And the Wheel on the Roulette table went round and round, round and round…March 31, 2009
Gamblers believe in stuff. They believe in lucky numbers, lucky breaks, lucky colours and even a lucky rabbit’s foot (It wasn’t so lucky for the rabbit.) But more than anything else gamblers believe in patterns.
If we flip a coin an infinite number of times Heads:Tails ratio will be 50:50. But if you think of infinity as a long, long ribbon with a HTTHTHHTTT pattern then random flips means any pattern is possible. 10 H in a row is possible… or 20 H. It’s just that we suddenly see meaning in this pattern. This is the Gambler’s Fallacy. We see 10 H in a row and we say ‘Aha! The next flip has to be Tails.’ But it doesn’t have to be Tails. The next flip – as with all flips – has a equal 50:50 chance of being Heads or Tails. That’s all. But we are surprised when we see an extended streak of, say, Heads. What has happened in the past does not effect THE NEXT FLIP!!!!!
Roulette Wheel has 36 numbers and an equal number of Red and Black slots. ‘The most famous example of such a phenomenon occurred in a Monte Carlo Casino in the summer of 1913 when a roulette wheel landed on black 26 times in a row.’ The Decisive Moment How the Brain Makes Up Its own Mind Jonah Lehrer (Text Publishing 2009)
What do you think the gamblers did that night??? After a few Reds in a row they started to think it was Blacks turn and kept backing Black.
The Casino kept raking in the francs that night. It was a very good night for the house.
So mathspigs try it. Each student should flip a coin for, say, 5 minutes and record HHT etc. How long was the longest run of H or T? You could convert this to a Bar Graph with the no. of Students on the X-axis and Number of H/T in a row on the Y-axis.