Fritz 6 versus Steve Ham

White: Fritz 6

1. e4, c5 2. Nf3, d6 3. Bb5+, Bd7

The move Fritz 6 played presents me with a problem that higher rated players don't like to experience. Namely, how much risk should be accepted in trying to win this game?

I am expected to win this game, even with Black, due to that fact that I'm the human (versus a machine in correspondence chess) and have a very high rating. However, the standard options for Black at this juncture are 3… Bd7, which leads to easy equality but minimal winning chances for Black due to simplification caused by exchanges, and 3… Nc6 and 3… Nd7 which are sharper but "theoretical fashion" questions their objective soundness. This is one of the reasons that higher rated players prefer only playing against other highly rated players. Then, in good conscience, one could play 3… Bd7 and later accept a draw as Black versus the high rated opponent.

I looked at 3… Nc6 and 3… Nd7 and could find nothing tangibly wrong with the lines leading from them. However, I don't think my style of play (technical, positional, read "dull") is well mated with those lines. My philosophy is to always play what I believe to be objectively best. If I still have options of similar value, then I subjectively select the path that most suits my style of play and understanding. Thus I rejected 3… Nc6 because it can lead to Ruy Lopez type positions, since Black usually follows with … e5. I don't have a "feel" for those positions because I don't play either side of the Ruy Lopez. 3… Nd7 is the sharpest line, thus the one to be considered if the risk/return ratio is acceptable to you. Still, it seems Black has to suffer though some convoluted and ugly pawn structures in order to generate compensation with piece activity. The sane course for me is to play 3… Bd7 and try to demonstrate greater technical skill than my silicon opponent, via grinding out a positional superiority in the middle game and end game. Let's see if I can do it.

4. Bxd7+, Qxd7 5. c4, Nc6 6. Nc3, g6

My last move transposes away from the recently completed Kasparov-Rest of the World, corr. 1999 game. We all saw how drawish those lines were. In fact, White never seemed to feel any pressure of loss. Kasparov's only problem was finding ways to win, given the drawish positions. I will try to find imbalances to exploit elsewhere.

7. d4, cxd4 8. Nxd4, Nf6

We now enter positions similar to the Maroczy Bind versus the Accelerated Dragon Sicilian. However, White's bind is now less effective since the light squared Bishops have been exchanged. Black therefore has plenty of freedom for his pieces.

9. O-O, Bg7 10. Nde2, …

Fritz 6 just won't cooperate with my attempts to create tension.

10… Qe6

In the aforementioned Kasparov game, this dynamic move was widely accepted as providing the greatest chances for exploiting imbalances in the position. Since this move is also new, I expected Fritz 6 to be out of its pre-programmed opening book. But I was wrong! This just goes to show how current the opening theory is in Fritz 6 (English Version). Very impressive work by ChessBase. The alternative is 10… O-O when most sources prefer White's position. I think Black can struggle to equality after 10… O-O but his winning chances are objectively very low.

11. Nd5, Qxe4

This is the point of Black's previous move. Black offers his undeveloped Queen's Rook in exchange for White's most active piece, the Knight on d5 and White's two center pawns. White will also force a Black concession in that Black must abandon castling and must accept doubled pawns on the b file. If Black instead elects to keep his Rook by preventing the fork, then 11… Rc8?! 12 f3, O-O 13 Be3 gives White an edge while Black's Queen is poorly positioned.

12. Nc7+, Kd7 13. Nxa8, Qxc4 14. Nb6+, axb6

Finally Fritz 6 is out of its opening book and on its own for the first

15. Nc3, …

Fritz 6 passed its first big test by finding Kasparov's move. The alternatives are clearly inferior. For example 15 Be3 (15 Nf4?, Ra8 gives Black an edge), Nd5 gives Black active pieces and at least equality. Instead 15 b3, Qd5 16 Bb2, Qxd1 17 Rfxd1, Rg8 and the endgame offers easy equality.

15… , b5!?

This is the first deviation from the game Kasparov-Rest of the World, corr. 1999. Black has 6 options here, but only three of them are acceptable. The move played in the game was 15… Ra8 which seems to hold equality. Also 15… Rd8 equalizes too, but lacks the dynamic tension I seek. The text move was discarded by the Rest of the World largely for being too sharp (initially it was thought unsound). However, the text move indeed seems to be the sharpest of the lines and the one that most appeals to my style in that it grabs space on the Queenside and prevents an immediate 16 Na4. Black thus defers moving his Rook until the best location is determined.

16. Bg5, …

Fritz 6 found this strong move after 9 hours and 38 minutes of calculation. It develops an unmoved piece so that it, in conjunction with a subsequent Re1, X-rays the delicate e7-square. Also, by vacating the c1-square, White can now occupy it with his Rook and thus threaten Black's Queen.

Irina Krush felt 16 Re1 was the most testing line, thus causing her to drop 15…b5 in favor of her 15…Ra8 in the game against Kasparov. She examined 16…b4 17 Na4, Qb5 18 a3, Rd8 19 axb4 and only subsequently found that 19…Ke8!? gives "Black a very comfortable game". Another line was 16 a4, b4 17 Nb5 when Irina liked 17…Nd5=, giving that move the ! diacritical mark. Instead I favor 18 Re1! (not considered by Irina),Rd8 19 Rb1, e6 (19…Ke8??20 Qxd5, Qxd5 21 Nc7+ wins) 20 Bg5 +. Therefore I planned to play instead 17…Ne4! 18 Re1, Rd8 19 Re2, Ke8 20 Be3, Nc5 21 Rc1, Qb3 22 Qxb3, Nxb3 23 Rd1, Kf8 (planning …Ra8) when Black has dynamic equality.

As a subsequent note, the rapid transit game, Rublevsky-van Wely, Frankfurt Masters 2000 saw 16 Be3, Ra8 17 Rc1, Ke8 18 a3, b4 19 b3, Qh4? 20 Nb5, Kd7?! (20…Kf8 21 Rc4, Qh5 22 Qxh5, Nxh5 23 a4 gives White and edge) and now White missed 21 Rc4 with a clear advantage. Instead, 19…Qa6 20 axb4, Nxb4 gives Black easy equality.

16… , Ne4

My text move encourages the exchange of White's only developed piece and uncovers Black's strong Bishop on g7. Another attractive line was 16… h6 17 Be3, Ra8 18 Rc1, Ke8 19 b3, Qh4. Although Black has equalized, he has potentially exploitable pawn weaknesses on b5 and h6. Black had some inferior options in 16… Rd8 (16… Ra8? 17 Re1, Qg4 18 Qd2, Qf5 19 a3, h5 [19… Ke8?? 20 Bxf5, Bxf6 21 Qxd6 wins] 20 Rac1 +) 17 Re1, Ke8 18 Rc1, Kf8 19 Qf3!?, d5 20 b3, Qc5 21 Qe2 when White has at least an edge.

