A particularly bizarre footnote to the whole incident is an article written by PHD mathematician and Senior Master Charles Kalme, and published in the November 1975 issue of Chess Life and Review, the longest article that magazine had ever published at the time, (and maybe still is) defending Fischer's match conditions. In this article, Kalme adopted an odd set of suppositions, tried to show a pattern, and shamelessly tossed out data willy-nilly whenever it didn't show what he wanted it to show.

The majority of the article was spent defending the Pure Wins system (despite the fact that FIDE had eventually agreed to it). Kalme believed that there were fixed and unalterable "Draw Expectations" in a chess match. He believed that these expectations were caused, not by the era in which the match was played, or by the playing styles of the two players, or by how close in strength they were. No, he believed that there was a fixed draw expectation that was determined solely by match conditions, and that an examination of the previous 26 Championship matches (at least the ones that he liked), could tell us what those expectations are. In short, he believed that a 10 Wins championship match held in 1975 shouldn't last longer than about 23 games, because that's about how long matches played under the same system in the 19th century lasted.

Kalme's theory was that a Pure Wins match system encouraged aggressive play. Since a person has to get a certain number of wins eventually, there's no reason not to go gunning for them as quickly as possible (he was unable to imagine the strategies employed in the 1984/5 match, obviously). On the other hand, he claimed, a Points match encourages passive play, because whoever is leading will be more predisposed to play for a draw. He claimed that an examination of the data demonstrated this, but his handling of said data was so manipulative as to make it worthless.

Starting with an already small statistical sample, Kalme whittled it down still further. The first to go was the 1927 Match, a Pure Wins match with 74% draws. Kalme couldn't begin to explain why the match format hadn't encouraged aggressive play in this case, so he threw the match out, calling it a statistical anomaly, unlikely to be repeated. (Remember that this was written before the 1978 and 1984/5 matches were played).

The next to go was the 1889 Steinitz-Tchigorin match, a Best of 20 affair that had a mere 1 draw in 17 games. Like 1927, this directly contradicted Kalme's claims, so he made an excuse and threw that match out too, claiming to be unsure about what format it was played under. (You can read Steinitz's own words, elsewhere on this site, attesting to the fact that it was a Best of 20, though this is hardly necessary, since the fact that the lone draw occurred in the final game proves conclusively that the match was not played under a Pure Wins format.

With the remaining data, Kalme discovered that in the late 19th and early 20th century, when Win Requirements were common, there were fewer draws, while in Post-World War II matches with no win requirements, the draw percentage was much higher. One might well point out that there were not only fewer draws in Championship Matches in those days, there were also fewer draws everywhere else, too! But Kalme was firmly convinced that this didn't matter, and that, given the same match rules, Karpov and Korchnoi would be no more likely to draw a game than Steinitz and Tchigorin. (He never actually demonstrated a causal relation, just thought that it stood to reason, which makes the whole argument rather circular) No matter who the players, he thought a 10 Wins match played in 1975 shouldn't have many more draws than a 10 Wins match played in 1875, which means Fischer was right all along!

But the data manipulation didn't stop there. Kalme went on to examine the FIDE World Championship matches, and concluded that they followed one of two patterns: either an early shootout with lots of decisive games, followed by a string of draws, OR an early string of draws with a late shootout of decisive games. To show this, he artificially divided up all FIDE matches into two stages, one of which was a quiet stage, the a decisive one. He was not at all consistent in doing this. When does Stage 2 in a 24 game match begin? You might imagine that it would be Game 13, but not a bit of it. For Kalme, Stage 2 might have begun any time between Game 13 and Game 20, depending on what fit his presuppositions the best. But even fudging the data in this way, there was one match that couldn't be made to fit. The 1961 Botvinnik-Tal match had lots of decisive games all the way through, no matter how you divided it. So, Kalme tossed THIS one out too, making a total of THREE entire matches tossed out for failing to fit the desired pattern.

With his data sample suffering from his own ravages, Kalme wanted to add to it a bit, and he saw a match that was not a World Championship match, but which he loved so much, that he couldn't resist including it, namely the Karpov-Korchnoi Finals match from the 1974 Candidates. Though this match had been an extremely aggressive one, with lots of long, hard-fought games (nearly 50 moves per game, on the average), that didn't matter. What mattered was the results. Despite the hard-fought nature of the games, they produced 19 draws out of 24, largely due to how evenly matched the two players were. But it was Kalme's claim that a "Wins OR Points" match produced even more draws than a Pure Points match, so he brought this one in to prove the point. However, in bringing it in, he ignored the other six 1974 Candidates Matches, that "proved" the exact opposite!

