h2g2 The Hitchhiker's Guide to the Galaxy: Earth Edition

Are we all familiar with the Playfair "system" for roulette?

Step one. Bet one on red. Lose, go to step two, or win, collect two, you are now one up. Start again.

Step two. Bet two on red. Lose, go to step three, or win, collect four, you are now one up. Start again.

Step three. Bet four on red. Lose, go to step four, or win, collect eight, you are now one up. Start again.

Step four. Bet eight on red.....

And so on, doubling your bet each time you lose, going back to the start each time you win. It's a guaranteed winner - I wonder why casinos are still in business? Hmm....

Yes, this is also known as the martingale. It is based on the Gambler's Fallacy (see http://www.nizkor.org/features/fallacies/gamblers-fallacy.html)
that trends must be reversed "soon".

While it is true that trends must be reversed in time, there is nothing to predict that time, and the gambler will often find himself either running out of cash or exceeding the house limit on bets.

My grandfather once tossed a half-crown with a friend, double or quits. Amazingly his friend won eleven times in a row by the time they were interrupted, and my grandfather owed him £128, which was about what the family was living on per year.

Fortunately his friend was a true friend, and next time they met he said "We never finished that game - your toss", lost, and said "Just my luck!"