|
|
Post by Eva Yojimbo on Mar 26, 2018 14:54:21 GMT
Taken from THIS THREAD. I first pose the experiment here: IMDB2.freeforums.net/post/1486464/thread -- anyone interested in the context can back up and read the discussion between Cham and I that starts here: IMDB2.freeforums.net/post/1480594/thread: I'll post a spoiler that offers a hint: It's really a trick question about a trick coin. The tricky answer is more about understanding the underlying problem with the question. One can still give a reasonable answer to it, but that's not really the point. |
|
|
|
Post by Lugh on Mar 26, 2018 17:19:22 GMT
what does that even mean? What predicts what? |
|
|
|
Post by Isapop on Mar 26, 2018 17:23:58 GMT
Lugh
No, WHO predicts what. |
|
Deleted
Deleted Member
@Deleted
Posts: 0
|
Post by Deleted on Mar 26, 2018 17:56:37 GMT
Are you unable to study the coin for some reason? If it has both a heads and tails side, then it's probably not a trick coin.
|
|
|
|
Post by Eva Yojimbo on Mar 27, 2018 1:25:09 GMT
what does that even mean? What predicts what? A fair coin has a 50/50 probability of landing on heads/tails, so a fair coin predicts that it will land on heads four times in a row 6% of the time (.5^4). A trick coin (at least the one in my scenario) has a 100/0 probability of landing on heads, so a trick coin predicts that it will land on heads four times in a row 100% of the time (1^4). Not sure what about that you're having difficulty with. |
|
|
|
Post by Eva Yojimbo on Mar 27, 2018 1:25:39 GMT
Are you unable to study the coin for some reason? If it has both a heads and tails side, then it's probably not a trick coin. It's a thought experiment. Studying the coin would be cheating at the thought experiment. |
|
Deleted
Deleted Member
@Deleted
Posts: 0
|
Post by Deleted on Mar 27, 2018 4:06:29 GMT
After the initial 4 tosses, I would still be assuming that it was a fair coin, based on the fact that 6% isn't really all that remote in terms of odds and trick coins constitute much less than 6% of all coins. After about 10 tosses, the chances of getting all heads would become so vanishingly remote that I might start to think that it's a trick coin. I'm not calculating what the odds of that are, though.
|
|
|
|
Post by Marv on Mar 27, 2018 4:17:06 GMT
I wouldn’t assume it’s a trick coin at all. It’s a 50/50 shot each time you flip. Lumping several flips together in order to create a smaller percentage than that makes no sense to me. The coin doesn’t know it landed on heads 3 times in a row, and it won’t know it landed on heads the next 3 times. That doesn’t mean it’s a trick coin and I wouldn’t assume as such.
|
|
|
|
Post by theoncomingstorm on Mar 27, 2018 4:34:23 GMT
I assume it's a trick coin before the first toss because that's how I roll.
|
|
|
|
Post by goz on Mar 27, 2018 4:47:53 GMT
Can I give a flip pant answer?
