Eventually, though, prizes began to be replaced by grants that awarded money upfront. Some of this was for good reason. As science became more advanced, scientists often needed to buy expensive equipment and hire a staff before having any chance of making a discovery.

But grants also became popular for a less worthy reason: they made life easier for the government bureaucrats who oversaw them and for the scientists who received them. Robin Hanson, an economist at George Mason University who has studied the history of prizes, points out that they create a lot of uncertainty — about who will receive money and when a government will have to pay it. Grants, on the other hand, allow a patron (and the scientists advising that patron) to choose who gets the money. “Bureaucracies like a steady flow of money, not uncertainty,” said Mr. Hanson, who worked as a physicist at NASA before becoming an economist. “But prizes are often more effective if what you want is scientific progress.”

In fact, when Netflix announced its prize in October, Mr. Hastings said he didn’t necessarily expect contestants to make a lot of quick progress. Computer scientists say that Cinematch, along with Amazon’s recommendation system, was already one of the most sophisticated. “We thought we built the best darn thing ever,” Mr. Hastings said.

But Mr. Hastings underestimated the power of an open competition. Within days, many of the top people in a field known as machine learning were downloading the 100 million movie ratings Netflix had made public. The experts have since been locked in a Darwinian competition to build a better Cinematch, with the latest results posted on a leader board at Netflix’s Web site.

Last week, I called Geoffrey Hinton, a professor of computer science at the University of Toronto whose team had been in first place when I last checked. But by the time I reached him, his team had been bumped down to second by a Hungarian team.

(The contestants have also turned up some good trivia about movie preferences. Benji Smith of Salt Lake City deserves credit for the “Oz”-“Lambs” connection.)

To claim the million-dollar prize, a team has to build a system that is at least 10 percent better than Cinematch at predicting how many stars someone would give a movie. There are a small number of people, for instance, who love “The Wizard of Oz” but can’t stomach “Silence of the Lambs.” Perhaps it is possible to identify them based on their attitude toward an eclectic group of other movies — but only an advanced algorithm can find this pattern.