Part of the problem is that sample sizes tend to be small — maybe 150 or 200 moves per player for an entire tournament. Another problem lies in how computerized chess programs evaluate positions. They are given in increments of one-hundredth of the value of a pawn, the least valuable piece.

“A change of a hundredth of a pawn might change the agreement with the computer,” Dr. Regan said.

The potential payoff for a proof of cheating goes well beyond chess. Jonathan Schaeffer, a professor of computer science at the University of Alberta and the inventor of Chinook, the computer that solved checkers, said that Dr. Regan’s research, and that of others who are also investigating this field, has great potential value.

“What he is doing, what these people are doing, is they are trying to model how people make decisions,” Dr. Schaeffer said.

That could also be of immense value to a big online retailer, like Amazon, that wants to customize its offerings, or for more important uses, like personalizing medical treatment.

Dr. Schaeffer said that these applications had probably occurred to Dr. Regan. “The thing I would say about Ken, although he is using this research in the context of his hobby and passion, he is a big thinker,” he said.

In analyzing the 2006 match, the first thing Dr. Regan tried to do was reproduce Mr. Danailov’s claims, but he did not know how. “Initially, I was just a newbie to computer chess,” he said. “I didn’t even know the right questions to ask.”

He tried to find articles on the subject, but turned up nothing. “It is one of those situations that it is hard to believe that this hasn’t already been covered in the literature,” he said.