17. Nxe4, …

17… , Qxe4 18. a4, …

Fritz 6 calculated 11 hours and 45 minutes to a depth of 16/44 ply and assessed the position as 0.09 pawns in my favor. White correctly forces Black to decide the future of his lead b pawn. Opening the a-file allows White's Rooks to penetrate Black's flank. The natural but erroneous alternative was 18 Re1?!, Qf5 19 Qd2 (19 Be3, Bxb2 20 Rb1, Bc3 gives Black an edge), h6! (19… Ra8 20 Rad1 [20 Bh6 is unclear], Be5=)20 Bf4, d5 (20 … Qf6!? may be strong) 21 Rac1, d4 when it seems Fritz and I found this line independently. Fritz said Black is better by 0.22 pawns and my notes show an edge for Black. Hence Fritz's ability to analyze technical positions well is quite impressive.

18… , b4

Related lines can transpose,

19. Re1, …

Fritz 6 calculated for 21 hours and 25 minutes to a search depth of 17/44 ply. It assessed the position as 0.28 pawns in my favor, an improvement over the 0.34 pawns assessment after the first 8 hours of calculations. The alternative was 19 Rb1, Ra8 (Fritz considered only 19… d5 20 Re1, Qf5 21 Be3?! [again I'd prefer 21 Qd2 here], e6 22 Qb3, Rd8 23 Rbc1, h6 which it assessed as 0.37 pawns better for Black) 20 b3, Ra5 (20… Qf5!?) 21 Be3 (21 Re1, Qd4 favors Black with an edge), Rd5 when although the position is objectively unclear, subjectively I'd favor Black's chances in the endgame.

19… , Qf5

I had a difficult choice to make. Picture this position with Queens removed; Black has the advantage and can target White's b and a-pawns. A similar motif was discussed in my notes to White's 17th move. Therefore consideration had to be given to 19… Qd4 20 Qf3 (obviously White should not agree to the Queen exchange), f6 21 Bc1, f5 22 Rb1, Be5 23 Be3, Qe4 24 Qd1, Ra8 25 b3, Ke8 26 Rc1, Ra5 27 Rc2, Kf7 28 f3, Qh4 29 g3, Qf6 when the position is sharpened and unclear. Clearly, this line is far from forced and so White had numerous possibilities that needed to be considered because the position is so sharp. Therefore, I chose the text move since the strategy supporting it is simpler and involves less calculation… Black strives to activate his Rook. Black will likely play to a8-a5, but given the opportunity may instead play … Rd8, … Ke8-f8 and then push the central pawns. Did I avoid the complex line that required deep calculations because my opponent is a calculating machine? No, my promise at the start of these matches was to play as if blind to the fact that my opponents are chess engines. Hence this move would have been my choice against a master-level human opponent. I believe in trying to always play the best moves/lines, regardless of the risk. But when presented with equivalent choices, I then believe one should select the choice that most suits one's strengths. Personally, I've always felt more comfortable with strategic planning than with intricate tactics.

20. Qd2, …

The text move is the only one worth considering, in that it activates the Queen and connects White's Rooks while also protecting the vulnerable b-pawn. Fritz 6, during its 10 hour and 30 minute calculation period, considered the two primary alternatives to be 20 Bc1 and 20 Qc1, correctly assessing Black to have a large advantage. Fritz assesses the present position as 0.37 pawns better for Black after searching to a depth of 16/43 ply.

20… , Ra8

Black had two plans to consider. Plan 1: immediate Rook activation with active pieces in a middlegame scenario, or Plan 2: attempt piece exchanges followed by the advance of the central pawns in an endgame scenario. In principle, the second plan fits well with my previous commentary. However, when developing long-range strategy, one should always support that plan with concrete analysis. This analysis convinced me that Plan 1 was the most effective and may actually bestow me with an advantage, due to White's pawn weaknesses on a4 and b2. This choice shows that one should not be totally locked into a plan and thus be unwilling to change plans as the battle develops. Just as in the stock market, one should not attach any emotional or sentimental attachments to our choices. One should instead be willing opportunists, keeping an open eye for discarding one choice for a better one when events unfold.

Plan 2's analytical summary is as follows: 20… h6!? (Black creates a target to bait White into piece exchanges that also cost White tempi, since his pieces will be drawn away from the central action. The immediate 20… d5?! fails to cost White these tempi.) 21 Bf4, d5 (21… Qf6 22 Rb1, Qd4 23 Qc1, b3 24 Bd2 [24 a5!?], Qxa4 25 Ra1 [25 Bc3!?], Qb5 26 Bc3, Bxc3 27 Qxc3, e5 is unclear) 22 a5 (22 Rac1, d4 is unclear), Ra8 23 Bxh6, Bxh6 24 Qxh6, Rxa5 25 Rxa5 (25 Rad1?!, d4 26 Qe3, e5 27 Qe2, Ke7 28 f3, Kf8 29 Qc4, Qd7 gives Black an edge), Nxa5 26 Qe3, Nc6 and Black plans … d4 with an unclear position.

21. Be3, …

Very well played! Fritz 6 has impressed me to date with a generally fine "understanding" of technical positions. Of course, this has been accomplished with very long "thinking" times on an extremely fast computer to reach a very deep search, but this amazes me nonetheless. Fritz 6 calculated for 16 hours and 40 minutes to a depth of 16/41 ply and assesses the position as 0.47 pawns in my favor. This pleases me too since Fritz 6 is gradually acknowledging that Black stands better.

The move chosen is the best of the candidate moves available. White voluntarily blocks his Rook's scope on the e-file in order to create possibilities or repositioning this Bishop on b6 or c5. The weaker alternative was 21 Bh6?! (White wishes to exchange off Black's superior Bishop), Bf6 (Black threatens to trap White's Bishop with … g5) 22 Be3, Ke8 (Black removes his King from the center to prepare the advance of his central pawns) 23 Re1, Ra5 24 Bb6, Rd5 25 Qe2, Re5 26 Qd1, Bg5 which gives Black an edge. White could try some tactics with 23 Bh6?!, Ra5 (23… g5? 24 Qxd6, Qg6 25 Rac1, Rd8 26 Qc7, Qxh6 27 Qxb7, Nd4 is unclear) 24 Rac1, Rxa4 25 Rc6 (25 Qxd6?, Be5 26 Qd2, Ra2 27 Ra1 [27 Rb1, Bc3 28 Qe2, Bxe1 29 Qxe1, g5 wins for Black], Bc3 28 Bxa2, Bxd2 29 Bxd2, Qc2 30 Bc1, Ne5 31 Bg5, f6 wins for Black), bxc6 26 Qxd6, Be5 27 Qxc6+, Qd7 28 Qc2, Ra5 gives Black a large advantage.

