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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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References

Baird, D. (1981). Significance Tests; Their Logic and Early History. Unpublished Ph.D. Dissertation, Stanford University.Google Scholar
Carnap, R. (1947). “On the Application of Inductive Logic.” Philosophy and Phenomenological Research 8: 133—148.CrossRefGoogle Scholar
Cox, D.R. and Hinkley, D.V. (1974). Theoretical Statistics . London: Chapman and Hall Ltd.CrossRefGoogle Scholar
Fisher, R.A. (1956). Statistical Methods and Scientific Inference. New York: Hafner Publishing Company.Google Scholar
Fisher, R.A. (1970). Statistical Methods for Research Workers. 14th ed. New York: Hafner Publishing Company.Google Scholar
Hacking, Ian. (1965). Logic of Statistical Inference. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
Hacking, Ian. (1980). “Grounding Probabilities from Below.” In PSA 1980, Volume 1. Edited by Asquith, P.D. and Giere, R.N.. East Lansing, Michigan: Philosophy of Science Association. Pages 110–116.Google Scholar
Neyman, J. (1952). First Course in Probability and Statistics. New York: H. Holt and Company.Google Scholar
Russell, B. (1935). Religion and Science. London: T. Butterworth.Google Scholar
Salmon, W. (1971). Statistical Explanation and Statistical Relevance. Pittsburgh: University of Pittsburgh Press.CrossRefGoogle Scholar
Seidenfeld, T. (1979). Philosophical Problems of Statistical Inference: Learning from R.A. Fisher. Dordrecht: Reidel.Google Scholar