By winning the 39th game, Dr Tinsley, who first won the world title in 1955, took a two-point lead, whereupon the final game was dispensed with as irrelevant.
When Chinook's programmers, led by Dr Jonathan Schaeffer of the University of Alberta, Canada, found themselves one down with two to play, they did a little tinkering with their machine to give it at least some chance of saving the match by steering it away from safe drawing lines.
In game 39, however, playing on the stronger side of the feared 'White Doctor' opening (the first three moves in each game are decided by random ballot), the machine, following orders, tried too hard to win and came unstuck. With the computer assessing its own position as hopeless, and Dr Tinsley in full agreement, the programmers resigned the game and the match. There was long applause from the spectators, a mixed bunch of interested draughts players, curious chessplayers and groupies wallowing in the atmosphere of intellectual might.
Then one of the arbiters came on to the stage to explain why the machine had given up. One white king would have wandered down the board, he said, to hold two black pieces, after which it was an easy win with three men against two on the rest of the board. 'I hope that's clear,' he added.
The crowd nodded sagely, some mumbled 'yes, it's clear', and the vast majority continued looking bemused. Perhaps the graphic display, on which it was hard to distinguish the kings from the other men, contributed to the general air of puzzlement, but the whole fortnight-long match had been a convincing demonstration of the incalculable difficulty of the game of draughts.
Go-As-You-Please draughts, without balloted openings, has been effectively dead at a top- class level for many years. Enough variations are known to lead to forced draws, for anyone with a sufficiently good memory to avoid losing.
When one world title match ended with every game drawn, they spiced up the game with the introduction of balloted openings. Dr Tinsley, 65, and Chinook needed to know the 142 balloted variations, all considered playable but ranging from a certain draw to excruciatingly difficult.
The playing schedule of four games a day seemed to favour the computer, especially when a jet- lagged and sleepless Dr Tinsley spent some 14 hours fruitlessly probing the machine's defences on the opening day's play. By the end of the week, he was borrowing sleeping pills from one of his opponent's programmers.
Dr Tinsley won the fifth game by calculating 25 moves ahead, while Chinook could only manage 20, but he lost the eighth through an oversight. For a man who has averaged around one loss every seven years for the past four decades, it was a disaster. Dr Tinsley went behind after game 14, forgetting a piece of analysis that he had discovered and published 30 years ago.
It was the computer, however, that wilted at the crucial stage of the match, overheating during game 18 and having to resign when its operators were unable to repair a fault that had caused it to seize up in mid-game.
By now, Dr Tinsley understood his opponent better and, in game 25, tricked it with a neat inversion of moves in the opening. Distracted from its book of published variations, the machine immediately went wrong. It had a chance to save the game later, but once again needed to see beyond its 20- move horizon.
By now sleeping much better, Dr Tinsley never looked in trouble as he steered the next 15 games to a draw. It was an impressive demonstration of precision, emphasised by the general inability of even the grandmaster draughts players among the spectators to understand many of the games.
Chinook had confirmed its position as second best in the world, with play that would have been called highly creative had it come from a human. With the certainty of exhaustive, brute-force calculation, it frequently demonstrated the playability of moves that humans would have rejected as reckless.
The result of the match, however, proves that one man is still the master of machine at the draughts board. To err is electronic, but Dr Tinsley, in a forgiving mood, has already indicated his willingness to give Chinook a return match next year.