Roshambo and Luck

Greg Costikyan has posted to his blog an essay on Roshambo (Rock Paper Scissors), as part of his current theme of seeing what familiar games have to teach contemorary game designers.

Surprisingly, Greg reaches a wrong conclusion:

Rock, Paper, Scissors is surely one of the earliest games each of us learns to play. It can be played in essentially two ways. The first way is by selecting your move entirely at random, making no effort to predict what your opponent will choose. In this case, you will win a third of the time, lose a third of the time, and draw a third of the time.

The second way to play is, if you will "in earnest:" that is, by trying to guess what move your opponent will make next, and selecting your own move in response. This can work, if your opponent is also playing in earnest, and you are smarter than he. In that case, you will win more frequently than with the random strategy.

However, if one player does indeed win more often than random selection would allow, the other player has a strong incentive to adopt a random strategy, since his win ratio will rise from less than one-third to one-third. And if either player (or both) selects a random strategy, the outcome will be random.

Thus, Rock, Paper, Scissors is what I call a degenerate game; it ultimately degenerates into a game with random outcomes, losing any element of strategy—and becomes dull.

What Greg identifies as degeneracy in Roshambo exists in idealized, theoretical Roshambo, but not in the real-world game played by real players.

People are predictable. People can be psyched. People are no damn good at all at being random without artificial aids like coins or dice.

Suppose you, a human being, are playing long sequence of Roshambo throws against a savvy human opponent. Early on, you discover that your opponent seems to be wiping the floor with you, so you defend by trying to be as random as you possibly can. (Perhaps for a bar bet once you've memorized the decimal expansion of pi to many, many places, and decide to throw in accordance with that sequence of digits, modulo 3.)

Your opponent might still mop the floor with you! The game of competitive Roshambo is, among other things, a game of tells. You might be choosing your next throw completely randomly, but giving it away by your stance, the how you hold your hand, the motion of your arm, and so on.

The next level of the game comes when both players are aware of the real-world dimension of Roshambo. They each strive to eliminate tells ... or cultivating them with the intention of using them to mislead.

This is the level of Roshambo at which Perry Friedman is said to play:

Roshambo tournaments are rife with verbal sparring, psychological one-upmanship and manipulating opponents into tells. Former [poker] World Champion Phil Hellmuth, Jr. is generally right at home in such an environment, but met his match in one quarterfinal against Tiltboy Perry Friedman.

Hellmuth strode forth confidently to center ring, his 6-foot-6 inches towering a good foot above Friedman. He assumed his usual table demeanor, threatening to "look into Perry's soul" as he often does with his poker tournament opponents. After a few early ties when both players threw rock, Friedman switched to scissors to beat Hellmuth's paper. Friedman disdainfully exclaimed "rock, rock, paper?!" in a manner that clearly suggested it was an amateurish maneuver. For the remainder of the match, Friedman would outtalk and out-throw Hellmuth, until, leading 9-6, he proclaimed (in his best Scotty Nguyen impersonation): "If you go rock, it all ova baby!" Hellmuth couldn't resist the challenge, threw a rock and lost to Friedman's paper, sending the smirking Friedman to the semifinals. Perry smiled and confessed to the audience that he actually had no soul.

(From "The 2001 World Roshambo Championship")

Could Phil Hellmuth have defended against Perry Friedman's onslaught by randomizing his throws? Perhaps. But he did commit one of the classic blunders. (Classic blunders: Never get involved in a land war in Asia. Never go up against a Sicilian when death is on the line. And never, ever take a Tiltboy on in a Roshambo match – or let him organize your PowerPoint presentation [but that's another story].)