Hostname: page-component-6bf8c574d5-xtvcr Total loading time: 0 Render date: 2025-02-14T09:50:10.390Z Has data issue: false hasContentIssue false
  • English
  • Français

The Matching Problem

Published online by Cambridge University Press:  01 January 2025

Edgar J. Gilbert
Edgar J. Gilbert*
Affiliation:
Harvard University
Get access Rights & Permissions [Opens in a new window]

Abstract

Tables of the exact distributions of number of matches are given for small decks having the same number of cards in each suit. Several approximate distributions are considered for use with larger decks, and some indication of the goodness of the approximations is given.

Type
Original Paper
Information
Psychometrika , Volume 21 , Issue 3 , September 1956 , pp. 253 - 266
Copyright
Copyright © 1956 The Psychometric Society

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Footnotes

*

The calculations for this paper were done while the writer was working on a project sponsored by funds from the Ford Foundation. The writer wishes to express his gratitude to Dr. Frederick Mosteller for his constant help and encouragement during the writing of this paper.

†

Now at University of California, Berkeley.

References

Anderson, T. W. On card matching. Ann. math. Statist., 1943, 14, 426–435CrossRefGoogle Scholar
Battin, I. L. On the problem of multiple matching. Ann. math. Statist., 1942, 13, 294–305CrossRefGoogle Scholar
Feller, W. An introduction to probability theory and its applications, Volume 1 (pp. 62–69). New York: Wiley, 1950Google Scholar
Greenwood, R. E. Probabilities of certain solitaire card games. J. Amer. statist. Ass., 1953, 48, 88–93CrossRefGoogle Scholar
Greville, T. N. E. Exact probabilities for the matching hypothesis. J. Parapsychology, 1938, 2, 55–59Google Scholar
Greville, T. N. E. The frequency distribution of a general matching problem. Ann. math. Statist., 1941, 12, 350–354CrossRefGoogle Scholar
Hamilton, C. H. Comment on question 8: variance of number of matches. Amer. Statistician, 1948, 2, 23–23Google Scholar
Huntington, E. V. Exact probabilities in certain card matching problems. Science, 1937, 86, 499–500CrossRefGoogle ScholarPubMed
Olds, E. G. A moment-generating function which is useful in solving certain matching problems. Bull. Amer. math. Soc., 1938, 44, 407–413CrossRefGoogle Scholar
Rietz, H. L. Mathematical statistics (pp. 60–76). Chicago: Open Court Publishing Co., 1927CrossRefGoogle Scholar
U. S. Department of Commerce, National Bureau of Standards. Tables of the binomial probability distribution, Washington: U.S. Government Printing Office, 1949Google Scholar