REPOST Derren Brown's "Deep Maths" is easy

If you didn't watch the lottery prediction or the event program you're crazy, go watch it online right now. But if you did you may have been interested by the "deep maths" of coin tossing that Derren claimed would take an hour to explain... not so, it's fairly simple really. So I'm going to try and explain it quickly and without anything more than common sense.

The game:

You take a coin and flip it a lot of times in a row, and you note every time that two different sequences of 3 results comes up.

The assumption:

Your initial reaction (and mine) was that all of the 2x2x2=8 results are equally likely to come up. Because if we flip a coin 3 times only this is true. You try and flip a coin 3 times and record weather your sequence came up or not and then start again. If you do this enough times (you'll need a few hours and nothing better to do) and you can easily show that all 8 results are just as likely. We are lead to believe this is true for the game above.

But:

This isn't what happens, in a long string of results HTHHHTHTHTTHTHTHTHTTTHTHTH

THTTHHTH etc it is possible for results to overlap. For instance HTHTH contains HTH twice, and HHHHH contains HHH 3 times. How can you use this overlapping to your advantage? You start by thinking about what happens if you nearly "win" but fall down at the end. What can you do if you predict HHH and it comes up HHT? You've got a result you dont want, and you have to start again from scratch. but what you can do is get a head start. If the last coin in your sequence is different from the first one something interesting happens. You pick THH, the first coin is a tail, you're happy, the second is a head, you're very happy, the third one is a tail ... you haven't won this time, but you're not upset, because you've already got the first coin of the sequence in place. To put it simply: with THH every time you predict a coin wrong you are already a third of the way through the next attempt, but if you pick HHH then every time you go wrong you have to start again at the beginning.

I predict THH: T win! 1/3 done, H win! 2/3 done, T ignore what happened before, start again with the first one right , 1/3 done

I predict HHH: H win! 1/3 done, H win! 2/3 done, T ignore what happened before, start again with the first one wrong, 0/3 done

Conclusion.

Pick a sequence where failing to get the end right means you are automatically in with a second chance. This means you can win far more often than you would think. The reason is just common sense, no deep maths, no psychology, no team thinking, no magic, just common sense.

As for how he predicted the lottery, there are dozens of equally plausible solutions, but however he did it I'll stab myself in the foot if a group of 24 people in a trance had the slightest involvement.