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

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.