Outwitting the Lying Oracle

On Thursday, Sept. 15, 2005, Dr Robb Koether gave the opening lecture for the Longwood University Department of Mathematics and Computer Science Colloquium Series for 2005-2006.  His talk, “Outwitting the Lying Oracle,” was based on work done in conjunction with Dr. John Osoinach and published in the April 2005 issue of Mathematics Magazine.  Dr. Koether’s talk concerned a coin-tossing game in which the player bets on the outcome of the toss against an all-knowing oracle who predicts the outcome of the toss, but may lie about the outcome.  In each of the three scenarios below the optimal playing strategy was developed using game trees, equations and game matrices: 

• A game of 5 coin tosses in which the oracle may lie up to 2 times and the player always agrees with the oracle
• A game of 5 coin tosses in which the oracle may lie up to 2 times and the player may or may not agree with the oracle
•  A game of 4 coin tosses with a prescribed set of “lie-patterns” available to the oracle with the player having the option of agreeing or disagreeing with the oracle.

In a “hands-on” approach, Dr. Koether adopted the role of the player and placed bets to a volunteer “oracle” from the audience.  Dr. Koether demonstrated that the player could double his money in the first scenario and more than triple it in the third scenario by using his “optimal playing strategy”. 

The Department of Mathematics and Computer Science Colloquium Series presents invited talks once a month to students and faculty and are open to the public.

Article by Cindy Koether, Hampden Sydney College

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