Sunday, 11 May 2014

How does James Bond win at rock-paper-scissors?

A recent study of 360 players at a rock-paper-scissors tournament at Zhejiang University in China revealed that players who win a round tend to stick to their winning action in the next round, while the losing player tends to play the next action in the sequence. Thus, a competitor who wins with paper against the opponent's rock will play paper in the next round, while the opponent will play paper.

This seems to contradict an earlier study by a team from University College London (UCL), which studied the results of two contests – one in which both players were blindfolded, and the other in which one player was blindfolded – which suggested that players tend to mimic each other's actions through 'automatic imitation', resulting in a high proportion of draws.

Both studies demonstrate that play is rarely random. Game theory suggests that the best strategy to adopt is one where decisions about which action to play are random, but in practice this approach appears to be difficult to sustain.

Rock-paper-scissors is a game with which James Bond is familiar. In the novel of You Only Live Twice, the head of the Japanese secret service, Tiger Tanaka, challenges Bond to a contest (chapter 1). The description of the contest, which deserves to join Moonraker's game of bridge and Goldfinger's golf match as a classic piece of sports writing, is sufficiently detailed to give us Bond's strategy over three games of rock-paper-scissors, each comprising the best of three rounds. Returning to the recent studies, how does Bond play?

Fleming tells us that Bond's strategy from the start is to play randomly. In the first round, Bond plays paper against Tiger's stone and wins. In the second round, Tiger plays stone to win against Bond's scissors. In the decider, Tiger keeps his stone, while Bond wins with paper. In this game, then, Bond does appear to play randomly, or least his strategy does not seem to fit the play typically encountered in the two studies. In contrast, Tiger's play is more calculated. By sticking to the same action over three rounds, he is likely to achieve some success against a random strategy simply by chance. But perhaps by the third round Bond's play is not so random. Fleming describes Bond's suspicions that Tiger would again choose stone, and this gives Bond the edge.

For much of the second game, Bond and Tiger show the same symbols and record a series of draws. The play appears to be consistent with 'automatic imitation' described in the UCL study. Tiger eventually wins the game, however, with Bond claiming to be continuing his random play.

In the third and final game, Bond wins the first round with stone against Tiger's scissors, and wins the second by playing paper against Tiger's stone. Again Bond can claim with some justification that his strategy was random – he “had had no method” – while Tiger appears to have adopted an approach which is consistent with the results of the study by Zhejiang University. Losing in the first round with scissors, he plays the next symbol in the sequence – rock (or stone) – in the second.

Of course, the game Fleming describes is fictional, with presumably no basis in fact. Bond was always going to win. But Fleming's writing is, as usual, so skilful and detailed that it offers a set of plausible results in the game of rock-paper-scissors that are consistent with standard and new theories of play.

Further reading:
Cook, R, Bird, G, L√ľnser, G and Huck, S, 2011 Automatic imitation in a strategic context: players of rock–paper–scissors imitate opponents' gestures, Proc. R. Soc. B, 22 February 2012 vol. 279 no. 1729 780-786, Published online before print 20 July 2011 doi: 10.1098/rspb.2011.1024
Wang, Z, Xu, B and Zhou, H-J, 2014 Social cycling and conditional responses in the Rock-Paper-Scissors game, arXiv:1404.5199v1 [physics.soc-ph]

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