Here is something that some will find interesting.

http://www.sciencenews.org/articles/20040228/fob2.asp

Hi,

Ths is related to something that I've long maintained: the idea of the gambler's fallacy is in itself a fallacy--when applied to the real world.

The gambler's fallacy is this: If for example a roulette wheel turns up red a hundred times in a row, then some gamblers will bet on black, thinking that it is now black's turn to occur, in order to start balancing out the probabilities.

On the other hand, some gamblers will continue to bet on red, on the theory that red is having a lucky streak, and therefore should continue with red.

The mathematician sneers at both of these lines of thought. In fact, she says, the roulette wheel has no brain and no memory, so that on each spin the probability of red or black is equal (assuming no other colors).

But in fact, in the real world, the second group of gamblers described above will probably have a better chance of winning than the first group of gamblers. Because, in fact, in the real world, bias exists in mechanical objects, and if there is in fact a run of 100 reds, then there's a good chance that somehow that roulette wheel has become biased. Perhaps for example the slots have become worn over time in such a way that they favor the ball falling into a red slot.

So, although I know I'll get flak from some of the mathematicians out there, sometimes betting with a "lucky streak" can be a better strategy than betting the theoretical odds.

Jack Shalom

Gamblers have long maintained that if you flip a coin 20 times, and every time it comes up heads, then you should bet heads. After a run like this, the coin is either biased, or double-headed.

Re: The mathematician sneers at both.

Both approaches have been shown useful.

We may ask ourselves IF the sun will come up tomorrow. We choose to expect a 'yes'

We estimate the expected lifetimes and similar actuarial considerations using similar reasoning.

To those who wish to sneer at the question... have a look at the Poisson and Exponential distribution functions and their simple applications to real life.

The notions of normal distribution and central tendency have served us very well.

I can believe bias exists in a coin toss. I'm sure who is throwing the coin matters too, i.e. how well they can repeat a nearly (and sufficiently) identical throw. For a roulette wheel, there are so many factors that determine where it stops, from the friction of the wheel, to how fast it spins, any minor wobbling, the earths spin, and gravitational forces in the region.

I think gamblers can expect a bias on any roulette wheel, but how close is the red-black bias to 50-50 in a particular site? To determine that would take recording a huge number of outcomes.

What probably determines this is another branch of mathematics, i.e. Chaos Theory.

-----------------------------------------
Update: I realized the red-black odds aren't 50-50, since 0 and the 00 are on the wheel. The point about chaos theory still applies.

A few years ago Thomas Bass published a book called Eudaemonic Pie. It told the story of a group of physics/math students who built a computer to predict the outcome of the roulette wheel. According to the book they were successful. It involved switches operated by their toes inside their shoes. A switch would be depressed as the ball passed a fixed position; from several such points the program could calculate the likely outcome with sufficient precision to make them some money. It's a very interesting read!

Another book that I haven't seen sounds like the same story:
Bringing Down the House: The Inside Story of Six M.I.T. Students Who Took Vegas for Millions by Ben Mezrich

At least one of the students went on to the Santa Fe Institute, a center for the study of complexity theory and the application of chaos theory to various problems. He subsequently got a position with a Wall St. firm analysing the stock market. Haven't heard anything else about him, though. Wonder what happened during the recent recession?

I tend to rely heavily upon the anthropic principle myself Jonathan. Below it's cosmological applications, I think it readily applies to the question of why a roulette wheel will stop on black or on red in any given number of spins. And further, why the "Gambler's Fallacy" would indeed tend to prove itself out at a decent level of accuracy.

Casinos true their roulette wheels every day.

And if one started to behave anomalously in the course of a day they'd close it down.

And those students... they sure must have had nimble toes.

No, I believe they weren't as fleet of foot as they needed to be. They got caught, if they're the same group that I watched a Discovery channel program about a few months back. So unless MIT started a graduate course in casino beating, it's most likely the same crew.

Roulette: don't forget the double zero green spot.

Coin toss: physics wasn't completely applied. Imperfections/differences between coins, temperature changes of the coin as the 'same' coin is tossed (repeated handling whether by machine or human), air current of area, distance allowed, etc.

We're just talented monkeys learning everyday but are far from actually 'knowing' any real truths—save death and taxes...haha.

Do you know Steve Blencoe?

He is a dealer who invented an ingenious way to toss a coin into the air and have it fall on the side you want it to fall on. It is a real coin, not double faced one.

Tell us more Roei.

December 1975 Pabular has an article by Fred Robinson explaining how to do this. I haven't tried it out though.

Jack Shalom

Hi Nir. Miss you.

So, Steve is a cool guy and he showed to me a way to toss a coin to fall on the desired side.

The idea is that the coin never spins on the horizontal line but it looks sooooooo good and fools everyone.

For a peek at a really incredible streak of coin tossing, check out the movie Rosencrantz and Guildenstern are Dead. Thousands of coin tosses, always heads...

The MIT students who took Vegas for millions were probably the carefully trained ring that played blackjack, not roulette. There have been numerous news stories and documentaries about how they did it (yes it's hard, yes it takes more than one person, yes most of them finally got caught, and yes the casinos know what to watch for now...)

-Reg {*}