Non-poker problem, I just want some replies

[Dice Man]

Right, I'm currently working on this problem and am wondering what people's intuitions are concerning it. It's very simple, which is why it's annoying me. It isn't poker-related but is about beliefs about probability, so has some kind of link.

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Imagine this experiment: We have a 100-sided die. Every time we roll the die if it lands 1-99 (i.e. 99% of the time) we will wake up Sleeping Beauty once. Every time it lands on 100 (1%) we will wake her up 1001 times. Suppose that whenever she wakes up she cannot remember any previous awakenings: all she will be able to remember is that this experiment is happening to her, she has woken up but she doesn't know where she is in the order of the awakenings: every time she wakes up will seem to her to be the first time she has woken up since sleeping. The important thing is she knows the rules of the experiment and all about the die etc...

Now imagine we do this in the long term...

Every 100 throws of the die we can expect one roll of 100 and 99 rolls of 1-99. So she should expect to be woken up 99 times for the rolls of 1-99 and 1001 times for the roll of 100, so in total she expects to be woken up 1100 times every 100 rolls.

Now every time she wakes up her thoughts will go like this:

"There is a 91% chance I have been woken up as a result of the die landing 100, and a 9% chance I have been woken up as a result of the die landing 1-99".

This is because she has done the calculations: 1001/1100= 0.91 and 99/1100-0.09.

As far as I can tell this is all to be agreed with so far. If not then object.

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Now suppose...we are only going to do this experiment once, we will only roll the die once, and she knows this. Before the experiment starts surely she believes the chance of rolling 100 is 1%. But according to the calculations, when she wakes up she will believe the chance that a 100 was rolled was 91%.

Furthermore, she knows this in advance. She might think:

"I believe now that the chance of 100 being rolled is 1%. But whenever I wake up I will believe it is 91%."

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Now does anybody else find that slightly weird? She is a rational thinker, and yet she has two very different beliefs about the probability of an event at different times. She is given no new information between the times of "before-waking-up" and "after-waking-up". Even weirder is at both times (before and after waking) she will know that before the experiment she believed 100 was 1% likely, and after she believes it is 91% likely. Is this not just a bit fucked up? Any solutions? Any other comments?

[waltypies]

Right, I'm currently working on this problem and am wondering what people's intuitions are concerning it. It's very simple, which is why it's annoying me. It isn't poker-related but is about beliefs about probability, so has some kind of link.

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Imagine this experiment: We have a 100-sided die.

Sorry i switched off here

[PokerWoody]

No, I don't find this weird.

[Dice Man]

No, I don't find this weird.

Do you mean that in a sarcastic way or do you mean you don't find her mental state being weird?

If the latter then the problem is that she is susceptible to being dutch-booked, as they say. That means that she will accept a bet pre-sleep and another bet post-sleep, and she is guaranteed to lose money.

For example pre-sleep she is offered this bet:

Wager $95 to win $100 back (inc wager) that the die will land 1-99. (good odds considering she believes it's 99% likely.)

Post-sleep she is offered this bet:

Wager $20 to win $30 back (inc. wager) that the die will land 100. (good odds considering she believes it's 91% likely)

We know the objective chance of rolling 100 is 1%.
So 1% of the time she will be $5 up from the first bet and lose $20 in the second bet and thus be $15 down.
99% of the time she will be $95 down from the first bet and win $10 in the second bet and thus be $75 down.

She loses either way. You could change the bets so that she ie equally down whatever happens if we want to reduce the variance of our profits as the bookies and make the same off her every time.

Hence even though she is rational and making wise bets based on her credences, she will get screwed over.

[Dice Man]

Sorry i switched off here

For you we can substitute the statement about the die for something else. We have Walty in the room with Sleeping Beauty, and let us also suppose that Sleeping Beauty is only thirteen years old...
If he tries to rape her then the guards pull him off and wake her up once. If he doesn't try to rape her then they wake her up 1001 times. Because the chance of Walty trying to rape a random sleeping female 13 year-old is 99% she will believe beforehand that she will be subjected to an attempted raping 99% of the time. But when she wakes up she will think she was subjected to an attempted raping only 9% of the time. Isn't that weird?

[Prowler]

can we have one thread where you dont spill paedophile shit out of your sick fkn head? jesus christ get some fkn help

[Dice Man]

You are offering a bet on what number the die will land on, but not taking into account whether a waking will occur.

If you created a new die with 1100 faces, with 1001 of them saying "100", and the other 99 numbered 1>99, what odds would you now offer on a 100 being rolled?

A waking will definitely occur as any roll of the die results in at least one waking.

With that new die she would say pre-sleep that the chances of 100 are 93%. But if the same conditions held as before, that she would be woken up 1001 times after rolling 100 or once rolling 1-99 then post-sleep she would believe the chances of rolling 100 were 99.9901%. (1001x1001)/(1001x1001+99)

So I think you have failed to see the actual point. The original argument might be easier to understand: I changed it to a 100 sided die to get a really drastic change of belief.
The original is that they are flipping a fair coin. If it's heads then they wake her up once and if it's tails then they wake her up twice. She knows pre-sleep that the chance of heads equals the chance of tails and both are 0.5. When she wakes up she thinks that the chance of tails is 2/3 and heads 1/3, because if it were tails then she would be woken up twice as often.

[PokerWoody]

If when Ann wakes up she is unaware of anything which has happened previous, and then has the situation explained to her by Bob, 91% is the correct answer always.

If when she wakes up she is told how many times she has been woken up then she can change this answer. When she is told this is the first time she has been woken up she will know the answer is 1%. I am unsure what her answer would be when she is told it's the second, third and fouth time she has been woken up etc, and I don't really wish to think about it.

Your question seems to rely on the knowledge Ann has of her situation.

I'm off to play poker...

[Dice Man]

Your question seems to rely on the knowledge Ann has of her situation.

Yes the question is all about credence, that's her subjective belief about the probability based on limited information. We, as the people who know all, know the objective probability, which is 1% for rolling 100. When she wakes up she is conditionalizing on the fact that she is awake, she thinks something like "Given the fact that I am awake, the chance of 100 is..." Obviously "being awake" isn't much information to have, in fact it essentially counts for nothing because she knew beforehand that she would wake up at some point: so she knows the information in advance. I think this could be the root of the problem but am not sure how. She's changing her belief about the probability based on knowledge which hasn't changed.

When she conditionalizes on being awake she is having a thought like this: "What could have caused me to wake up?" She knows that she would be woken up 1001 times if the die rolled 100 and so on average (in the long-term) any state where she wakes up (that's all the knowledge she has about that state) is preceded by a roll of 100 93% of the time. I see no reason why she shouldn't play the averages game even if she knows it's only one trial and not a long term. After all, when we play poker and get all our chips in with AA pre-flop and lose, we tell ourselves we did the right thing because on average playing AA like that is +EV.

Going back to the Dutch-book idea, it seems that she is making +EV moves by accepting both bets, the one before and the one after sleep, where she is guaranteed to lose money.

I suppose the meta-conclusion of this is that acting according to what is +EV in any sense can be -EV.

But basically I find that conclusion so bizarre and counter-intuitive that I'm focussing on finding the flaw in the original argument but it's tough to find.

[Raiser]

Right,

I always knew u were.....

Whats the rest of the post about?