## Abstract

Mathematical ideas arise frequently in popular TV game shows, either in pointing the way towards good tactics, or simply adding to the viewer’s enjoyment. The general idea of the *Utility* of a sum of money has a strong influence on whether a contestant will play safe, or take a riskier but potentially more rewarding path. We look at Monty Hall’s game, and its extension to more than three boxes; maths comes up in The Price is Right, both in making sensible guesses at the value of prizes, and in the final part, when three contestants spin a giant wheel, seeking the largest score from one or two spins *without going over* the score 100. Newer games such as Pointless and ‘Two Tribes throw up subtle but interesting maths—how really unlucky could a contestant be, or how a game could be made fairer to all players. Utility can explain many actions in the Million Pound Drop, Deal or No Deal and Who wants to be a Millionaire?. We consider when contestants in The Weakest Link should bank the accumulated funds. The idea of Backwards Induction, applied to the short-lived The Colour of Money, proves that there *was* some optimal strategy at all stages of the game. Several formats have used variations on the well-known Prisoner’s Dilemma to split, or share, a prize. Teams of different sizes arise—can we find a good handicapping system in pub quizzes?

## References and Further Reading

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*The American Statistician*49(3) pages 271–5.Google Scholar - Grosjean J H (1998) Beating the Showcase Showdown.
*Chance*11(1) pages 14–19Google Scholar - Haigh J (2003) The weakest link.
*The Statistician*53(2) pages 219–26.Google Scholar - Haigh J (2014) Pointless: The maths of TV Game Shows.
*Plus Magazine*Google Scholar - Haigh J (2015) Making Two Tribes Fairer.
*Plus Magazine*Google Scholar - Percy D F and Scarf P A (2008) On the development of decision rules for bar quiz handicapping.
*Journal of the Operations Research Society*59(10) pages 1406–14.Google Scholar - Thomas L C (2003) The best banking strategy when playing the Weakest Link.
*Journal of the Operational Research Society*54(7) pages 747–50Google Scholar - Wolstenholme L and Haigh J (2006) Deal or no deal?
*Significance*3(4) pages 191–2Google Scholar