Simple probability.

I've mentioned the "gambler's fallacy" before without properly explaining it. It goes something like this - if I toss a coin twice then, assuming no jiggery-pokery, four things can happen - I get a head followed by another head, a head followed by a tail, a tail followed by a head, or a tail followed by another tail. So the chances of me getting two heads is one in four - right? So I toss the coin and get a head. The gambler's fallacy says that the odds must favour getting a tail on the next throw. After all, there's only one chance in four of getting two heads, isn't there? The fallacy of course is that the probability before you start of getting two heads is indeed one in four, but once you've got your first head, the probability of getting a second head is only one in two. It's the same false reasoning which says if you're playing roulette and red has come up ten times in a row that the odds must heavily favour black on the next roll. Probability depends on the information available to you - different information, different probability. Once I know that I have got a head on the first toss, it alters the probability of getting two heads.