|
|
|
|
Post by Eva Yojimbo on Mar 27, 2018 6:25:22 GMT
After the initial 4 tosses, I would still be assuming that it was a fair coin, based on the fact that 6% isn't really all that remote in terms of odds and trick coins constitute much less than 6% of all coins. After about 10 tosses, the chances of getting all heads would become so vanishingly remote that I might start to think that it's a trick coin. I'm not calculating what the odds of that are, though. I think 10 tosses is a reasonable point to start thinking you might have a trick coin (.5^10 = 0.1%) , but the bolded part really gets to the heart of the issue.  If after 10 tosses you thought it was 50/50 you had a trick coin that would translate to you thinking the ratio of fair to trick coins is about 1000:1 (if my shaky algebra is right). |
|
|
|
Post by Eva Yojimbo on Mar 27, 2018 6:27:47 GMT
I wouldn’t assume it’s a trick coin at all. It’s a 50/50 shot each time you flip. Lumping several flips together in order to create a smaller percentage than that makes no sense to me. The coin doesn’t know it landed on heads 3 times in a row, and it won’t know it landed on heads the next 3 times. That doesn’t mean it’s a trick coin and I wouldn’t assume as such. So you get all heads 50 times in a row. Still not thinking it's a trick coin? |
|
|
|
Post by Eva Yojimbo on Mar 27, 2018 6:30:24 GMT
I assume it's a trick coin before the first toss because that's how I roll. I'll just quote Yudkowsky: |
|
|
|
Post by Marv on Mar 27, 2018 8:16:57 GMT
I wouldn’t assume it’s a trick coin at all. It’s a 50/50 shot each time you flip. Lumping several flips together in order to create a smaller percentage than that makes no sense to me. The coin doesn’t know it landed on heads 3 times in a row, and it won’t know it landed on heads the next 3 times. That doesn’t mean it’s a trick coin and I wouldn’t assume as such. So you get all heads 50 times in a row. Still not thinking it's a trick coin? I wouldn’t assume it was a trick coin, correct. |
|
|
|
Post by Eva Yojimbo on Mar 27, 2018 9:29:08 GMT
So you get all heads 50 times in a row. Still not thinking it's a trick coin? I wouldn’t assume it was a trick coin, correct. You're not assuming anything. The number of flips are evidence that should be altering your initial assumption that the coin is fair. 5000 heads in a row? There has to be some point where you start to think the coin probably isn't fair. |
|
|
|
Post by Lugh on Mar 27, 2018 10:05:27 GMT
what does that even mean? What predicts what? A fair coin has a 50/50 probability of landing on heads/tails, so a fair coin predicts that it will land on heads four times in a row 6% of the time (.5^4). A trick coin (at least the one in my scenario) has a 100/0 probability of landing on heads, so a trick coin predicts that it will land on heads four times in a row 100% of the time (1^4). Not sure what about that you're having difficulty with. Coins do not predict anything, they're coins. Or is that just some maths jargon I am unaware of? |
|
|
|
Post by FilmFlaneur on Mar 27, 2018 10:20:14 GMT
I am sure I remember seeing somewhere that, due to the inevitable difference in the surface contours of each side of a coin (i.e. a raised 'head' side has, even if minutely, greater airflow resistance) the eventual odds were never the same.
|
|
|
|
Post by Marv on Mar 27, 2018 10:43:08 GMT
I wouldn’t assume it was a trick coin, correct. You're not assuming anything. The number of flips are evidence that should be altering your initial assumption that the coin is fair. 5000 heads in a row? There has to be some point where you start to think the coin probably isn't fair. Why tho? If the first coin flip is 50/50, why isn’t the second one? |
|
|
|
Post by Eva Yojimbo on Mar 27, 2018 10:47:42 GMT
A fair coin has a 50/50 probability of landing on heads/tails, so a fair coin predicts that it will land on heads four times in a row 6% of the time (.5^4). A trick coin (at least the one in my scenario) has a 100/0 probability of landing on heads, so a trick coin predicts that it will land on heads four times in a row 100% of the time (1^4). Not sure what about that you're having difficulty with. Coins do not predict anything, they're coins. Or is that just some maths jargon I am unaware of? My OP said:It's the hypotheses that predict the results, not the coins themselves. A "fair-coin hypothesis" predicts 50/50 heads/tails; a "trick-coin hypothesis" predicts 100/0 heads/tails. |
|
|
|
Post by Lugh on Mar 27, 2018 10:51:52 GMT
Coins do not predict anything, they're coins. Or is that just some maths jargon I am unaware of? My OP said:It's the hypotheses that predict the results, not the coins themselves. A "fair-coin hypothesis" predicts 50/50 heads/tails; a "trick-coin hypothesis" predicts 100/0 heads/tails. oh ok. My reading comprehension has always been very poor. |
|
