The Paradox of Parrondo’s Games

 In News

The AMSI Summer School 2016 included a series of lunchtime lectures. Professor Peter Taylor (The University of Melbourne) discusses the Paradox of Parrondo’s Games.


In 1998, a colleague at the University of Adelaide knocked on Professor Peter Taylor’s door and showed him some interesting simulations, implementations of two games developed by a Spanish physicist Juan Parrondo, which are both biased against the player. However, if the player alternates between the games or chooses which game to play in a random fashion, the ensuing game is biased in favour of the player.

This talk discusses the definition of what it means for a game to be fair, a rigorous proof that Parrondo’s drift criteria do imply that a game is losing, fair or winning respectively and the observation that the phenomenon observed by Parrondo should be thought of as ubiquitous, rather than unusual. Peter also shares the story of his involvement with Parrondo’s games.


Peter Taylor received a BSc (Hons) and a PhD in Applied Mathematics from the University of Adelaide in 1980 and 1987 respectively. In between, he spent time working for the Australian Public Service in Canberra. After periods at the Universities of Western Australia and Adelaide, he moved at the beginning of 2002 to the University of Melbourne. In January 2003, he took up a position as the inaugural Professor of Operations Research, and was Head of the Department of Mathematics and Statistics from 2005 until 2010.

Peter’s research interests lie in the fields of stochastic modelling and applied probability, with particular emphasis on applications in telecommunications, biological modelling, healthcare and disaster management. Recently, he has become interested in the interaction of stochastic modelling with optimisation and optimal control under conditions of uncertainty. He is regularly invited to present plenary papers at international conferences. He has also acted on organising and program committees for many conferences.

Peter is the editor-in-chief of ‘Stochastic Models’, and on the editorial boards of ‘Queueing Systems’, the ‘Journal of Applied Probability’ and ‘Advances in Applied Probability’. He served on the Awards Committee of the Applied Probability Section of the Institute for Operations Research and Management Science (INFORMS) from 2005-2007 and is currently on the committee for the Nicholson Prize, awarded for the best student paper in operations research. In 2008, Peter became one of the five trustees of the Applied Probability Trust. This trust, which is based in Sheffield UK, is the body which publishes the Applied Probability journals plus ‘The Mathematical Scientist’ and ‘Spectrum’.

From February 2006 to February 2008, Peter was Chair of the Australia and New Zealand Division of Industrial and Applied Mathematics (ANZIAM), and from September 2010 to September 2012 he was the President of the Australian Mathematical Society. In 2013 he was awarded a Laureate Fellowship by the Australian Research Council.

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