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Last Updated: Friday, 6 May, 2005, 10:55 GMT 11:55 UK
Scissors, paper, stone - a strategic game
By Steve Tomkins

You probably thought scissors, paper, stone was a game of chance not strategy. But you'd be wrong. Christie's auction house won a 10.5m contract by playing the game tactically - so is there more to such games than meets the eye?

The ability of scissors to cut paper has doubtless had all kinds of effects on the history of art, but surely none odder than in Tokyo last month.

The Maspro Denkoh electronics corporation was selling its $20 million collection of Picassos and Van Goghs, but the director could not decide whether Sotheby's or Christie's should have the privilege of auctioning them.

So he announced that the deal would go to the winner of a single round of scissors, paper, stone - the children's game that relies on quick fire hand gestures, where stone beats scissors, scissors beat paper, and paper beats stone.

Sotheby's reluctantly accepted this as a 50/50 game of chance, but Christie's asked the experts, Flora and Alice, 11-year-old daughters of the company's director of Impressionist and modern art, and aficionados of the game.

They explained their strategy:

1. Stone is the one that "feels" the strongest
2. Therefore a novice will expect their opponent to go for stone, and will go for paper to beat stone
3. Therefore go for scissors first

Sure enough, the novices at Sotheby's went for paper, and Christie's scissors got them an enormously lucrative cut.

All of which makes one wonder what cunning strategies might lurk within the simple family games beloved of caravan holidays and wet half-terms.

Lord Archer - Monopoly
Fair play... it's widely expected
Neil Thomson has studied Monopoly mathematically, using probability matrices. It turns out the best properties are the orange ones - Vine Street, Marlborough Street, Bow Street in the London version. But, he says, the key is to buy every street you land on, and to put hotels on one set before you put houses on another. And the stations are rubbish, but the utilities are even worse.

Connect Four has been the subject of computer research. At the University of Limburg in Maastricht, Victor Allen got his masters degree in 1990 by proving that the player who goes first can win whatever their opponent does - at least if they're a computer.

The trick with this game - an elaborate version of noughts and crosses - is in what the experts call "holes": the gaps at the end of your row of three that you need to fill with your "coin" in order to win. Apparently, if you go first you want to get all your holes on the odd-numbered rows of the board. If you go second, you want to get all your holes on the even numbered rows.

Get more holes in the correct rows than your opponent, and you'll be the hero of your caravan. Player one should always start by dropping their "coin" in the middle column.

Scrabble meanwhile is a matter of fierce international championships, though it hasn't attracted so much interest from computers. Top players agree that one of the keys is learning all those two-letter words that seem to exist solely for the sake of Scrabble - like "aa" (a kind of lava) and "xu" (a monetary unit in Vietnam).

Nought to learn

The other is to look out for seven-letter words that net you that all important 50-point bonus. Find common prefixes and suffixes, like -ING from among your seven letters, then you just have to jiggle about your remaining N, I, W and N for the winning combination.

Draughts
To be a draughts champ, the tip from the top is to get your pieces into the centre of the board - unless you're getting beaten, in which case skulking in the corners is a way to cause the ascendant enemy problems.

Othello (aka Reversi), like Scrabble, inspires devotion, sporting federations and ferocious international competitions. It also has its exotic jargon - "C-squares", "wedges", and "the baited tempo swindle".

David Parsons, the president of the United States Othello Association says that the best strategies are "counter-intuitive, surprising, subtle, and artistic".

How to win Othello? Well, it's all very complicated. But try to get your pieces in the corners where they can't be "flipped", and then - and only then - in the squares next to the corners.

When it comes to noughts and crosses though, there simply is no way to do better than draw unless you're playing against someone who hasn't got the hang of it. Your best bet, as most of us will remember from all those years ago, is to get three corners, and if any two of them are not blocked, you're laughing - probably cruelly and smugly at your opponent's slackness of brain... especially if you've just won commission on 10.5m.


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