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The OP is essentially correct. I was definitely confused and assumed it was about 'looking like' randomness. But I did a lot of double clicking of things, bec

The OP is essentially correct. I was definitely confused and assumed it was about 'looking like' randomness. But I did a lot of double clicking of things, because I felt that in 'real life' you're not going to get 1 roll of each number, but odd things happen. But this is a bit moot - the people clicking 'all the same number' have obviously come to some different conclusion as the others - i.e. 'all possible values are the same' and therefore. So what the study is really 'testing' probably, is how people react to the question. They really need to change the question substantially in order to get randomness. I don't see any insightful aspect in the experiment or the debate. It's pedantic -> some people read the question differently and do different things.

posix86 4y ago
I disagree. You want people to click numbers s.t. if you asked them 10k times, a uniform distribution would emerge. But that is not what's happening. They think all numbers have the same probablity, but if you click only 1, then the probability of your choice being random is low. Edit: Maybe this will convince you: You said each sequence of numbers is equally likely, hence, we can't tell. I'm going to disagree with that statement. Let's say I give you a coin, and tell you: I've flipped this coin 100 times in a row, 10k times. And you look at the flips, and each flip result is 1111...111. Would you guess it's random, or biased? The probability of that happening is as high as any other sequence, but clearly, if you'd guess it was random, you'd be a fool. This is exactly what is happening here, just on a smaller scale: 111111111 being the result of the coinflip has a lower probability of being random than the result 100101101110. 11111 has to happen at some point if the experiment is really random. The probability that it happens with YOU is low, however. Thus, it is rational to decide that the sequence is not random. Because it most cases, it won't be.
- denton-scratch 4y ago
  > Would you guess it's random, or biased? Well, I'd guess that it's not a coin-flip at all; even a biased coin won't produce 10,000 heads and no tails, unless it's a two-headed coin. Let's go back to the actual case in hand: suppose you provide me with "111111", and not 10,000 1s. I simply have no way at all of determining whether that is more or less likely to have come from a random source. So I would decline your bet. If it was 10,000 1s, then maybe I'd be a fool to bet it was of random origin; but you can't convince me that a string of 6 1s is or isn't of random origin. So no bet. This is all irrelevant. We're discussing a single sequence of 6 digits. There are not enough samples to perform statistical analysis. Probability doesn't come into it.

posix86 4y ago

I disagree. You want people to click numbers s.t. if you asked them 10k times, a uniform distribution would emerge. But that is not what's happening. They think all numbers have the same probablity, but if you click only 1, then the probability of your choice being random is low. Edit: Maybe this will convince you: You said each sequence of numbers is equally likely, hence, we can't tell. I'm going to disagree with that statement. Let's say I give you a coin, and tell you: I've flipped this coin 100 times in a row, 10k times. And you look at the flips, and each flip result is 1111...111. Would you guess it's random, or biased? The probability of that happening is as high as any other sequence, but clearly, if you'd guess it was random, you'd be a fool. This is exactly what is happening here, just on a smaller scale: 111111111 being the result of the coinflip has a lower probability of being random than the result 100101101110. 11111 has to happen at some point if the experiment is really random. The probability that it happens with YOU is low, however. Thus, it is rational to decide that the sequence is not random. Because it most cases, it won't be.

denton-scratch 4y ago
> Would you guess it's random, or biased? Well, I'd guess that it's not a coin-flip at all; even a biased coin won't produce 10,000 heads and no tails, unless it's a two-headed coin. Let's go back to the actual case in hand: suppose you provide me with "111111", and not 10,000 1s. I simply have no way at all of determining whether that is more or less likely to have come from a random source. So I would decline your bet. If it was 10,000 1s, then maybe I'd be a fool to bet it was of random origin; but you can't convince me that a string of 6 1s is or isn't of random origin. So no bet. This is all irrelevant. We're discussing a single sequence of 6 digits. There are not enough samples to perform statistical analysis. Probability doesn't come into it.