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Best of Alan Krigman

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What Can Gamblers Learn from Superstitious Pigeons?

26 August 2003

Superstition is the presumption of a cause-and-effect relation that can neither be conclusively proved nor refuted. Increased knowledge occasionally reveals a connection and shows such an inference to be valid. Often, however, superstitions are without merit and what appears to be causality is merely coincidence. Especially, coincidence that is remembered or reported to occur repeatedly. Absent proof, superstitions may be rationalized, but explanations aren't essential and many are taken on faith alone.

The eminent Harvard behavioral psychologist, B F Skinner, conducted a classic experiment in 1948 showing that pigeons were superstitious. More precisely, Dr Skinner elicited superstitious behavior in the birds. He put eight hungry pigeons into cages and dispensed food pellets to them regularly. They were fed every 15 seconds, wholly independently of anything they did. Six of the eight developed bizarre rituals, all different. For instance, one banged its head against a corner of the cage while others spun around, rocked back and forth in particular ways, and so forth.

Dr Skinner surmised that the pigeons were carrying out arbitrary actions when the food first appeared. They got fed again after replicating the gestures, although the pellets would have come anyway. Dr Skinner concluded that "reinforcement is contingent with a response" even when no causality exists. The phenomenon has subsequently been shown to apply broadly, to humans as well as animals. That is, events that occur together repeatedly seem to have a dependency, irrespective of any genuine link.

Many gamblers think they can influence chance occurrences in some manner, or can anticipate them from past events. The beliefs are typically manifest as the illusion of control or of fundamental patterns or trends. In truly random games, such notions are superstitions. These conjectures have been widely studied. One example involves a series of tests involving a dice game, performed at the University of Malaga in Spain.

The first experiment investigated if players who won more in the first few rounds when they, or someone else, threw the dice would be more confident of success with the same roller later. To assess degree of certainty, players were asked to state what they estimated as their probability of winning. Pure chance would be 50 percent. The data showed a reasonable correlation between subjects' confidence of winning with themselves or others as shooters, and outcomes of early rounds implemented both ways.

In the second test players alternately chose which numbers would win, or had to bet on pre-established results. This, whether or not they were rolling the dice. The upshot in these cases was a correlation between confidence and success during early rounds when choosing or being given the point to be hit.

In the third set of trials, participants always threw the dice themselves, in some rounds while wearing a "biomagnetic" bracelet and in others without it. Correlations were stronger here than in either of the first two experiments. Players who won more in the initial throws wearing the bracelets clearly considered them to be lucky charms; those who lost more in the conditioning rounds with the bracelets, later had low confidence while wearing them.

These and other analyses bolster the idea that gamblers are inherently superstitious. That is, players' estimates of the probabilities of random incidents are biased by observed juxtaposition of events in the past, without regard to etiology. More, they frequently act on these estimates. Interestingly, the study did not support the widely-held theory that illusion of skill -- physical as in shooting dice or mental as in choosing or predicting outcomes -- gives solid citizens a sense of control. A lot like Skinner's pigeons. Of course, any similarity between pigeons in a box and gamblers in a casino has to be purely coincidental. Or does it? Perhaps the popular poet, Sumner A Ingmark, envisioned that enigma in his oft quoted quatrain:

What's worked before, may work again,
The problem comes in telling when.
Though few profess to understand,
They go with things they've seen first hand.

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.