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Wallet Game: Probability, Likelihood, and Extended Likelihood

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  • Yudi Pawitan
  • Youngjo Lee

Abstract

We propose a likelihood explanation to the two-person wallet game, a probability-related paradox, where an obviously fair game may appear favorable to both players. Yet a small variation of the game, without changing its fairness, turns it to seem unfavorable. The extended likelihood concept seems logically necessary if we want to allow the sense of uncertainty associated with a realized but still unobserved random outcome, while at the same time avoid potential probability-related paradoxes.

Suggested Citation

  • Yudi Pawitan & Youngjo Lee, 2017. "Wallet Game: Probability, Likelihood, and Extended Likelihood," The American Statistician, Taylor & Francis Journals, vol. 71(2), pages 120-122, April.
    • Handle: RePEc:taf:amstat:v:71:y:2017:i:2:p:120-122
    DOI: 10.1080/00031305.2016.1202140
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    References listed on IDEAS

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    1. Youngjo Lee & John A. Nelder, 2006. "Double hierarchical generalized linear models (with discussion)," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 55(2), pages 139-185, April.
    2. Youngjo Lee & Jan F. Bjørnstad, 2013. "Extended likelihood approach to large-scale multiple testing," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 75(3), pages 553-575, June.
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    Cited by:

    1. Lee Youngjo & Gwangsu Kim, 2020. "Properties of h‐Likelihood Estimators in Clustered Data," International Statistical Review, International Statistical Institute, vol. 88(2), pages 380-395, August.

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