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Here's an amplification that might clarify it. If you flip heads, I'll wake you up zero times. If you flip tails, I'll wake you up once. Now what's the probabil

Here's an amplification that might clarify it. If you flip heads, I'll wake you up zero times. If you flip tails, I'll wake you up once. Now what's the probability that you flipped tails. 100%, right? Why? The coin still has a 50% chance of giving either heads or tails. Here's another -- if you flip heads, I'll wake you up once. If you flip tails, I'll wake you up a million times. When I wake you up, is it more likely that you flipped tails or heads, remembering that you don't know which day it is. You are right, by the way, that there is no new information -- the tendency to answer "50%" the night before is the logical error. You are conflating the odds of flipping heads or tails with the odds of WHETHER you flipped heads or tails in light of the known outcome (which is not 1:1 with flipping heads or tails). Also, if you believe in statistics, the right answer in the continuous case (infinite repeats) is also the right answer in the singular case (one repeat). Your point about "there aren't three volunteers, only one" is fallacious.

CamperBob2 11y ago
Here's an amplification that might clarify it. If you flip heads, I'll wake you up zero times. If you flip tails, I'll wake you up once. Now what's the probability that you flipped tails. 100%, right? Why? The coin still has a 50% chance of giving either heads or tails. I do like that, it's a strong argument. But it still relies on monkeying with the participant's awareness in a way that is likely to (or in this case, will) keep them from making the right decision over time. You use the term "known outcome," but there isn't a known outcome if you're dead or asleep forever. Your point about "there aren't three volunteers, only one" is fallacious. But so is treating it as any other problem (like gambling) that only converges on an answer after multiple trials. The strength of your argument is that it doesn't rely on answering a different question, just changing a parameter in the question that was asked. But it's an awfully important parameter. Implicit in the question is the premise that you will be alive/aware at some point in the future, so that you can be asked what you think. Edit: another way to rebut your particular argument is by sticking with the original terms of the problem, except that if the coin lands on heads, they shoot you after you answer. That doesn't help you answer the question.
- URSpider94 11y ago
  I think you're starting to grasp it. The key here is that if you are dead or asleep forever, then you are not waking up to answer the question. Therefore, the simple fact that you are waking up brings new information to the situation -- you know for sure that you didn't flip heads.
  - Retra 11y ago
    But in the original question, you were already guaranteed to wake up, so how does it give you any information?

CamperBob2 11y ago

Here's an amplification that might clarify it. If you flip heads, I'll wake you up zero times. If you flip tails, I'll wake you up once. Now what's the probability that you flipped tails. 100%, right? Why? The coin still has a 50% chance of giving either heads or tails. I do like that, it's a strong argument. But it still relies on monkeying with the participant's awareness in a way that is likely to (or in this case, will) keep them from making the right decision over time. You use the term "known outcome," but there isn't a known outcome if you're dead or asleep forever. Your point about "there aren't three volunteers, only one" is fallacious. But so is treating it as any other problem (like gambling) that only converges on an answer after multiple trials. The strength of your argument is that it doesn't rely on answering a different question, just changing a parameter in the question that was asked. But it's an awfully important parameter. Implicit in the question is the premise that you will be alive/aware at some point in the future, so that you can be asked what you think. Edit: another way to rebut your particular argument is by sticking with the original terms of the problem, except that if the coin lands on heads, they shoot you after you answer. That doesn't help you answer the question.

URSpider94 11y ago
I think you're starting to grasp it. The key here is that if you are dead or asleep forever, then you are not waking up to answer the question. Therefore, the simple fact that you are waking up brings new information to the situation -- you know for sure that you didn't flip heads.
- Retra 11y ago
  But in the original question, you were already guaranteed to wake up, so how does it give you any information?