21… , Ke8

Black removes the King from behind the central pawns in order to prepare for their eventual advancement, the ultimate destination of the King being f8. The present position offers White some cheap shots based upon threats of Qxd6, so Black must calculate carefully. However, the alternatives were not attractive. For example, 21… Ra5 (21… d5? 22 Bc5 +) 22 Bb6, Rd5 23 Qc1 gives Black some initiative, but I was unable to find anything concrete after an hour of searching. So I wrote that position off mentally as unclear and chose the text move, which seems to retain Black's edge.

22. h3, …

This move was a bit of a surprise, although I didn't know what to expect. Fritz 6 calculated for 9 hours and 30 minutes to a depth of 16/16 ply and assessed the position as 0.37 pawns in my favor. I would have probably chosen this move at some point myself to keep Black's Queen off g4 (where it lands in certain variations) and to avoid a back-rank mate. As such it's a fine waiting move. Instead, White gets into trouble in more forcing lines such as: 22 Bh6 (22 Bb6, Kf8 23 f3, Rd5 gives Black an edge), Bd4 (22… Bf6 23 Re3 [23 Qxd6?, Bxb2 24 Rad1, Be5 gives Black a large advantage], Be5 24 Rf3, Qh5 25 Rh3, Qg4 when the position is unclear but subjectively I favor Black) 23 h3, Ra5 (the game position can transpose into this line with 23 Bh6, Bd4) 24 Be3, Rd5 (24… Be5!?) 25 Bxd4, Rxd4 26 Qh6, g5 (26… Qf6!?, 26… Qh5!?) 27 Qg7, Rd2 28 Rf1, Nd4 when Black has an edge.

It should now be announced that Fritz 6 has been upgraded by ChessBase to Fritz 6a, a "new and improved" chess engine that is more powerful that Fritz 6. Hence, the remainder of this game will be played by Fritz 6a.

22… , Ra5 23. Bb6, …

It is interesting to note that Fritz 6a agrees with my comments to White's 21st move, namely that White's Bishop is best positioned along this diagonal. For example, I calculated that 23 Bh6, Rd5 (23… Bd4 also favors Black, while 23… Bf6 [planning to trap White's Bishop with … g5] is unclear) gives Black a clear advantage. White can instead leave the Bishop momentarily parked with 23 Re2, but then 23… Rd5 (23… Kf8!? 24 Bh6 [Fritz 6a considered only a line beginning with 24 Qd1. This makes little sense to me.], Rd5 25 Bxg7, Kxg7 retains Black's edge) 24 Qc1, Rd3 25 Qc4, Qd5 26 Qc2, Kf8 27 Rae1, b3 when Black is better.

Fritz 6a calculated for 8 hours and 30 minutes to a depth of 17/43 ply. However, the discomforting fact is that it now believes it has totally equalized this position!

23… , Rd5

Gradually Black's plan is coming to fruition. The once inactive Rook is now active and centrally positioned. Black is prepared to fight either an aggressive middlegame or exchange selected pieces to reach an endgame where Black's central pawns have greater influence. Meanwhile, White's pieces are funding less scope of action. Thus I'm curious to discover how long Fritz 6a believes it has equality, when I think Black has the edge.

24. Qe2, …

Fritz 6a calculated for 13 hours and 40 minutes to a depth of 19/19 ply. Again, it believes that it has totally equalized. However, it is comforting that the chess engine tacitly acknowledged that it is walking a positional tightrope in that it significantly downgraded its other candidate moves. For example, its analysis of another candidate was 24 Qe3 (White offers its weak b-pawn in exchange for Black's strong central pawn), Bxb2 25 Rad1, Rxd1 26 Rxd1, Qc2 27 Rxd6, b3 28 Rd3, Qb1+ when it believes Black has a winning position. My notes continued with 29 Kh2, Be5+ 30 g3, b2 when I too believe White is lost.

24… , Qd3

This was the only move I considered since I still believe in what I wrote earlier; Black has an attractive endgame with Queens removed. This may seem curious since my pieces presently appear more active while White's are pushed into passive positions. However, when envisaging the board with the heavy pieces removed, Black's connected central pawns should advance with great effect. This is the first position I've found where I can exchange Queens without damaging my position, so I'll take advantage of this opportunity.

25.Qg4

Surprise! Fritz 6a calculated for 17 hours and 30 minutes to a depth of 19/45 ply (a new record?) and assessed the position as 0.31 pawns in my favor, meaning that Black has a clear edge. This is heartening, given it thought the position was dead even on its last deep search. Still, does its avoidance of the Queen exchange mean that it "knows" its endgame is inferior without Queens? Does it think I'll miss 26 Qc8+ followed by checkmate? I suspect one shouldn't read too much into this coincidental crossing-up of my plan. Instead, I suspect Fritz 6a's heuristics have a built in contempt factor for Queen exchanges, unless it calculates that it benefits from Queen exchanges. After all, Fritz 6a is a very deep calculator and thus generally has an advantage versus humans when there is a great deal to calculate. Keeping Queens on the board increases the positions to calculate.

Fritz 6a's rejected candidates were lines that I thought it would likely play. For example, it calculated 25 Rac1, Qxe2 26 Rxe2, Kd7?! 27 Kf1, e6 28 Ke1, b3 29 a5 and said Black is better by 0.66 pawns. I wish that were true, but this terminal position is unclear. Instead I examined 26… Rd3 (26… b3 27 Be3, e6 also gives Black an edge) 27 Kf1, Rb3 (27… d5 28 Rec2, b3 29 Re2, e6 is a bit more unclear) 28 Rcc2, d5 29 Red2, e6 maintains Black's advantage.

Fritz also calculated 25 a5, h5?! (Why?) 26 g3?! (Why not 26 Rc1 with

25… , e6

This is the only way to maintain Black's advantage, but I had to consider 25… Rf5?!, when White has at least one attractive continuation. For example, 26 Rab1 (26 Rad1?!, Qa6 27 a5, Kf8 is clearly advantageous for Black), Qa6 27 Be3, Qxa4 28 Ra1, Qb3 29 Re2, d5 30 Rd2, d4 (31… e6 31 Ra8+, Kd7 32 Qe2 is unclear) 31 Ra8+, Kd7 32 Qe2 is probably equal.

