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25 May 1998

Players bring a lot of scientific gobbledygook into the casino. Leading the list are ideas involving events coming "due."

Sometimes, theories of coming due are rejection of chaos and confidence in order. They may be explained by programming, like a slot machine supposedly set so it builds to a jackpot. Or they may be accepted based on observation and memory, such as seven in craps "almost always" rolling after dice have gone off the table.

More often, principles of coming due are misunderstandings of mathematics. Solid citizens may invoke a presumed law of averages to count red and black columns on roulette toteboards and bet on a color when it's behind by five or more. Or they may use what they consider a law of maturity of chances to record every hit in three keno games and buy all other numbers in the fourth round.

Here's a nuts and bolts case showing the allure and the flaw in theories that results come due in gambling. Imagine you're going to bet on three tosses of an unbiased coin. On one hand, everyone knows the chance of heads on each toss is one-out-of-two, or 50 percent. On the other hand, you heard - correctly - the chance of three successive heads is one-out-of-eight, or 12.5 percent.

Your personal 900-PSYCHIC advisor said to bet tails. Heads shows on the first two throws, losing \$5 per round. You reason that the chance of three successive heads is only 12.5 percent, making tails due - in fact, you calculate it's favored 7-to-1 - on the next toss. Since you're sure the odds are with you, you bet \$25. Sorry, your chance is still 50 percent. Picture the situation by enumerating all possible results of one, two, and three tosses:

 first toss second toss third toss H H H H H H H H T H T H T H H T T T T H T H H T H T T T T T H T T T

One toss has two equally-likely results, H or T, each with a one-out-of-two or 50 percent probability. Two tosses have four equally-likely results, HH, HT, TH, or TT, each with a one-out-of-four or 25 percent probability; however, if the first toss was heads, the second will yield either HH or HT, each with a one-out-of-two or 50 percent probability. Three tosses have eight equally-likely results, HHH, HHT, HTH, HTT, THH, THT, TTH, TTT, each with a one-out-of-eight or 12.5 percent probability; however, if the first two tosses are HH, the third will yield either HHH or HHT, each with a one-out-of-two or 50 percent probability.

Gamblers aren't alone in misconstruing the laws of nature. In his book, Broca's Brain, the late Carl Sagan noted that "many claims have been made at the edge or border of science... These ... often imply something hopeful; for example, that we have vast, untapped powers, or that unseen forces are about to save us from ourselves, or that there is a still unacknowledged pattern and harmony to the universe."

Professor Sagan continued that other aspects of human nature also contribute to the proliferation of pseudo-science. He recalled once dreaming, wrongly, that a relative had died. Suppose the person did die that night, he wrote. "You would have a difficult time convincing me that it was merely coincidence. But it's easy to calculate that if each American has such a premonitory experience a few times in his lifetime, the actuarial statistics would produce a few apparent precognitive events somewhere in America each year... Such a coincidence must happen to someone every few months. But those who experience a correct precognition understandably resist its explanation by coincidence."

Dr Sagan blamed the prevalence of false science on "schools, the press, and commercial television for their sparse, unimaginative and ineffective efforts at scientific education ... [and on] us scientists, for doing so little to popularize our subject."

The poet, Sumner A Ingmark, agreed - putting it this way:

Science gets leery,
When gamblers talk theory.

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Best of Alan Krigman
Alan Krigman

Alan Krigman was a weekly syndicated newspaper gaming columnist and Editor & Publisher of Winning Ways, a monthly newsletter for casino aficionados. His columns focused on gambling probability and statistics. He passed away in October, 2013.
Alan Krigman
Alan Krigman was a weekly syndicated newspaper gaming columnist and Editor & Publisher of Winning Ways, a monthly newsletter for casino aficionados. His columns focused on gambling probability and statistics. He passed away in October, 2013.