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The lying oracle game with a biased coin

Part of: Game theory General and miscellaneous specific topics Combinatorial probability

Published online by Cambridge University Press:  01 July 2016

Robb Koether ,
Marcus Pendergrass  and
John Osoinach
Robb Koether*
Affiliation:
Hampden-Sydney College
Marcus Pendergrass*
Affiliation:
Hampden-Sydney College
John Osoinach*
Affiliation:
Millsaps College
*
∗ Postal address: Box 166, Department of Mathematics and Computer Science, Hampden-Sydney College, Hampden-Sydney, VA 23943, USA.
∗∗ Postal address: Box 174, Department of Mathematics and Computer Science, Hampden-Sydney College, Hampden-Sydney, VA 23943, USA.
∗∗∗ Current address: University of Dallas, 1845 E. Northgate Drive, Irving, TX 75062-4736, USA. Email address: josoinach@udallas.edu
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Abstract

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The lying oracle problem is a problem of finding the optimal strategies in a two-person game where an oracle predicts the outcomes of coin flips and a player bets on the outcomes. The oracle announces whether the coin will land heads or tails, but may at times lie. We analyze the variant of the game which uses a biased coin, where the probability p that the coin lands heads is common knowledge. We determine optimal strategies for both the oracle and player, and we give an explicit expression for the expected payoff to the player when the coin is flipped n times and the oracle may lie at most k times.

Keywords

Lying oracleprobabilistic gameoptimal strategyexpected payoffharmonic mean

MSC classification

Primary: 91A60: Probabilistic games; gambling
Secondary: 91A05: 2-person games 60C05: Combinatorial probability 00A08: Recreational mathematics
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 41 , Issue 4 , December 2009 , pp. 1023 - 1040
Copyright
Copyright © Applied Probability Trust 2009 

References

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