Comment by jsprogrammer
9 years ago
>The fundamental result behind the gambler's ruin is the human tendency to perceive patterns in genuine randomness.
I don't think pattern recognition drives most gamblers. There are all kinds of other benefits, perceived or real, that are not accounted for in a purely monetary payoff grid.
I don't know how you can generate random noise. I assume you are using a standard, pixelated display to read this message. Even if a random process was choosing what to display on that screen, there are only a finite number of configurations. Exactly what you are viewing now could be recreated by such a random process.
The problem that hasn't been addressed yet is that "pattern" is not well-defined. If a random display shows a horizontal line pattern, it is still a pattern by some definition (and you would have no way to distinguish it from a "intentionally patterned" display that has the same configuration).
Of course you could have an intersection between recognizable images and random noise. The odds of this occurring with any regularity are infinitesimal, hence the design of experiments. (Recall that there is nothing like a mathematical proof in the physical world -- at a molecular level, some water molecules are moving upstream at any given moment, but by reaching into a stream or tossing some objects into the flow you are taking a large enough sample to determine where most of them are going).
Since you're not going to get proof one way or another, all a well designed and experiment can do is give you evidence. This happens to be more valuable than just about anything else that science has come up with, but it isn't proof.
Which is why the gold standard for a result is replication in a large sample. I could have this very page generated by convolving couple of high entropy random streams. Is it likely to happen repeatedly? Not if the generator is any good. Same principle for randomized trials. You can end up with unbalanced arms (I'm proofing a manuscript where we had exactly this problem). But it's unlikely that they'll be consistently unbalanced across trials with sufficient sample sizes.