A more complex line involves allowing the Queen exchange only after deflecting Black's Rook to the less active post on f5. For example, 26 Qe2, Qxe2 27 Rxe2, d5 (27… Re5!?) is pretty unclear, while 27… Ne5? (planning … Nc4) 28 Rc1 forces a retreat back with 28… Nc6.

26. Rad1, …

Most humans, including yours truly, would first analyze the Rook sac line commencing with 26 Rxe6. Surprisingly this tricky shot was not among the top three candidates that Fritz 6a considered. My analysis continues with 26… fxe6 27 Qxe6, Ne7 28 Rc1, Bc3! (28… Rc5 29 Bxc5, dxc5 30 Rxc5, Qd1+ 31 Kh2, Qd8=) 29 bxc3, Re5! 30 Qb3 (30 Qa2, Re2 is to Black's advantage, while 30 Qf6??, b3 wins for Black), Qd2 when Black is clearly better. There's something about these tactical shots that naturally draws the human eye's attention. Perhaps it's due to solving find-the-mate puzzles or something similar. Still, this line had my attention many moves earlier when I was planning my strategy and it took me a long time to find Black's 28th and 29th move combination.

Instead Fritz 6a calculated for 16 hours and 30 minutes to a depth of 18/45 ply and assessed the position as 0.25 pawns in my favor. One of its top candidate lines was 26 Rab1, which it rejected after 26… h5 (I would have played 26… Qa6 with a Black advantage) 27 Qh4, Qf5 (again I'd favor 27… Qa6 28 Be3, Qxa4 when Black is better) 28 b3, Rd3 29 Qc4 (At first I thought White could improve with 29 Rec1 [White plans 30 Rxc6 and 31 Qd8 checkmate], but 29… , Rc3 30 Re1, d5 and Black is better), Rc3 30 Qe2, Qc2 when it assessed the position as 0.41 pawns in Black's favor. I disagree because 30… , Qc2?? loses to 31 Qb5, Rxb3 32 Rbc1 (White threatens 33 Rxc6), Qd2 33 Be3, Qd5 34 Qxb7, Rc3 35 Rcd1. Instead 30… Kf8 favors Black with an edge since he's ready now to start advancing the central pawns.

26… , Qb3 27. Rxd5, …

Fritz calculated 17 hours and 40 minutes to a depth of 19/45 ply and now evaluates the position as totally equal. I still favor Black. Just as on the previous move, I think most humans would have first analyzed the piece sac with 27 Rxe6+??, fxe6 28 Qe6+, Ne7 29 Re1, Be5 (29… Re5?? 30 Rxe5 wins) 30 f4, Qxb2 31 fxe5, Rxe5 32 Rxe5, Qxe5 when Black wins. This line was not in Fritz 6a's top three candidates. Instead, Fritz's top alternative was 27 a5, Rxd1?! 28 Qxd1, Qxd1 29 Rxd1, d5 30 b3, Kd7 31 Kf1, Kd6, which it evaluated as 0.47 pawns in Black's favor. Instead I think 32 Ke2, Bc3 is unclear and so would have played 27… Ne5 28 Qe2, Nd3 29 Qf3, Qc4 when Black is better.

27… , Qxd5 28. Rd1, …

Fritz 6a calculated for 19 hours and 15 minutes to a depth of 19/19 ply and still favors my position by 0.37 pawns, meaning a Black edge. White really had no viable options since 28 Qh4?! (28 Rb1?, Qa2 29 Qd1, b3 30 Qc1, Qxa4 31 Qd2, d5 gives Black a very large advantage. Black then plans … Qc4-c2.) h5 (28… Qd2 is also better for Black) when Black has a clear advantage.

28… , Qb3

29. Rxd6

Fritz 6a calculated for 18 hours and 45 minutes to depth of 20/20 ply, a new depth record for this game! While this great search depth is quite intimidating, I feel vindicated by the fact that Fritz 6a now downgraded its assessment of the position to 0.41 pawns in my favor.

29… , Qxb2

Black had a choice between winning White's b-pawn (the text move) or first winning White's a-pawn with 29… Qxa4. Initially I thought the later move was less logical because Black's primary threat is to quickly advance the b-pawn to it's Queening square. However, rather than immediately dismissing 29… Qxa4, I looked deeper and saw 30 Qe2, Be5. Now White decide where to retreat his Rook. The first line I examined continued with 31 Rd2, Qa1+ 32 Rd1, Qxb2 33 Qd3, Qc3 34 Qd7+, Kf8 35 Be3, Kg7 (35… b3?? 36 Bh6+, Bg7 37 Qc8+, Ke7 38 Bg5+, Qf6 39 Rd7 checkmate) 36 Rc1, Qb2 37 Qxb7, Nd4 when Black has at least an edge and probably something even larger. Therefore it seems White needs to find a better retreating 31st move. I then found 31 Rd1 (31 Rd3?, Qa6 32 Be3, Bxb2 gives Black a large advantage), Bxb2 32 Bc5, e5 when Black has at least an edge. So it seems that in this line Black can win both of White's Queenside pawns. While this is very attractive for Black, the text move lines I examined looked even better for Black. Now Black is able to exchange Queens in most lines I

30. Qd1?!, …

Fritz 6a calculated for 17 hours and 15 minutes to a depth of 20/50 ply (yet another depth record for this game). It assesses the position now as 0.37 pawns in my favor. However, I suspect Fritz 6a will significantly downgrade its assessment of its position once Queens are removed from the board. As previously mentioned, White has a number of mating threats. Presently White threatens 31 Rd8+, Nxd8 32 Qxd8 checkmate. However, for the first time in this game, Fritz 6a acquiesces to allowing me to exchange Queens.

Instead, I think White had a slightly better option at its disposal, which avoids any Queen exchange. As White, I would have played 30 Rd1, Qc2 31 Qf3, Qxa4 32 Qd2, Kf8 (32… , b3?? 33 Qd7+, Kf8 34 Bc5+, Ne7 35 Qxe7+, Kg8 36 Rd8 checkmate) 33 Bc5+, Kg8 34 Rb1, Bc3 (34… h5!? provides Black with an escape route for his King which can be handy in some lines) 35 Qd7, Qa8 (35… Qa2? 36 Qe8+, Kg7 37 Qf8+, Kf6 38 Rd1 is unclear. Ultimately, Black may prove better here too, but White has nasty threats of Qh8+ and Rd7, which are awkward to deal with in the short term.) 36 Be3, Be5, when Black has a large advantage. Black prepares to advance the passed b-pawn.

30… , Qa1 31. Qxa1, Bxa1

The last two moves look "forced". Fritz 6a calculated for 20 hours to a depth of 22/48 ply (yet another depth record for this game!) at an average speed of 401 kilonodes/second. Perhaps it reached that depth in such a short time because it really had no options to consider. Fritz 6a now believes it is inferior by 0.37 pawns.

