I believe that under today's FIDE Rules, Fischer would have won, since the forfeit win would have been counted as a draw against himself. On the other hand, if you count the forfeit win against Kemper as if it had actually been played, Bisguier would have won.

It seems that the rules weren't clear at the time, and they made something up on the spot to handle it. Bisguier appealed, but it was rejected. It seems like really bad form to reverse a decision 2 days later though (Chess Life doesn't mention that any reversal had happened at all, Chess Review does), so I don't know why they didn't just declare co-Champions in that case, especially if the rules were unclear.

These days they do it all the time. In 2004 and 2007, we had a full seven co-US Open Champions (and six in 2009), which seems like going too far the other way.

It is axiomatic that no tie-breaking system is completely satisfactory; yet the United States Chess Federation seems to insist that there be one player on whom they can pin the label of champion. So be it, though the current championship really seemed to pinpoint the weaknesses of the system now in use. When Al Horowitz asked me to write the story of the Open Championship I begged off at first since I was quite bitter about the USCF decision, and I felt anything I wrote on the subject would sound cry-baby and sour grapes. Still, if there's a chance that the situation be recognized and remedied in the future because of this article, then I feel that I should risk the latter appellations. I would like to emphasize, however, that anything I might say or point out should detract not one whit from the great success of Bobby Fischer. He played splendidly, achieved a wonderful score, and much kudos would be due him even if he were only a co-champion or, heaven forbid, even if he had taken second place.

To start with, in the first round, I played Don Richardson, a young Canadian player of promise who extended me to an adjournment and seventy-odd moves of difficult play (my only adjournment of the tourney) before I garnered the point. Richardson eventually achieved a respectable score of 7-5 in the tournament. Bobby was given a BYE in the first round and scored without having to make a move. The winner of the championship title should at least play a full schedule.

Under the existing tie-breaking systems, I would win by at least 4.5 points (Solkoff) or 5.25 points (Sonnenborn) – even after Fischer was given 4 points as an adjustment for two of his players who withdrew without completing their schedules. Under the Median tie-breaking system in use by the USCF, the scores of all the opponents of the players who come out in a tie are totaled except that (evidently for purposes of averaging) the two opponents who scored the most points are thrown out and not computed. Under this particular system, Fischer won by one half point. The computations are also not sachems of the USCF. Theoretically, at least, the two opponents who scored highest and the two who scored lowest are to be disregarded in the computations (why two and not one is also not completely clear – again if only the one highest and one lowest were disregarded, I would have defended my title successfully). Cancelling the scores of the two top opponents yielded neither Fischer nor myslf an advantage since we both played Donald Byrne and each other (the top two opponents); but dropping the two lowest rated players cost me the tournament. First of all, Fischer's first opponent, BYE, who naturally could score no points, was disregarded. His next lowest opponent was J. Rinaldo who scored 4.5 points. Since Rinaldo left 5 rounds before the finish, however, it was assumed that he would have averaged one half point a game and hence Fischer was given 7 median points for Rinaldo. After Rinaldo, Fischer's next lowest scorijng opponent was C. Witte, who scored 5 points. Unfortunately, he too decided to leave two rounds before the end, and so his 5 points were adjusted to 6 points. This "adjustment" left E. Stephans who had scored 5.5 points as his lowest scoring opponent, and so his score was disregarded.My lowest scoring opponents were T. Ellison and Dr. Brunoo Schmidt who scored 5 and 6 points respectively. So I lost 5 points as compared to Bobby by dropping Ellison as against BYE and one half point by dropping Schmidt as against Stepans. All this, after Rinaldo's 4.5 points were adjusted to 7, and Witte's 5 points adjusted to 6. Presumably, these players who withdrew were despondent about their play and might not have scored so well. When I beat Ken Smith in the tenth round, he had been playing well and had a score of 7-3. The loss affected him adversely, and he did not play up to his full strength and lost his last two games. Had I managed to persuade him to quit the tournament even just before the last round, I would have been granted the half-point necessary to enable me to retain my 1956 title of Open Champion. Too bad he wasn't a quitter. The cross-table totals for Fischer and myself are appended for those of you who like to fool around with figures and might like to check my observations. Incidentally, I would welcome comments from anyone who cares to write – even it is just to tell me I'm a sorehead – I certainly have to admit to being prejudiced in my own favor.

