The Big Throwdown

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Regardless of whether the weapon is rock, slug, or earwig, our brightest and least-laid computer programmers are using advanced technology to devise strategies for success. RPS is often used to prove the game theory of nontransitivity, which rebukes the more logical theorem of transitivity, namely: If A beats B, and B beats C, then A also beats C. Notice the contrast with the rules of RPS: rock beats scissors, scissors beats paper, but then rock loses to paper.

This nontransitive neutrality can be compared to chess, in which both sides have the same number of identical pieces and the same number of potential moves. Because of the bluffing that can occur, some draw parallels between RPS and poker (not surprisingly, RPS has become a popular pastime on the World Series of Poker circuit). There is a major difference, however: In poker, you ultimately have to show your hand; in RPS, your bluff is your hand.

Looking at RPS from a mathematical perspective, playing the game in its purest form would mean making totally random throws. But alas, we humans are utterly incapable of random behavior. What we're wearing, what we've had for breakfast, our mood, how much we can bench press . . . these all influence our choice of throws, and a keen opponent can pick up our tendencies rather easily.

In an effort to remove this psychological element, some computer geeks have developed programs that simulate random throws. Truly random play would make for a dull game, though: One-third of the time you would win, one-third you would lose, and one-third you would tie. In the long run, you would break even. That won't get you very far in tournament play, as demonstrated in the 2003 International World RPS championships, when a computer program called Deep Mauve was used to feed random throws to a player who was summarily ousted in the qualifying round.

More advanced nerds have created algorithms that track past throws to detect patterns that may predict future throws. One program, Iocaine Powder from Dan Egnor, devises throws based on the concept of Sicilian reasoning, which uses six levels of meta?reasoning to make predictions. Subsequent programs have used this concept to create new strategies, such as Stratmove, which looks at the history of competing robots to determine how long certain patterns are played. Another, Bayesmove (named for mathematician Thomas Bayes), looks for any strange numbers to determine whether the competing robot is using random moves or employing specific strategies.

If Iocaine Powder and Sicilian reasoning sound familiar, you're probably a fan of the 1987 movie The Princess Bride. In the following scene, Westley (played by Cary Elwes) challenges the Sicilian Vizzini (Wallace Shawn) to a battle of wits to gain the freedom of Princess Buttercup. Two glasses are placed on the table, each containing wine and one containing poison:

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