32. Rd1, …

Bravo for Fritz 6a! It made the correct move. It calculated for 18 hours to a depth of 23/23 ply (yet another record search depth!) at an average speed of 398 kilonodes/second. It now believes it is inferior by 0.28 pawns.

While it is normally desirable to attack the square immediately in front of a passed pawn, Fritz 6a saw that it gains a tempo by first attacking Black's Bishop. For example, I prepared to meet 32 Rd3 with 32… e5! 33 Kf1 (33 Rb3, Kd7 34 Kf1, Bc3 35 Ke2, Nd4 gives Black a large advantage), Nd4 34 Bxd4, exd4 35 Rb3, Bc3 36 Ke2, Kd7 37 Kd3, Kc6 38 Kc4, Kb6 39 Rb1, Ka5 40 Kb3, d3 when Black has a large advantage. Fritz's move also requires Black to consider tempi when executing his technique.

32… , Bf6

I think this move is best since in some lines, the Bishop needs to be re-deployed along the a3-f8 diagonal. Now the Bishop can move to e7 where it is protected by Black's King, should White's Bishop occupy that diagonal first. Instead, 32… Bc3?? 33 Kf1, b3 34 Ke2, g5 (34… e5 35 Rb1 +) 35 Rb1, b2 36 Kd3, Bf6 37 Bc5, Ne5+ (37… Kd7 38 Kc2, Na5 39 Rd1+, Kc6 40 Bd4 gives White a large and possibly decisive advantage) 38 Kc3!, Nc6 39 Kc2, Na5 40 Bb4, Nc4 41 Kb3, Nb6 42 Ba3 and White wins Black's passed b-pawn.

33. Kf1, …

Fritz 6a correctly moves his King closer to my passed b-pawn, with intentions of entering the "box". For beginners following this game, the box I refer to is created by running a diagonal from my passed pawn on b4 to e1 and then envisioning a line from e1 to e4. This line creates the right side boundary to the box. Once White's King enters this "box" his King can catch my passed pawn before it can do any damage. This visualization saves having to calculate everything out. Fritz 6a made this technically correct move after searching to its former record depth of 23/23 ply in a period of 18 hours. Its speed was on average 390 kilonodes/second. It still believes I am better by 0.28 pawns. Fritz 6a correctly avoided 33. Rb1?, which then frees Black's King to advance to the Queenside and menace White's a-pawn, as illustrated in my notes to White's 32nd move. Black would then enjoy as significantly large and probably decisive advantage.

33. … , h5

Fritz's last move effectively nullifies chances for successfully advancing my passed b-pawn in the near future. However, Black has yet another trump card to play. Black enjoys a 4 on 3 Kingside pawn advantage. This advantage though is not as effective as a 3 on 2 advantage, which is yet less desirable than a 2 on 1 advantage. Thus Black needs to exploit this advantage by advancing the Kingside pawns in the hope of creating exchanges that eventually lead to a 2 on 1 pawn ratio. Which pawn is the best candidate for passing? All things being equal, I want the most remote potential passed pawn, so my h-pawn is my best candidate. However, one of the early chess principles I learned was that when trying to create passed pawns in the transition from middlegame to endgame, one should ensure that all pieces are first developed to their best locations. Well, my knight is needed on c6 to guard the passed b-pawn while my Bishop controls a vital long diagonal and can move to e7 to also cover that pawn. But the "fly in my ointment" is my passively posted King. It's immobile due to White's Rook, which controls the d-file. Therefore I would like to centralize my King along the e-file. However 33… e5?? 34 Rd5, Be7 35 Be3, h5 36 Rb5, f5 36 Rxb7 should win for White since his a-pawn threatens to be a

34. Ke2, Be7

Fritz 6a calculated for 17 hours and 30 minutes to a depth of 23/23 ply, at an average speed of 395 kilonodes/second. Now it has retracted my advantage, claiming total equality at 0.00 pawns. While, Black's edge is indeed very slim, I think that with best play, any winning chances belong to Black. But what is best play here?

It's not enough to have strong technical ideas if tactical refutations exist. I write this because I just discovered that my initial plan had a gaping tactical hole in it! I'll show you this line when we diverge from it later. Since mere technique is inadequate now, I was forced to calculate hard evidence to support my new plan. Black had many options here. My first reaction is that I need to find a way to activate my King. Since White's Bishop minimizes my King's mobility, my plan is to exchange it. I'll concern myself with advancing Kingside pawns later.

I dismissed the notion of advancing my Kingside pawns onto dark squares while each side has a dark-squared Bishop. Therefore 34… g5?! (34… Ne7?? 35 Rd8 checkmate!) 35 Rb1, Be7 36 Kd2, Kd7 (36… f5?! 37 Kc2, Bd6 38 Rd1, Ke7 39 f3, e5 40 Be3 gives White an edge) 37 Kc2, e5 38 Rd1+, Ke6 39 g3, f5 40 Kb3, e4 is unclear.

For similar reasons I also dismissed 34… h4?! 35 Rb1, Bc3 (35… Kd7 36 Kd3, Bc3 37 Bc5 transposes) 36 Bc5, Kd7 37 Kd3, Ne5+ 38 Kc2, Nc6 39 Rd1+, which is unclear. Instead, Black can push too hard and lose after 37… e5?? (37… Kc7?? 38 Kc4, g5 39 Rd1, f6 40 Kb5, e5 41 Bb6+, Kc8 42 Kc4, Bd4 43 Bxd4, exd4 44 Re1, Kd7 45 f4 wins) 38 Kc4, f6 39 Rd1+, Kc7 40 Bd6+, Kb6 41 Rd5, Na5+ 42 Kd3, Kc6 43 Rxa5, Kxd6 44 Kc4, e4 45 Ra8, Be1 46 Re8, f5 47 f3, Kd7 48 Rg8, e3 49 Rg7+, Kc6 50 Rxg6+, Kc7 51 Re6, f4 52 Kd3, Bd2 (52… b3 53 Re5 wins) 53 Re5, Kb6 54 Rf5 wins. Black has an alternative in 35… Be7 36 Kd3, Ne5+ 37 Kd4, Nd7 38 Bc7, Nf6 (38… Bc5+ 39 Kc4, Bxf2 40 Rxb4, b6 41 Kb5, e5 42 Rc4, Ke7 [42… f6?? 43 Rc6, Bc5 44 Kc4, Ke7 45 Kd5 and a subsequent Bd6 gives White a large advantage] 43 Rc6, e4=.) 39 Kc4, Nd5 (39… Ne4 40 Rb2, Kd7 41 Ba5, Bc5 42 f3, Nc3 43 Bxb4, Na4 44 Rd2+, Kc6 45 Bxc5, Nxc5 46 Rd8, Nd7 is unclear) 40 Be5, Kd7 41 Bd4, g5 42 Rd1, f6 43 Kb3=. This last variant, starting with 35… Be7, is similar enough to the text idea to convince me that it is best to first organize my pieces before trying to create a remote passed pawn on the Kingside.

