Beginning in 1968, Levy made a famous bet with four Artificial Intelligence (AI) luminaries, ultimately totaling 1,250 British pounds, that no computer program would win a chess match against him within ten years. In 1973, he wrote:
Clearly, I shall win my ... bet in 1978, and I would still win if the period were to be extended for another ten years. Prompted by the lack of conceptual progress over more than two decades, I am tempted to speculate that a computer program will not gain the title of International Master before the turn of the century and that the idea of an electronic world champion belongs only in the pages of a science fiction book.
Until 1977, no computer program was good enough to pose a serious threat to Levy. In April 1977, he played a two-game match against Chess 4.5, a program written by David Slate and Larry Atkin of Northwestern University that had done well in human events, including winning the 1977 Minnesota Open. After Levy won the first game, the second was not played since Levy could not possibly lose the match. On 17 December, Levy played a two-game match against KAISSA; once again Levy won the first game and the match was terminated. In August 1978, Levy played a two-game match against MacHack; this time both games were played, Levy winning 2-0.
The final match necessary for Levy to win the bet also was played in late August 1978, this time against Chess 4.7, the successor to Chess 4.5. In 1978 Levy won the bet, defeating the Chess 4.7 in a six-game match by a score of 4.5-1.5. The computer scored a draw in game two (after getting a completely winning position but being outplayed by Levy in the endgame) and a win in game four, when Levy essayed the very sharp, dubious Latvian Gambit. Levy wrote, "I had proved that my 1968 assessment had been correct, but on the other hand my opponent in this match was very, very much stronger than I had thought possible when I started the bet." He observed that, "Now nothing would surprise me (very much)."
In order to further stimulate the growth of computer chess, Levy offered $1,000 to the authors of the first chess program to defeat him in a four- or six-game match;
Omni magazine added $4,000 to this, for a total of $5,000. In 1989, the authors of the Deep Thought program won the prize when their program beat Levy.
In 1996, Popular Science asked Levy about Garry Kasparov's impending match against Deep Blue. Levy confidently stated that "...Kasparov can take the match 6 to 0 if he wants to. 'I'm positive, I'd stake my life on it.'" In fact, Kasparov lost the first game, and won the match by a score of only 4-2. The following year, he lost their historic rematch 2.5-3.5.