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- 22 December 2007
- NewScientist.com news service
- Michael Brooks
YOU know the score: paper wraps rock, rock blunts scissors, scissors cut paper… It’s just a trivial way of making decisions about whose round it is at the bar, who gets the TV remote, that kind of thing. It’s something like tossing a coin, right?
You couldn’t be more wrong. Rock, paper, scissors (RPS) – also known as RoShamBo – is a startling game of strategy that reveals both the fickleness and the limitations of the human mind. There are RPS world championships worth big money, fiercely contested tournaments to find the best RPS computer programs, and heated arguments over which is the optimal RPS strategy. When millions of dollars have been made on the throw of a hand, it is hard to argue this is an insignificant debate. So, how do you win at RPS?
From a mathematical perspective, RPS is a function known as an intransitive relation, which means it creates a loop of preferences that has no beginning and no end, defying standard notions of hierarchy. Though each item is better than some other item, it is impossible to define what is “best”, and this makes it interesting to mathematicians. “It makes you think precisely about what you mean by ‘is better than’,” says John Haigh, a mathematician at the University of Sussex in the UK. “Context is everything.”
Given the interest among mathematicians, it was almost inevitable that computer programmers would get involved and try to produce the ultimate player. According to game theory, the optimal strategy is straightforward: make your throws random. If no one can guess what you’re going to play, they can’t devise a winning strategy against you. That may sound like a simple thing to do, but it isn’t – not even for computers – as David Bolton, a programmer for a finance company based in London, has demonstrated.
Bolton, an RPS enthusiast, has been running a computer RPS league on www.cplus.about.com. The competitors supplying their game-playing code come from as far afield as the Philippines, South Africa, Sweden and China, and their programs, or bots, use a wide range of strategies. Surprisingly, the least successful bots are those that seem to make their choice based on nothing more than random numbers. “These all tend to be at the bottom of the league,” Bolton says.
The explanation must be that these poor performers are not truly random. If there are any patterns at all, well-programmed bots will pick them out – and work out how to exploit them. Iliatsi, currently the leader in Bolton’s league, has 10 strategies to deploy against its opponents, analysing their previous moves, for instance, to find a pattern and thus work out the most likely next move. Iliatsi, created by a Greek programmer, looks set to win when the championship winds up this month.
Though competitions between programs are a challenge for the programmers, they are of limited interest to everyone else, says Perry Friedman, who created RoShamBot, one of the first RPS bots. Computer RPS players are simply too good. “It’s much more interesting to find games that play well against people,” Friedman says. So when Friedman created RoShamBot, he deliberately refrained from making it invincible. While the program is powerful, its charm, he says, is that it doesn’t just mash you into a pulp. You can play against RoShamBot at http://zonker.stanford.edu/cgi-bin/roshambot.
Since graduating from Stanford, Friedman has worked as a programmer for IBM and Oracle and as a professional poker player. In the latter pursuit, playing RPS against other humans has been a big help, Friedman says, because live-action RPS teaches you about the peculiarities of human thought. In RPS, the golden rule is to be unpredictable, but without extensive training humans are hopeless at this. “People tend to fall into patterns,” Friedman says. “They tell themselves things like, ‘I just went rock twice, so I shouldn’t do rock a third time, because that’s not random’.”
Worse, people tend to project patterns on their opponents. “They see patterns where there are none,” Friedman says. This, he adds, is a major source of complaints in online gaming: when players lose because of something they perceive as a too-lucky dice throw, say, they think the computer they are playing against must be rigged. “What are the odds double-six came up right when he needed it?” players ask. The thing is, as Friedman points out, “They don’t notice all the times it didn’t come up.”
If you are going to win at RPS, Friedman’s advice is to think – but not too much. Of course you want to randomise your throws, but once the game is under way you should look for patterns. If your opponent is human, the chances are he or she works – consciously or unconsciously – with a sequence in their head. Spot it, and they are toast.
Another tip is don’t throw rock in your first game. This strategy won the auction house Christie’s millions of dollars in 2005 when a wealthy Japanese art collector couldn’t decide which firm of auctioneers should sell his corporation’s collection of Impressionist paintings. He suggested they play RPS for it. Christie’s asked for suggestions from their employees, one of whom turned out to have daughters who played RPS in the schoolyard. “Everybody expects you to choose rock,” the girls said, so their advice was: go for scissors. Christie’s acted on this expert tip, while rival auction house Sotheby’s went for paper – and lost the business.
Scissors is still a good starting throw even if you are playing against someone experienced: they won’t go for rock because that’s seen as a rookie move, so the worst you are likely to do is tie. Once things are under way, different techniques come in. You could try the double bluff, where you tell your opponent what you’re going to throw – then do it: no one believes you’ll do it, so they won’t play the throw that beats the throw you are playing. Then, if your mind goes blank, play the throw that would have been beaten by your opponent’s previous throw: some kind of subconscious activity seems to encourage players – especially those who are not feeling at the top of their game – to aim to beat their own preceding throw.
When all else fails, the rule is “go with paper”, because rock comes up more often than it would by chance. In 1998, Mitsui Yoshizawa, a mathematician at Tokyo University of Science, studied throws from 725 people and found that they threw rock 35 per cent of the time. Paper came in at 33 per cent and scissors at 31 per cent. Facebook has an online game called Roshambull which has logged 10 million throws in over 1.6 million games. Here the statistics are 36 per cent rock, 30 per cent paper and 34 per cent scissors. “Players clearly have a slight preference for rock, and that affects the distribution of all the plays,” says Graham Walker of the World RPS Society. This pleases him, since it shows how winning something like the world RPS championship involves skill, not luck. “Given people’s preference for rock, it is impossible to claim that RPS is a game of chance,” he says.
So there you go: if arguments over which TV channel to watch are a regular feature of your holidays, now you know how to get your own way more often than not. Do a little study, practise against an online trainer, then, wide-eyed, make what looks like an innocent suggestion: shall we settle this with rock, paper, scissors?
From issue 2635 of New Scientist magazine, 22 December 2007, page 66-67
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The science behind everything….
I love these articles that are about nothing really, but are still so interesting you read them.
Maybe I’m just sadder than i originally thought.
Munch Me 