35.Kd3, Ne5+

Fritz 6a calculated for 21 hours and 15 minutes to a depth of 23/23 ply, at an average speed of 391 kilonodes/second. It still evaluates the position as dead equal at 0.00 pawns. Franklin mentioned that the top candidate initially was 35 a5. I think this move is suspect because it leaves that pawn en prise if White's Bishop vacates that diagonal. Pawn moves are just too committal now… pawns can never retreat. I offered the computer a conditional sequence now, "if 36 Kd4, then 36… Nd7", which is part of my previously mentioned plan to remove White's Bishop from the board.

36.Kc2, …

Fritz 6a showed sound judgement in choosing to retain its Bishop at the expense of an immediately more passive King position. This move envisages activation of White's passive Bishop, giving White hope for some initiative if Black stumbles. It reached this conclusion after 19 hours of calculations to a depth of 23/23 ply, over an average speed of 390 kilonodes/second. Fritz 6a continues to evaluate the position as total equality, 0.00 pawn advantage. I think this I accurate.

Instead, I hoped it would play 36 Kd4?!, Nd7 37 a5, Nxb6 (the desired exchange of the Bishop) 38 axb6, Kd7 39 Rc1, Bf6+ (alternatives are: 39… Bd8 [39… b3?? 40 Rc7+ wins] 40 Kc5, Be7 41 Kb5=. Also, 41 Kc4 repeats the position, suggesting a draw. Finally 39… Bd6 40 f3, f6 [40… g5!?] 41 Re1 is unclear) 40 Kc4, Bc3 (my commentary to Black's 34th move made reference to having an initial plan with a gaping tactical hole in it. At this point I originally thought 40… Kc6?? 41Kxb4+, Kxb6 42 Rc8, Bd4 looked at least equal for Black. White's King is frozen to the Queenside to block Black's passed pawn, leaving Black free to try to create a passed pawn on the Kingside. Here, I was so busy conceiving long-range plans that I overlooked short-range tactics. Eventually the fog lifted and I saw that 43 f3 followed by Kc4 and then Rf8 wins for White. If Black reacts with … Bc5, then White plays Rg8-g7, winning Black's pawns.) 41 Kc5, g5 (41… e5 [41… f6 42 Rd1+, Ke7=] 42 Kd5, f5 [42… h4 is unclear] 43 h4, e4 44 g3, Ke7=) 42 Rd1+ ( possibly White's best line is 42 g4!?, hxg4 43 hxg4, f5 44 Rh1, b3 45 gxh5, exf5 46 Kc4, Ba5 47 Rh7+. Kd6 48 Kxb3, Bxb6 49 Rh6+, Kc5 50 f3 looks pretty drawish), Ke7 (Black plans … f5) when the position is probably equal, but Black has some practical winning chances due to the active Kingside pawns.

36. … , Nd7

Black continues with the plan to exchange White's Bishop for Black's Knight. With pawns on both sides of the board, it is desirable for Black to have the only Bishop (a "long-range" piece, compared to the short range of the Knight). With White's Bishop gone, Black would dominate the dark-squares. Regardless, the text move is forced in light of 36… Nc6?? 37 Kb3, Bf6 38 Kc4, Bc3 39 Kb5, e5 40 Bc5, Nd4+ 41 Kb6, b3 42 Kxb7 with a winning position.

37. Bd4, Nc5

Fritz 6a calculated for 21 hours and 25 minutes to a depth of 22/22 ply, over an average speed of 387 kilonodes/second. Fritz continues to evaluate the position correctly as totally equal.

White correctly avoided the exchange of his Bishop for Black's Knight so Black must devise a new plan. Black finds it desirable to transfer his Knight to d5. The d5 square is a superior post to the former one on c6 in that it controls more central squares, but more importantly, if offers a shield behind which Black's King can advance along the d-file in order to get back into the game. However, for tactical reasons, I can't find any way to maneuver my Knight to d5 presently. Therefore Black's last move seems forced. For example,

• 37… Nf6?? 38 Bxf6, Bxf6 39 Kb3, Be7 (39… Bc3 40 Rd6 [plans Rb6] wins) 40 Kc4 (plans Kb5-b6) wins.
  
• 37… b6?? 38 Kb3, f5 (38… e5 39 Be3, f5 40 Rd5 wins) 39 Be3, g5 (39… e5 40 Rd5 wins) 40 f3, g4 41 hxg6, fxg4 42 fxg4, hxg4 43 Bd2 wins.
  
• 37… Kd8?? 38 Kb3, Kc7 39 Rc1+, Kd8 40 Be3, Bd6 (40… Nf6 41 Bb6+, Kd7 42 Rc7+ wins) 41 Rd1, Ke7 42 f3, Ne5 (42… Nf6 43 Bg5, Bc5 44 Kc4, b6 45 a5 wins) 43 Bf4, f6 44 g4, hxg4 45 hxg4, g5 46 Bxe5, fxe5 47 Rh1, b6 48 Kc4 wins.

38. Bxc5, Bxc5

Fritz 6a calculated for 18 hours and 15 minutes to a depth of 24/28 ply (a new search depth record!), over an average speed of 396 kilonodes/second. It now favors its position by 0.28 pawns. Again, I disagree with the evaluation… the position is totally equal, with Black having the only practical winning chances due to the extra pawns. Fritz 6a's move is a mild surprise, given its previous aversion to this exchange. Still, the move is logical, White's King can now advance to b3 and penetrate Black's Queenside, and computer chess engines are supremely logical. However, Black's King may now transfer to the Queenside after playing … Ke7 and … Bd6, using the Bishop as a shield. Also, Black now has dominance of the dark-squares and thus has fewer worries about what color squares his pawns occupy. In fact, it can prove advantageous to advance them all to dark squares so the Bishop can protect them. This liquidation simplifies matters from a technical standpoint. With fewer pieces on the board, the tactical possibilities are reduced.