At this point, Kalme's argument was in ruins. He'd begun with an extremely shaky premise, that there were fixed Draw Expectations determined by Match Conditions, and then attempted to prove the point by simply throwing out any data that he didn't happen to care for. And he still hadn't even touched on the point that had actually killed the match! The 9-9 tie clause, remember that? Well, Kalme did too. Eventually. Just before the end of the article, he remembered it, and spluttered a bit about how the Champion's advantage was traditional, and claimed that Fischer's 2-point tie clause was actually less of an advantage than the 1-point clause in the old system. To argue this, he examined two similar situations: a) an 8-8 tie in Fischer's system versus b) an 11½-11½ score in a Best of 24 match. In a), the Challenger must win the next 2 decisive games to win the title, while in b) the Challenger only has to win 1, but it MUST be the very next game. a) is easier than b) said Kalme, so you see, though Fischer had broken his promise to abolish the champion's advantage, he'd actually asked for a smaller one than had existed before. This argument was completely subjective, and a matter of taste, and didn't quite manage to obscure the fact that the Challenger still had to win by 2 points in Fischer's system.

He also claimed that we had to have a 2-point clause, because after a long struggle, the outcome of a single game was "irrelevant" in determining who was the better player. In this, Kalme committed an elementary logical and mathematical blunder, for in claiming, in effect that the relevance of a single game was zero, it would logically follow that any margin of victory however large, would also be meaningless. In other words, one game is meaningless because 1x0=0. But similarly 2x0 also equals zero. So also does 10x0=0, so by Kalme's reasoning, a 10-0 victory would be meaningless in determining who is the better player, since it would be composed of 10 meaningless games. In actual fact, a 1 point margin of victory must have some meaning, in order for a 2 point margin to have more. Perhaps not as much meaning as one might like, but that's a subjective question, not a mathematical one, as Kalme tried to present it as being.

In addition, as Kalme had done so many times in the article already, he ignored inconvenient historical precedent when making his claim. We needed a 2 point margin of victory because only that would show for sure who the better player is, while a 1 point margin does not. But does it really? Botvinnik showed in 1958 and 1961, that it was possible to lose a match by 3 or 4 points, and still come back and beat the same guy a year later. So, even a 10-8 victory in Fischer's system doesn't really prove that the Challenger was better. Maybe we need a 10 Wins match with a 5-5 tie clause, forcing the Challenger to win by 10-4 or better, to be really sure that the better player won. The problem with that proposal is the same as the problem with Fischer's proposal, that it ignores basic fairness in the process. The Champion does not have the same obligation to prove his superiority that the Challenger does, despite getting to call himself "the best". Making the Challenger win by one point when the Champion doesn't have to do the same is bad enough. Any more than that is simply not acceptable to too many people.

Kalme's article was supposed to be continued in the next month's issue, but the plug was pulled, and the article never appeared. The letters column in the March 1976 issue featured a slew of feedback on Kalme's article, much positive, and much negative. Amusingly, most of the people who absolutely loved the article still disagreed with him on the one point that actually mattered: the 9-9 tie clause. But the best rebuttal to the article came from a man who still writes a column in Chess Life to this day; GM Andy Soltis, whose letter is good enough to bear repeating in full:

The logic of [Kalme's] piece folds up when you consider a sentence like "Once the match stands even after a long struggle, the outcome of a single game is irrelevant to determining who is the better player." To buy that you have to conclude that other sporting contests - almost all of whom recognize that ties sometimes occur and that they have to be broken by a margin of one game - are somehow unfair.

Aside from aerobatic leaps in logic, the piece annoyed me because it assumes that playing styles - the ingrained personalities of the players - are just so much plastic decoration to be remolded as often as the match rules are revised. To wit: "We have already seen . . . how this match system virtually forced both Karpov and Korchnoi to play cautiously . . . " It's odd that other players who found themselves under the same match conditions were not "virtually forced" to play cautiously. Anyone who believes that Karpov was playing differently in that match than he has in the past is kidding himself.

One of the few players who actually did change his playing style for a match was Alekhine in 1927. But that had nothing to do with match rules. The conditions were six-wins, draws not counting. This insures fighting chess, Kalme tells us. But Alekhine played the most conservative chess of his life in 1927 against Capablanca because the Russian's natural enterprising style had failed miserably in previous meetings. That is why there were 25 draws in 34 games.

And aside from the logic and the assumptions, the most disturbing note to the Kalme piece is the implication that we, the chess public, didn't really try to understand Bobby - that what Bobby wanted was obviously true and fair but we intentionally closed our minds to it. But just how were we to understand the "9-9" issue, the single point of controversy that cost us a world championship and gravely affected the growth of chess in this country? Certainly Bobby didn't try to explain it to us. His communications with the outside world on "9-9" have been confined largely to his telegrams to the FIDE meetings at Helsinki and Nice.

And what about Bobby's representatives? Fred Cramer mentioned "9-9" in his lengthy reports on Helsinki (Jan. 1974 CL&R) and Nice (Oct. 1974). There was no explanation whatsoever in either report of what the controversy was about, or how strongly the champion felt about the matter or of what the rest of the world was saying. Cramer confined his Nice report - when it had become clear to a very few insiders that "9-9" was the key sticking point - to the comment in a footnote that the issue was not debated at Nice. Period. So much for Fischer's explanation of the issue to the 60,000 plus members of the USCF.

Now, six months after the April 1 deadline, 15 months after Nice, nearly two years since Helsinki, we are given a statistics lesson and told that we misunderstood the whole matter.

Andy Soltis
New York, N.Y.