Hill needs only one point to clinch the championship, whereas his Williams- Renault team-mate, the Canadian Jacques Villeneuve, must win, with Hill out of the top six, if he is to steal the crown.
"If I were Damon and could take a lead and control the race, that's what I would do," Stewart added. "But if I realised I couldn't do that, then I would be playing a pretty damned canny game. I wouldn't care if I was fourth or fifth, I'd just be out to win that championship."
Stewart was the victor of 27 grands prix and world champion three times, but such was his superiority that in 1969, '71 and '73 he did not need to go to a final-race showdown. But he does understand what Jacques Villeneuve will be feeling, for he was one of the three contenders in 1968 when the Mexican Grand Prix decided the outcome. Graham Hill nursed a three-point advantage over Stewart, who himself was three ahead of the reigning champion, Denny Hulme. Any one of them could have been champion. Stewart and Hulme retired, and Hill won both the race and the championship.
"I saw myself as the long-shot with Denny, for whom I had the highest respect, as the rank outsider," Stewart said. "I thought I could do it, and I had won some excellent races, at Zandvoort and the Nurburgring. And I had just won at Watkins Glen, where I suddenly learned how to control a Formula One race. I knew that Graham's Lotus 49 was amazing, tough to beat. But I knew I had a decent chance. Graham and I passed each other several times, until my fuel pump went wrong.
"I walked away not feeling dejected in any way, because I had always thought I was the outsider. It was my first year of being in contention. I was in a psychological position rather like Jacques'. And I tell you this, it was right that Graham won that championship, and I gained enormously by being his understudy for that championship year.
"I think the greatest degree of pressure unquestionably is on Damon, because I think he must obviously be sensitive to having lost two world championships in the last two years. And now he finds himself having come from a very dominant position, to an extremely vulnerable, albeit advantaged, position. I suppose there are a lot of things going through his head.
"Jacques has very little to lose. Nobody ever expected him to have the success that he has enjoyed this year, I don't think even Jacques himself. He has shown that he is definitely capable of taking the best grand prix car in the world and making it work, and his adjustment to F1 is probably in excess of anyone else who has come into the sport. So if he were to win the world championship this year, it could almost be too good to be true and, I suggest, would not necessarily be the very best thing for his long-term career.
"Now a lot of people would say `don't be ridiculous', but I say that because he hasn't yet served the apprenticeship. If he didn't win the world championship this year, he would be the understudy. Everybody would be impressed by what he had done and he would have to sing for his supper a little bit. That would be good for him.
"As world champion you have to do things. And you should do them, not only for yourself and your future, but for the sport. Damon would do them very well. He would be so thrilled to have won a world championship, as his father had done, and he would carry it off well, I think. And it would give him a tremendous feeling of satisfaction and achievement.
"I see all of those things, so therefore I say in a way that Damon has got to be carrying more weight on his shoulders than Jacques is."
Stewart thinks it will have been beneficial to Hill to have decided his future by signing for TWR Arrows. "I think that being out of his mind will have helped. But I'm sure he doesn't feel that he can win the world championship next year, whereas Jacques could. Jacques can say `well now I know something I never knew before. In fact, I know 16 things I never knew before'! Whereas Damon is saying this could be the last hurrah.
"And there is also the sneaking concern that the suppliers, the sponsors and the team itself must all stand to profit considerably more from Jacques Villeneuve being world champion than Damon Hill, because they would lose Damon immediately. We are not talking simply about morals, and we all should have them at the highest level, but we are talking about enormous commercial interests and loyalties.
"Maybe I'm being cynical in coming out and saying that, maybe nobody else is saying it, I don't know. But I'm saying it's there, whether you like it or not. It is a serious consideration. And, without taking anything away from Jacques, it would be an even greater rosette for Williams if he won the championship. You know, this guy comes in and wins first time, this car must be unbelievable!"
Stewart added: "So Damon can only get into that car and do the best job that he can do. He can't be looking over his shoulder all the time about anything. He can't make mistakes. He's just got to get out there and go for it."