Most importantly, a player's adjusted score for an unplayed game (forfeit, bye, withdraw, etc.) was 1/2 point. This was specifically spelled out in the case of Harry Borochow, who scored 2.5 points in four games before withdrawing. His adjusted score was 6.5 points: 2.5 in played games plus 4.0 for eight unplayed games.

Hence, Kemper's adjusted score would have been 6.0 points (1/2 point for each of 12 game). The merits of this can be argued, but I'm sure that should have been the ruling under the then-current USCF policies.

Granting that, Fischer beat Bisguier on all three tiebreaks:

Fischer 176 Kemper 1.0 0.0 6.0 6.00
103 Stepans 1.0 5.5 5.5 5.50
28 Pitschak 0.5 7.5 7.5 7.5 3.75
132 Rinaldo 1.0 4.5 7.0 7.0 7.00
2 Bisguier 0.5 10.0 10.0 5.00
113 Witte 1.0 5.0 6.0 6.0 6.00
54 Garais 1.0 6.5 6.5 6.5 6.50
5 Mednis 1.0 9.0 9.0 9.0 9.00
3 D Byrne 1.0 9.5 9.5 9.50
4 R Byrne 0.5 9.0 9.0 9.0 4.50
14 Addison 1.0 8.0 8.0 8.0 8.00
7 Shipman 0.5 9.0 9.0 9.0 4.50

10.0 62.0 93.0 75.25

Bisguier 42 Richardson 1.0 7.0 7.0 7.0 7.00
114 Ellison 1.0 5.0 5.0 5.00
74 Schmidt 1.0 6.0 6.0 6.00
10 Brandts 0.5 8.5 8.5 8.5 4.25
1 Fischer 0.5 10.0 10.0 5.00
14 Addison 0.0 8.0 8.0 8.0 0.00
41 Gross 1.0 7.0 7.0 7.0 7.00
18 Hudson 1.0 8.0 8.0 8.0 8.00
32 Marchand 1.0 7.5 7.5 7.5 7.50
36 Smith 1.0 7.0 7.0 7.0 7.00
11 Saidy 1.0 8.5 8.5 8.5 8.50
3 D Byrne 1.0 9.5 9.5 9.50

10.0 61.5 92.0 74.75

Frank Brady's (extremely unreliable) book Endgame claims (sourcelessly) that Fischer took the draw for financial reasons. It quotes Bisguier as saying of this that "Evidently, his mature judgment is not solely confined to the chessboard." I believe that that Bisguier comment is actually something he said years later, about a completely different subject, but I don't remember where it's from now, and Brady doesn't source that either. (In fact, digression here, for a book with 44 pages of footnotes, I've only had about a 30% success rate in finding sources for things I've looked up, and often times they've been nonsensical sources, like "Unidentified Newspaper".)

<"Rather surprisingly, Bobby acquiesced to a very early draw against Shipman in the last round, thus depriving himself the opportunity to finish in undisputed possession of first place since then Donald Byrne or myself had to at least tie with him depending on the result of our own encounter.">

(Donald Byrne and Fischer had 9.5 coming into the last round, Bisguier 9.0. Therefore, a draw did not ensure first place for Fischer; Byrne could have passed him with a win. -- PB)

<"When queried as to why he had taken the draw (there was still ample opportunity for play in the position), he replied he felt he had much more to lose than to gain by this decision.">

(Judging by the context, "this decision" refers to playing for a win. -- PB)

<"He felt that, with the White pieces, I would either draw or win against Donald Byrne and so assure him of at least a tie for first place and $750.00. Had he lost, he might only tie for second, third and fourth prizes and $330.00. Evidently, his mature judgment is not solely confined to the chessboard.">

