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How to Commit the Gambler's Fallacy and Get Away with It

Published online by Cambridge University Press:  28 February 2022

Davis Baird  and
Richard E. Otte
Davis Baird
Affiliation:
University of Arizona
Richard E. Otte
Affiliation:
University of Arizona and University of Pittsburgh
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Extract

The gambler's fallacy runs like this: We know

  • 1) the bias for heads of a certain coin and flipping device is 1/2, and

  • 2) flips of the coin with the flipping device are independent.

Given these facts we can easily compute the probability of 4 heads or fewer turning up in 20 flips, P(h≤4), to be

Suppose we flip the coin 15 times and get—improbably enough—all tails. If the coin lands tails up once more in the next 5 flips the improbable event of 4 or fewer heads in 20 flips, h≤4, will have occurred. Since P(h≤4) is so small we might be tempted to infer that all of the next five flips will be heads.

Type
Part IV. Probability and Statistical Inference
Information
PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association , Volume 1982 , Issue 1: Volume One: Contributed Papers 1982 , 1982 , pp. 169 - 180
Copyright
Copyright © Philosophy of Science Association 1982

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