TV Game Shows



It may surprise many people how often mathematical ideas arise 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, rather than its actual amount, has a strong influence on whether a contestant will play safe, or take a riskier but potentially more rewarding path. We look at (of course) “Monty Hall’s” game, but also its extension to more then 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?”, and we consider at what stage 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 might arise in some formats, (in pub quizzes, can we find a good handicapping system to use?).


Correct Answer Final Round Large Team Golden Ball Original Choice 
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.


  1. Coe P R and Butterworth W (1995) Optimal Stopping in “The Showcase Showdown”. The American Statistician 49(3) pages 271–5.Google Scholar
  2. Grosjean J H (1998) Beating the Showcase Showdown. Chance 11(1) pages 14–19Google Scholar
  3. Haigh J (2003) The weakest link. The Statistician 53(2) pages 219–26.Google Scholar
  4. Haigh J (2014) Pointless: The maths of TV Game Shows. Plus Magazine Google Scholar
  5. Haigh J (2015) Making Two Tribes Fairer. Plus Magazine Google Scholar
  6. 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
  7. 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
  8. Wolstenholme L and Haigh J (2006) Deal or no deal? Significance 3(4) pages 191–2Google Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.University of SussexBrightonUK

Personalised recommendations