hell, then the temperature and pressure will drop until Hell freezes over.
So which is it?
If we accept the postulate given to me by Ms. Therese Banyan during my Freshman year, "That it will be a cold night in Hell before I sleep with you," and take into account the fact that I still have not succeeded in that area, then (2) cannot be true, and so Hell is exothermic.
The student got the only A.
Quote: MangoJThe key catch phrase is "there is no strategy". So the probability is one, for "obvious" reasons:
nah.. just a classic particle absorption problem
I find the solution to this one quite counter intuitive. From any state there is a positive probability of reaching 0.. but if you play forever (literally) there is a chance of never reaching 0.
Quote: Wizard1/2
Let p be the answer.
p = (1/3) + (2/3)*p^2 = pr(winning on first flip) + pr(not winning on first flip)*pr(having to lose a $1 twice starting with second flip)
3p = 1 + 2*p^2
2*p^2 - 3p + 1 = 0
Using the Quadratic Formula, p=1/2.
It's been a while since my probability days... but how did you get that last part about "pr(having to lose a $1 twice starting with second flip)"? If you win twice, you would then have to lose 3 times... and there would be several combinations of wins and losses that could get you to zero. How did you simplify this into (2/3)p^2?
There are two ways to do that: you can lose the first bet, or you can win the first bet, then go through a sequence of bets where you lose one unit, and then go through another sequence of bets where you lose another unit.
It's a good, simple, clean solution. I like it a lot.
