Rock, paper or scissors

December 20, 2007

[spoiler]

  • 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

 

[/spoiler]

 

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.


Is the biofuel dream over?

December 14, 2007
  • 15 December 2007
  • From New Scientist Print Edition.
  • Fred Pearce
  • Peter Aldhous

Can biofuels help save our planet from a climate catastrophe? Farmers and fuel companies certainly seem to think so, but fresh doubts have arisen about the wisdom of jumping wholesale onto the biofuels bandwagon…….

About 12 million hectares, or around 1 per cent of the world’s fields, are currently devoted to growing biofuels. Sugar cane and maize, for example, are turned into bioethanol, a substitute for gasoline, while rapeseed and palm oil are made into biodiesel. That figure will grow because oil is so costly, and because biofuels supposedly emit fewer greenhouse gases than fossil fuels.

But a slew of new studies question the logic behind expanding biofuel production. For a start, there may not be enough land to grow the crops on or water to irrigate them, given other demands on global agriculture. Worse, any cuts in carbon dioxide emissions gained by burning less fossil fuels may be wiped out by increased emissions of the greenhouse gas nitrous oxide from fertilisers used on biofuel crops.

In parts of the world, shortage of water is already putting a brake on agricultural productivity. According to Johan Rockström, executive director of the Stockholm Environment Institute in Sweden, switching 50 per cent of the fossil fuels that will be devoted to electricity generation and transport by 2050 to biofuels would use between 4000 and 12,000 extra cubic kilometres of water per year. To put that in perspective, the total annual flow down the world’s rivers is about 14,000 km3.

A more modest target of quadrupling world biofuel production to 140 billion litres a year by 2030 – enough to replace 7.5 per cent of current gasoline use, would require an extra 180 km3 of water to be extracted from rivers and underground reserves, calculates Charlotte de Fraiture at the International Water Management Institute, based near Columbo in Sri Lanka.

That target may be manageable across much of the globe. But in China and India, where water is in short supply and most crops require artificial irrigation, de Fraiture argues that there is not enough water even to meet existing government plans to expand biofuel production.

Another contentious issue is how much land is available to grow biofuels (New Scientist, 25 September 2006, p 36). And the answer appears to be not much, a point that Sten Nilsson, deputy director of the International Institute for Applied Systems Analysis in Laxenburg, Austria, makes using a “cartographic strip-tease” based on a new global mapping study.

Beginning with a world map showing land not yet built upon or cultivated, Nilsson progressively strips forests, deserts and other non-vegetated areas, mountains, protected areas, land with an unsuitable climate, and pastures needed for grazing (see Maps). That leaves just 250 to 300 million hectares for growing biofuels, an area about the size of Argentina.

Even using a future generation of biofuel crops – woody plants with large amounts of cellulose that enable more biomass to be converted to fuel – Nilsson calculates that it will take 290 million hectares to meet a tenth of the world’s projected energy demands in 2030. But another 200 million hectares will be needed by then to feed an extra 2 to 3 billion people, with a further 25 million hectares absorbed by expanding timber and pulp industries.

So if biofuels expand as much as Nilsson anticipates, there will be no choice but to impinge upon land needed for growing food, or to destroy forests and other pristine areas like peat bogs. That would release carbon now stashed away in forests and peat soils (New Scientist, 1 December, p 50), turning biofuels into a major contributor to global warming

De Fraiture is more optimistic. Her modest projection for a quadrupling of biofuel production assumes that maize production will be boosted by 20 per cent, sugar cane by 25 per cent and oil crops for biodiesel by 80 per cent. Assuming future improvements in crop yields, de Fraiture estimates that this might be done on just 30 million hectares of land – or 2.5 times the area now under cultivation.

Even today’s biofuel yields depend on generous applications of nitrogen-containing fertiliser. That contributes to global warming, as some of the added nitrogen gets converted into nitrous oxide, which is a potent greenhouse gas. Over 100 years it creates 300 times the warming effect of CO2, molecule for molecule. And now researchers led by Paul Crutzen of the Max Planck Institute for Chemistry in Mainz, Germany, who won a share of a Nobel prize for his work on the destruction of the ozone layer, claim that we have underestimated these emissions. Factor in their revised figures, and cuts in CO2 emissions as a result of replacing fossil fuels may be wiped out altogether.

“Fertilisers contribute to global warming, as some of the added nitrogen gets converted into a potent greenhouse gas”

The Intergovernmental Panel on Climate Change suggests that between 1 and 2 per cent of nitrogen added to fields gets converted to nitrous oxide, based on direct measurements of emissions from fertilised soils. But nitrogen from fertiliser also gets into water and moves around the environment, continuing to emit nitrous oxide as it goes. To estimate these “indirect” emissions, Crutzen and his colleagues calculated how much nitrogen has built up in the atmosphere since pre-industrial times, and estimated how much of this could be attributed to the use of fertilisers.

This suggested that between 3 and 5 per cent of the nitrogen added to the soil in fertilisers ends up in the atmosphere as nitrous oxide. Crucially, that would be enough to negate cuts in CO2 emissions made by replacing fossil fuels. Biodiesel from rapeseed came off worse – the warming caused by nitrous oxide emissions being 1 to 1.7 times as much as the cooling caused by replacing fossil fuels. For maize bioethanol, the range was 0.9 to 1.5. Only bioethanol from sugar cane came out with a net cooling effect, its nitrous oxide emissions causing between 0.5 and 0.9 times as much warming as the cooling due to fossil fuel replacement.

These simple calculations, which set increased nitrous oxide emissions against reductions in CO2 emissions caused by replacing gasoline or diesel with biofuels, do not account for all the greenhouse gas emissions associated with producing, processing and distributing the various fuels. Now Michael Wang of the Argonne National Laboratory in Illinois has taken Crutzen’s upper estimate for nitrous oxide emissions and plugged it into a sophisticated computer model which does just that. When he did so, bioethanol from maize went from giving about a 20 per cent cut in greenhouse gas emissions, compared to gasoline, to providing no advantage at all. Still, Wang suspects that Crutzen’s method may overestimate nitrous oxide emissions. “It is a very interesting approach,” he says. “But there may be systematic biases.”

Crutzen stresses that his paper is still being revised in response to comments he has received since August, when a preliminary version appeared online. “Here and there the numbers may change. But the principle doesn’t,” he says. “It’s really telling us about a general problem with our lack of knowledge about the nitrogen cycle.”

With governments and businesses backing biofuels as part of a “green” future, that represents a disturbing gap in our knowledge.

From issue 2634 of New Scientist magazine, 15 December 2007, page 6-7

So the biofuel solution is running into problems, well its an emerging technology and it isn’t the only solution / possibility for humans to switch away from fossil fuels and other green house contributors.

Onwards, always onwards 🙂