Instead, I think White had a better option in retaining the tension with 38 a5(!) for the following reason. Let's assume that Black, knowing the position is equal, desires to play safely for the draw in this complex position. This is best done with piece moves; pawn moves irretrievably change the position while a piece can be shuffled back and forth to mark time. But in this position, Black has few acceptable piece moves. Since White threatens a Rook invasion, any Black King move potentially allows Rd7. If Black's Bishop moves off the d8-h4 diagonal, then White plays Bf6, threatening checkmate. So by default, the safest piece to move is the Knight. Therefore 38… Na6 (38… f6!? is unclear) 39 Be5 (39 Kb3 [39 Bb6, Nc5 40 f3 (40 Ra1?, b3+ gives Black an advantage) Nd7 41 Bd4, Bd8 42 Ra1 is unclear], Nc7 41 Rc8+, Kd7 is equal), Bd8 40 Ra1, Kd7 41 Kb3, Nc5+ 42 Kc4, Kc6 43 Rd1, Be7 44 f3, Nd7 (44… f6 is unclear), when Black maintains equality. This however required Black to be more careful than he needs to be after the text move.

39. f3?!, …

Fritz 6a calculated for 18 hours and 45 minutes at an average speed of 387 kilonodes/second, to a depth of 25/45 ply (yet another search depth record!), only to play a superfluous move! This is amazing. Worse yet, it now favors its position by 0.31 pawns, meaning a small edge. In reality, the position was equal before this move and also after this move. However, the move is totally unnecessary since Black can't afford to capture White's f-pawn. Therefore the most precise move order is 39 Kb3, when Black must play as in the game, 39… Ke7 planning to build a bridge to the Queenside with … Bd6 and … Kd7-c7 and so on. Instead, if Black assumes that he can afford to give up his b4-pawn because he has another b-pawn to replace it, and thus take White's f-pawn in order to create a 2-pawn Kingside advantage, then he loses. For example 39… Bxf2?? 40 Kxb4, e5 (40… Ke7 41 a5, g5 42 Kc4, g4 43 hxg4, hxg4 44 Rb1, f5 45 Rxb7+ wins) 41 Rd5, f6 42 Kc4, e4 43 a5, Bg3 (43… e3 44 Kd3 wins) 44 Rb5, Bc7 45 g4! (White expends a tempo to lure Black's King onto the 7th rank in order to pin the Bishop to it after Rxb7), hxg4 46 hxg4, Kd8 47 Kd4, e3 48 Kxe3, Kc8 49 Kd4, Bd8 50 Kd5 should win for White.

White's wasted tempo really isn't consequential, so White never lost its grasp on equality.

40. g4!?, …

I suppose this move is more typical of a computer chess engine than a human. It was certainly unexpected to me, although Franklin indicated that Fritz 6a chose this move fairly early in its calculation process. My thinking was that in a King and pawn endgame, White doesn't want to exchange pawns, since that increases the likelihood of Black obtaining a passed pawn.

For example, Black now has a 4 to 3 pawn majority on the Kingside. After a pawn exchange, Black will enjoy a 3 to 2 majority, from which it is even easier to generate a passed pawn. The difference here is that White still has a Rook, which will enjoy the open file created after a pawn exchange, for penetration into Black's position. Fritz 6a calculated for 20 hours and 40 minutes to a depth of 25/25 ply (yet another record search depth!), over an average speed of 396 kilonodes/second. It now favors its position by 0.31 pawns. While I maintain that the position remains equal, I think Fritz has now sharpened/unbalanced the situation so that both sides must be totally accurate in their calculations in order to avoid defeat. This should lead to interesting chess for you viewers.

Instead I expected the more human looking and dull 40 Kb3, Bd6 (40… b6?? 41 Kc4 allows 42 a5 and White wins) 41 Kc4, Kd7 42 Kb5, Kc7 43 Rc1, Kb8 44 Kb6, Be5 (44… Be7 is also equal), when the position is equal. White has no practical winning chances, while Black has some potential, again due to his Kingside pawn majority.

40. … , hxg4

This natural move seems forced. Instead, 40… h4?? (at first glance this seems playable but meets with a tactical refutation) 41 Kb3, Bd6 42 Kc4, f5 (42… Kd7 43 g5 [White plans Rd4], e5 44 Kd5, Kc7 45 Re1, Kd7 46 Re4, b6 47 Kc4! wins) 43 gxf5, gxf5 and now the simple win is 44 Rd4, f4 45 Kb5, b3 46 Rd3, b2 47 Rb3, Be5 48 Kc5 when White follows with 49 Rxb7+ and wins. A more complex win is seen in 44 Kb5, e5 45 Kb6, e4 46 fxe4 (46 Kxb7??, exf3 47 a5, b3 48 a6, Bc5 49 a7, Bxa7 50 Kxa7, Ke6 51 Kb6, Ke5 52 Kc5, Kf4 53 Kd4, Kg3 54 Ke3, f4+ wins for Black), fxe4 47 Re1, Ke6 48 Rxe4+, Kd5 49 Rxh4 (49 Re1??, Kc4 50 Kxb7, b3 51 a5, b2 52 a6, Bc5 53 Kc6 only draws), b3 50 Rh5+, Kc4 51 Rf5, b2 52 Rf1, Kc3 53 Kxb7, Bf4 54 Rb1, Kc2 55 Rxb2+, Kxb2 55 a5, Kc3 56 h4, Kd4 57 a6 wins by a tempo.

41. hxg4, Bd6

Fritz 6a calculated for 20 hours and 45 minutes to a new record search depth of 26/26 ply. It calculated at an average speed of 406 kilonodes/second and favored White by 0.31 pawns. My first reaction upon seeing this is, how on earth can a human compete with a 26-27 ply search depth by the highest rated chess engine teamed with a Pentium III computer? Well, I'll just have to keep plugging along. Maybe I'll learn something in the process (one can only hope!).

