Random Thoughts: Taking a Chance – How Would You Bet on the Next Spin-Which Number Will Again Be Even? Or Odd?

Random Thoughts: Taking a Chance – How Would You Bet on the Next Spin-Which Number Will Again Be Even? Or Odd?

By Mr Ghaz, November 19, 2010

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Random Thoughts: Taking a Chance – How Would You Bet on the Next Spin-Which Number Will Again Be Even? Or Odd?

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Imagine that you are in a casino in Las Vegas, betting at the roulette table, and that 10 consecutive spins of the wheel produce even numbers. How would you bet on the next spin-which number will again be even? Or odd?

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Many would be prepared to stake a lot of money that the next number will be odd. They believe that the “law of averages” will soon compel the wheel to turn up some odd numbers to compensate for the freak run. Statisticians call this the Monte Carlo Fallacy, and it has been responsible for some heavy losses at gambling tables all over the world.

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In fact, the law of averages does not exist. There is no unseen influence that somehow balances out the wheel’s past and future results to guarantee that odd and even numbers turn up equally. If the wheel is indeed totally unbiased, there is still a fifty-fifty chance that the next spin-and all subsequent spins-will turn up an even number. If anything, the run of even numbers makes it slightly more likely that the bias is toward even numbers-which might justify staking a very small amount that the number turned up by the next spin of the wheel will be even, not odd.

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Chance Selection

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Whenever an event occurs that is completely unpredictable based on its context or the history of such events-such as a particular number coming up in a game of chance-it is called random.

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Randomness is obviously important in many games: the deck of cards must be well shuffled before the next hand is dealt, the space invaders in a video game must always pop up in unpredictable places on the screen, and the dice must not come up double-six too often.

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In science, too, randomness is often essential. For example, when people are selected for a survey or for a psychological experiment, they must be picked at random, or the results may be misleading.

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It is not an easy job to get a truly random sequence of events or numbers. Simply trying to think up random numbers will not work-we all have psychological quirks that bias us, say, toward odd numbers or away from 7’s. And for most scientific purposes, the shuffling of a deck of cards is not truly efficient.

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Computer Know-How

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An obvious solution might seem to be to use computers. True, computers can certainly produce apparently random numbers if needed. But in reality these are only “pseudorandom” numbers. They are obtained by complicated arithmetic-and if the sequence includes a large enough number of digits, it will repeat itself. Also, the same sequence will be obtained every time that the computer is commanded to produce the random numbers. Ultimately, the sequence will no longer be random; it becomes completely predictable.

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One activity that depends on obtaining the most random numbers possible is a state lottery, for which the draw must be scrupulously fair. In some cases the winning numbers are selected by electronic equipment. The choice depends on the behavior of individual atoms-according to present scientific theories, the most perfectly unpredictable happening of all.

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