# Monte Carlo Simulation - Roulette

Computer Science Teacher

### Monte Carlo Simulation - Roulette

In theory, theory and practice as the same. In practice, all too often, they are not. Sometimes running a simulation can help one separate theory and reality. For example, about a month ago I received an email that promised me success at the roulette tables. This is a game I’m not into because it seems too much about luck. But there was this email and it sounded good. Part of it is below.

you know in roulette you can bet on blacks or reds. If you bet \$1 on black and it goes black you win \$1 but if it goes red you loose your \$1.

So I found a way you can win everytime:

bet \$1 on black if it goes black you win \$1

now again bet \$1 on black, if it goes red bet \$3 on black, if it goes red again bet \$8 on black, if red again bet \$20 on black, red again bet \$52 on black (always multiple you previous lost bet around 2.5), if now is black you win \$52 so you have \$104 and you bet:

\$1 + \$3 + \$8 + \$20 + \$52 = \$84 So you just won \$20 :)

now when you won you start with \$1 on blacks again etc etc. its always bound to go black eventually (it`s 50/50) so that way you eventually always win.

Not the best written piece of prose but it caught my attention. As far as I can tell it was really a come on to try this scheme at an online casino. Not a chance in the world I’m going to try that. But would this work? I’m sure there is a solid mathematical way to find out but I don’t know what it is. So I decided to run a simulation.

Low and behold it seemed to work just fine. But then I looked into it some more. It turns out that you don’t ahve a 50/50 chance of winning. There are two locations on the wheel in the US that are neither red or black (0 and 00). So the odds are 1.111 against you not 1 to 1 as the email I received would indicate. Does that make a difference? Turns out it does. You can still win but it is not a sure thing. And in fact at times the amount one has to bet can get very large very quickly. This runs the risk that the better will run into a limit on the amount the casino allows a better to make. In fact in several simulations I ran the program tried to bet in the billions of dollars and crashed.

I leave creating your own simulation as an exercise for the user. What do you see as a result?

• Wow, thanks for this post. Interesting to see that it isn't actually 50/50, but due to the fact that everybody thinks it is, you take it for granted. I am going to try to simulate this too. Thanks again and have a very good 2010 in advance.

• I believe this betting technique is called the Martingale system and, much like so-called perpetual motion machines, can't overcome the inevitable friction of the house advantage without cheating.

I like the idea of CS experiments that help validate or illustrate stats concepts. One of my students has been (of his own accord) working on a program to demonstrate that human selections of random answers to a multiple choice test question are no more (or less) likely to be correct than machine-generated random answers in the long run.

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