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Hopefully you’re familiar with the children’s game of Rock, Paper, Scissors. It serves as a lovely example of how games can illustrate mathematical principles, and conversely how mathematical principles can be used to facilitate games. Rock, Paper, Scissors, at heart, is simply a set of transitive relationships. The diagram below can be used to represent how the three ‘states’ of ‘Rock’, ‘Paper’ and ‘Scissors’ relate to one another.

Where a card lies on top of another, the instance of that card will ‘beat’ the instance of the other. For example, Rock will beat Scissors, Scissors will beat Paper, and Paper will beat Rock. In the event that both instances are the same, the event is declared a draw and the winner is determined by a further subsequent event, so the players just repeat a round until there is a winner.

So, as we all probably know, the game requires two players to simultaneously present one of three possible states and, via the rules above, the combination of states determines who wins, or whether the event is a draw.

Assuming that this is simply a purely random event, i.e. the players are just randomly selecting a state, what is the probability of winning? Discuss.

We’re happy to accept solutions sent to any of the North East regional team and we’ll provide a solution in the next North East regional newsletter.

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