Mathematics and Roulette: New Scientist gets it wrong.

 New Scientist is traditionally one of the more worthy publications on the newsagent’s shelves. It is a magazine that has brought many great achievements of science and technology to the attention of ordinary people, and this information is presented in such a way that ordinary people can understand. Unfortunately, the magazine does not always get it right, and a major article in the latest edition that attempts to show where mathematics may be used to improve gambling odds in favour of the punter, is a good example of how to get it very wrong.

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The article, written by magazine staff in collaboration with E Thorpe of Blackjack card counting fame, explores the relationship between a number of gambling games and mathematics. It suggests that the correct application of mathematics can be used to beat lady luck. In particular it looks at Roulette.
The author states that whilst roulette is random, this fact does not preclude from winning every time. She points out that roulette is similar to tossing a coin in that every possible outcome has an equal chance of occurring. She then proceeds to make some serious errors.
The first error is simply flawed logic. In her system she recommends always betting on the same colour, as eventually that colour will turn up. This flies in the face of her previous statement that every outcome is equally possible. If you bet on red and it loses, then there is no need to bet on red again. You are just as likely to win on the next spin whether you bet on red or black.
The second error is the recommendation of a Martindale type of betting system. Her way of guaranteeing a win is to double the stake after every loss. Naturally this will work if only a few consecutive losses are experienced, but when the sequence of losses grows beyond a few, then very serious stakes must be wagered and these are likely to be higher than the maximum allowed bet. Thus, even given an unlimited bankroll, the system is doomed to failure.  
Many people have attempted to beat the roulette wheel, and have also discovered the impossibility of doing so. Roulette is one of the most glamorous of all casino games and is a game of pure chance. Mathematics will never beat it.

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