(That last sentence is the Brady quote. -- PB)

<"Actually, had Donald Byrne even drawn our game, he would have won the title by about as close a tie-breaking margin as Fischer did in winning it from me.">

I wish that Bisguier were a clearer writer, or that <Chess Review> had better editors! I think Bisguier is saying that Byrne would have beaten Fischer on tiebreaks had they tied, but I believe Fischer would have prevailed by 1 point on the third tiebreak. Here are Byrne's totals:

1 Sprague (W) 6.5*
2 Schwartz (W) 6.0*
3 O'Keefe (W) 5.5
4 Wanetick (W) 8.5
5 Fuster (W) 7.0
6 Berliner (D) 8.0
7 Burger (W) 7.0*
8 Addison (W) 8.0
9 Fischer (L) 10.0
10 Popovych (W) 8.0
11 R Byrne (W) 9.0
12 Bisguier (D) 9.5

The asterisks (*) indicate those confounded adjusted scores, which I have a feeling accounted for the whole Bisguier fiasco in the first place. The directors may have neglected to add them in before Bisguier had crossed the border into New York.

At any rate, Fischer's tiebreaks were:
Median 62.0
Solkoff 93.0
Sonnenborg-Berger 75.25

Byrne:
Median 62.0
Solkoff 93.0
Sonnenborg-Berger 74.25

The Byrne-Bisguier game isn't in the database, so it's hard to gauge. Perhaps at the time Fischer agreed to the draw, he had evaluated that Byrne's chances of winning were nil (he must have had some idea of how that game was going). There's no way to tell without seeing the game.

<"He felt that, with the White pieces, I would either draw or win against Donald Byrne and so assure him of at least a tie for first place and $750.00. Had he lost, he might only tie for second, third and fourth prizes and $330.00. Evidently, his mature judgment is not solely confined to the chessboard.">

Okay, then Brady got that right.

<I wish that Bisguier were a clearer writer, or that <Chess Review> had better editors! I think Bisguier is saying that Byrne would have beaten Fischer on tiebreaks had they tied,>

Considering how difficult the tiebreak was, I don't think anyone could know with confidence who would have won on tiebreak before the last round was played. You don't know the final scores of any of your opponents. Bisguier might have thought he knew, but if he did, he was wrong. Or maybe he was only talking in hindsight.

<So Bobby had it in the bag all along. Actually, part of the reason he took the early might have been that he hadn't yet developed the mature confidence of his later years.>

Bisguier, Arthur - Byrne, Donald [B77]
USA op (12), 1957

1.e4 c5 2.Nf3 d6 3.d4 cxd4 4.Nxd4 Nf6 5.Nc3 g6 6.f3 Bg7 7.Be3 Nc6 8.Qd2 0-0 9.Bc4 Nd7 10.Nxc6 bxc6 11.Bh6 Bxh6 12.Qxh6 e6 13.h4 Qf6 14.0-0-0 Nb6 15.Be2 d5 16.h5 Qg7 17.Qe3 Bb7 18.f4 Rad8 19.e5 f6 20.hxg6 hxg6 21.Rh4 f5 22.Rdh1 Rf7 23.Qg3 Nd7 24.Rh8+ Qxh8 25.Rxh8+ Kxh8 26.Qh4+ 1-0

<"Considering how difficult the tiebreak was, I don't think anyone could know with confidence who would have won on tiebreak before the last round was played. You don't know the final scores of any of your opponents. Bisguier might have thought he knew, but if he did, he was wrong. Or maybe he was only talking in hindsight.">

I would guess he was talking in hindsight.

He did take a quick draw at the end of the US Championship, but there's a slight difference there. In that case, Fischer might still have ended up clear first (and did). In this case, the draw meant no chance of clear first, and a possible loss on tiebreak. A tie for first in the US Championship would probably have meant a Fischer-Reshevsky playoff match, which Fischer might have welcomed at that time.