, Volume 36, Issue 1, pp 1–19 | Cite as

Bias and runs in dice throwing and recording: A few million throws

  • Gudmund R. Iversen
  • Willard H. Longcor
  • Frederick Mosteller
  • John P. Gilbert
  • Cleo Youtz


An experimenter threw individually 219 different dice of four different brands and recorded even and odd outcomes for one block of 20,000 trials for each die—4,380,000 throws in all. The resulting data on runs offer a basis for comparing the observed properties of such a physical randomizing process with theory and with simulations based on pseudo-random numbers and RAND Corporation random numbers. Although generally the results are close to those forecast by theory, some notable exceptions raise questions about the surprise value that should be associated with occurrences two standard deviations from the mean. These data suggest that the usual significance level may well actually be running from 7 to 15 percent instead of the theoretical 5 percent.

The data base is the largest of its kind. A set generated by one brand of dice contains 2,000,000 bits and is the first handmade empirical data of such size to fail to show a significant departure from ideal theory in either location or scale.


Standard Deviation Public Policy Random Number Data Base Empirical Data 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Psychometric Society 1971

Authors and Affiliations

  • Gudmund R. Iversen
  • Willard H. Longcor
  • Frederick Mosteller
  • John P. Gilbert
  • Cleo Youtz

There are no affiliations available

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