## 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.

1. Nice insight there. Good blog post too. I’m looking forward for some exchange of thoughts. Thanks

• Me too!!! The more brains the better I think. Mathspig

2. Ahhh, but if you were to bet on 26 occurances of black at the start of the run, the probability of a win would be 0.5^26 = 1.4E-8. So you wouldn’t really want to do that unless it paid stupidly well.

One way gamblers try to make runs like this pay is by doubling their bet on each spin of the wheel when they lose. So, on the first spin they would bet \$1.00. On the second spin they would bet \$2.00 and so on. The problem here is that the casino has much deeper pockets than most gamblers and in this case your final bet would be \$33,554,432. Ouch.

• Wow! Losing \$33plus million would hurt. Of course, if you started with \$1 and bet on Black and kept doubling your winnings on the 26th throw you would win \$33,554,432. But being a gambler, on the 27th throw you would lose your \$33,554,452.

As Mathspig is for all not just maths buffs I’ll explain some of this maths. If you double your money every spin then you can calculate your winnings, in this case, by multiplying 2 by 2 (26 times).

As for the squiggly equation 0.5^26 = 1.4E-8
.5 by .5 (26 times) = 1.4 divided by 10 to the -8 = 0.000000014

but Mathspig says just consider your chance of landing on 26 Black in a row in roulette as 14 in a Trillion!!!!!!!!

3. […] run of Black in a row was 26. (See: Mathspig The Wheel on the Roulette Table Went Round and Round #mce_temp_url#   […]

4. […] As Alex Bellos explains, we humans try and impose order on chaos. Our imagined results show a pattern. The real results are more… well, random. The problem is when we write HH we then think it is T turn. Whereas random results for tossing a coin can have any number of Hs or Ts together!!!!!!!!!!! The longest recorded run for Black on roulette was 26. See an earlier mathspig post, The Wheel on the Roulette Table went round and round, round and round. […]

5. […] value, they just can’t be exchanged back into money. But people love it anyway. I guess a superstition of odds is […]

6. […] As with the flip of a coin there is a 50:50 chance in roulette of the ball landing on Red or Black. But the odds of 50:50 only apply over an infinite number of spins of the roulette wheel. It is possible that a roulette ball will land on Black 10, 15 or even 20 times in a row.  In fact, the highest recored run of  Black in a row was 26. (See: Mathspig The Wheel on the Roulette Table Went Round and Round ) […]