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How ‘random’ are the numbers?

Jun 15, 2004 3:32 AM

The issue of random numbers has become more and more important in the last few years, not only to the owners of casinos but to gamblers as well. Billions of dollars are wagered each year on slot machines, keno machines and video poker machines and all of them depend upon little chips of silicon to produce the outcome of the wager.

Since there has been one recent scandal involving video poker machines, and an ongoing controversy regarding "near miss" machines, the issue is worth investigating. There are also some random number generators either in action or proposed in live keno games around the state, and although they haven’t proven very popular, they are seen as a viable ball selection option by smaller keno games, both in the aspect of game security and economy.

What is a random number? Some mathematicians argue that there is no such thing, but most generally agree on the following: A series of random numbers is a series of numbers such that any particular number in the series cannot be determined by the numbers preceding it. For example, the series 7, 45, 23, 19, 18, 2, 52, 22 might be regarded as random if you cannot determine the next number by what is known so far. The series 2, 4, 6, 8, 10, 12, 14 might not be a random series, because the next apparent number in the series will probably be 16. It is entirely possible however, that a truly random series might produce the series 2, 4, 6, 8, etc! It’s just as likely as any other series.

Mathematicians apply several tests to a series of numbers, to determine if they possess random properties. One test is a pure distribution test. Any series of random numbers should contain the digits 0 through 9 on an approximately even basis, given a large enough sample. Another test that is frequently applied is the runs test, in which a series of random numbers is tested for runs up and runs down in sequence. Another test that is applied is the gap test, which tests the average gap between occurrences of each number in the sequence.

It is possible to produce a series of numbers that will pass every test for randomness, yet nevertheless are not random! For instance, the series 1, 4, 1, 5, 9, 2, 6, 5, 3, 5 will pass every test for randomness, but I can tell you that the next number in the sequence is 8! That’s because this series is taken from the decimal expansion of pi, and is well known to all mathematicians.

Well that’s it for this week, good luck! I’ll see you in line!