Can a game of Monopoly last forever?

A game of Monopoly ends when all but one player has been driven into bankruptcy. “There is a chance, at any point in time, that any player could fall on a run of bad luck and lose their cash. This probability is small enough that the players' wealth simply grows to infinity,” the researchers wrote in their study.

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MONOPOLY FACTS 52 design errors, but changed its mind. Monopoly made its debut in 1935 and quickly became the game maker's best-selling product. •More than 250 million sets have been sold, played by an estimated 750 million people. There are dozens of versions in 27 languages. •The most expensive Monopoly game, made with real gold houses and silver hotels, sold for $25,000. An all-chocolate version sold for $600. •The total amount of money in a standard Monopoly game is $15,140. There are 22 properties that can be built upon. •The properties in Monopoly are loosely based on streets, places or services in Atlantic City, N.J. But there are errors, such as Marven Gardens misspelled as Marvin Gardens. SOURCE: Hasbro The world record for the longest game of Monopoly is 70 consecutive days, or roughly 1,680 straight hours of passing the Go square without stopping.

For the players, that session probably felt like it would never end.

Anybody who has ever played Monopoly knows the feeling. The game can be interminable, with no victor ever seeming to emerge. That's a real mathematical possibility, Cornell University researchers said in a new study. They calculate that there's a 12 percent probability of a simple, two-player game of Monopoly never concluding. “We mean over an infinite horizon, and not just that the game lasts longer than reasonable players might be willing to play,” said Shane G. Henderson, a Cornell professor and mathematician. Henderson will present a paper on the topic during the annual meeting of the Institute for Operations Research and the Management Sciences, which will start Sunday at the San Diego Convention Center. “There's no way to know if something is really, actually endless,” said Henderson, who wrote the paper with Eric J. Friedman, Thomas Byuen and German Gutierrez Gallardo. Nonetheless, the paper's findings are the result of very real science. The endeavor involved computer simulations, statistical sampling, Markov chains and Brownian motion, the latter two being mathematical formulas that describe random movement. “Surprisingly, there have been few academic studies of the game of Monopoly,” Henderson said. His observation is only partly tongue-in-cheek. Henderson specializes in the study of operations research and information engineering, a diverse and widely used science that tries to characterize and predict human behavior using mathematics, statistics, economics, computer science and psychology. More than 4,000 of these analysts are expected to attend the San Diego conference. They'll discuss topics such as the economy, swine flu, California's wildfires, cardiac care and, of course, the never-ending Monopoly game.

But why study Monopoly?

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“First, it's fun,” Henderson said. “Second, Monopoly is a game of decision-making over a period of time under conditions of uncertainty and competition, which sounds a lot like what businesses face in real life.”

Determining what makes a strong Monopoly strategy could have practical applications.

“You might be able to extrapolate the information to real, complex situations,” Henderson said. “Or at least it might help fill in gaps between what our algorithms say and what people actually do.” To conduct their experiments, the Cornell researchers limited the game to two players who follow a few basic rules. Among them: Buy properties whenever possible. Build houses or hotels whenever possible. Always maintain a modest cash reserve for contingencies. The scientists ultimately arrived upon the 12 percent probability that Monopoly will reach a point “where players continue to accumulate cash indefinitely.” A game of Monopoly ends when all but one player has been driven into bankruptcy. “There is a chance, at any point in time, that any player could fall on a run of bad luck and lose their cash. This probability is small enough that the players' wealth simply grows to infinity,” the researchers wrote in their study. “There is no shortage of cash in the game since the rules of Monopoly state that if the bank ever runs out of money, one can simply ‘print more’ on extra sheets of paper.” Henderson played Monopoly during childhood and still does occasionally with his children. He ranks his game as “not good at all.” In contrast, Richard Marinaccio of Buffalo, N.Y., is very good. Marinaccio won the Monopoly U.S. National Championship in April. He agrees that a no-time-limit game of Monopoly could theoretically go on forever. “This is a trading game. I guess if you were stubborn and didn't make transactions, you could play for a very long time,” Marinaccio said. “But the point is to be aggressive.” Marinaccio will compete this month in the Monopoly World Championship in Las Vegas. He isn't worried about games that never end, or even long ones. In competitive Monopoly, he said, a game never lasts more than 75 minutes.

sandiegouniontribune.com - More than just fun and games - The San Diego Union-Tribune

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