This is an interesting and somewhat unique endgame. Generally, the side with the extra pawns uses the King to support the advance of the passed pawns. However, here Black's Bishop is unable to support both the Queenside pawns long enough to enable Black's King and Kingside pawns to activate. That's because White's King will invade to b5 and then play a5. Therefore, Black's King is left to hold down the Queenside while the Kingside pawns will get some support from the Bishop. This less effective maneuvering limits Black's winning chances, so the position is equal. My primary challenge is to continue to unbalance matters in the hope of activating my Kingside pawn majority to exploit any errors by White, in hopes of exploiting any White mistakes. Therefore, my primary choice all along was 41… f5, since it appeared to be the most dynamic. After all, it converts my 3 to 2 Kingside majority to an even more attractive 2 to 1 majority. However, late last night, a very obvious fact only then became clear to me, Black must struggle to draw after 41… f5?! 42 gxf5, gxf5 43 Kb3, Bd6 44 Kc4, Kd7 45 Kb5, Kc7 (45… e5?? 46 Kb6, e4 47 fxe4, fxe4 48 Kxb7, Ke6 49 a5, Ke5 50 a6, Bc6 51 a7, Bxa7 52 Ka7 wins) 46 Rg1, e5 47 Rg7+, Kc8 48 Kc4, e4 49 fxe4, fxe4 50 Rg4, and here I thought that White could win by creating zugzwang positions. However, upon further examination, 50… e3 51 Re4, b3 52 Kxb3, Bc5 53 Kc4, Ba7 54 Kd5, Kd7 55 a5, Kc8 it seems clear that White can not win this Rook + pawn versus Bishop + 2 pawns ending. But, there is some hope of a win, theoretically, if White can convert this ending into a Rook versus Bishop ending and then drive Black's King to the edge of the board and into a dark squared corner. However, 56 a6, bxa6 57 Kc6, Kd8 58 Re5, Bb8 59 Rxe3, a5 60 Ra3, Ke7 61 Rxa5, Ke6 62 Ra8, Bg3 63 Re8+, Kf5 64 Kd5, Kf4 draws. Similarly, 56 Re7, Kd8 57 Rxb7, e2 58 Rb1, Bf2 59 a6, Kc7 60 a7, Bxa7 61 Re1, Kd7 62 Rxe2 also draws. In summary, Black can just barely draw, so this is hardly the way to maximize winning chances. Therefore, I selected the text move, which creates a shield enabling Black's King to transfer to c6 to protect the b7 pawn and prevent White King invasions. Once secure, then the Kingside pawns will be advanced.

42. Kb3, Kd7

On its move, Fritz 6a calculated 9 hours and 30 minutes to a depth of 26/26 ply, tying its search depth record set on the previous move. It calculated at an average speed of 409 kilonodes/second and now favors its position by 0.50 pawns. This concerns me. While I do believe this endgame is objectively equal, I subjectively prefer Black since its Kingside pawn mass will start to advance and create a passed pawn once the Black King marches over to c6. However, White just created another avenue for Rook penetration, which I may be simply undervaluing. Therefore, I personally find this endgame difficult to evaluate since certain middlegame motifs have been reintroduced. Well, let's see what happens.

43. Kc4, …

Franklin Campbell sent me the following meaningful e-mail prior to finalizing the computer's move. "A quick check this morning showed Fritz-Ham probably continuing 43.Kc4 depth=25/25 (1/19) 407 kN/s with an evaluation of +/=0.41. That's after 6:20, (6 hours and 20 minutes) so I'm letting it run all day before accepting the move as final. As in the past, I doubt it will change its "mind". I think we're going to be seeing some bigger depth numbers as the pieces dwindle down and the number of possible moves decreases. But will this lead to stronger play? Somehow I doubt it. However, we'll have to wait to see. If there's a strong tactical shot there I'm sure the chess engines will spot it with this kind of depth. Don't leave any pieces hanging!" Fritz 6a searched for a total of 17 hours and 10 minutes to confirm the text move. It searched to a record depth of 26/26 ply, at an average speed of 411 kilonodes/second. It now favors its position by 0.53 pawns.

43. …, f5!?

I double checked and then triple checked my analysis to minimize errors on my part since this endgame is very wild. While I still believe the position is objectively even, it is also highly unbalanced; winning chances abound if one side errs and it is easy to err in this line. My notes show that I first found a win for one side and then on second review found an improvement allowing the other side to win! Finally, it seems that a drawn endgame is reached with best play. Humans are supposed to have an advantage when playing endgames against computers in OTB chess. This is because the computer search depth is limited in OTB chess and they also lack the general endgame "concepts" which most strong humans have mastered. However, in correspondence chess, there may be exceptions and this may be one such example. This position is so sharp that general endgame concepts take a distant second place to sheer brute force calculation skills. Since brute force calculating is what Fritz 6a does best, I admit to being a little unnerved.

Black has two candidate lines to analyze here, the text move and 43…Kc6. Initially, 43…Kc6 seems to prevent further penetration by White's King. But upon review, it loses two tempi compared to the text move line if White invades with his Rook along the h-file. Regardless, Black seems to draw and so I question you readers to show me whether a flaw exists in my analysis. For example, 43…Kc6 44 Rh1, Kd7 45 Kb5, Kc7 (Black has lost tempi with his King, allowing White to penetrate with his King and also with his Rook. How does he survive this? Watch!) 46 Rh7, b3 47 Rxf7+, Kc8 48 Rh7, b2 49 Rh1, Bf4 (Black threatens to win by blocking White's Rook from the Queening square with 50…Bc1) 50 Rb1, Bc1 51 Kc5, Kc7 52 f4 (52 a5, g5=), b6+ 53 Kb5, Kb7 54 Kc4, Ka6 55 Kb4, Bd2+ 56 Kb3, Bc1 draws. Of course, White need not invade with his Rook along the h-file, but then Black has an easy time in the endgame, first stopping White's King and then advancing the Kingside pawns. One may therefore question why I didn't select this choice, since Black seems entitled to bail out with a draw after such a grueling game. I have two reasons for selecting the text move instead. First, Black offers White more chances to err after the text move, and second, I'm psychologically troubled with the notion that Black can really draw after squandering two important tempi with 43…Kc6. In principle, White should be better in this line, but I just don't see it. I know how razor sharp 43…f5!? is and know that lost tempi lead to lost positions there, so I just find it difficult to accept 43…Kc6 on principle. Now let's see what happens in the battle of wits with the highest rated commercially available chess program.

44. g5!?, …

Fritz 6a is trying to match me for playing the most unbalancing lines. The text move is very wild since it fixes Black's g-pawn on a light colored square, meaning Black's Bishop can't protect it. However, White's g-pawn is vulnerable to attack from Black's Bishop since it's on a dark square. Black's response requires great precision. Fritz 6a calculated for 9 hours to a depth of 25/25 ply, at an average speed of 420 kilonodes/second. Surprisingly it now favors White by 1.22 pawns! I suppose this is a tough position for a chess program to assess accurately. It sees that Black's defense will have to abandon a pawn and thus perhaps loses its ability to judge.

White had two other lines that I had to consider. First, 44 Rh1, g5 45 Rh7+, Be7 46 a6 (46 gxf5, exf5 47 Rg7 [47 Kb5?, b3 48 Rh1, b2 49 Rb1, Bf6 gives Black a large advantage], Ke6 48 Rg8, Kd7 49 Rg6, Kc7=), Kd8 (46…fxg4?? 47 fxg4, Ke8 48 Rh6, Kd7 49 Rg6 wins) 47 gxf5, exf5 48 Rf7, f4 49 Rf5, Kd7 50 Rb5, Kc6 51 Rb6+, Kc7 52 Kd5, g4 53 Re6, Bg5 54 fxg4, f3 55 Re1 (55 Rg6??, b3 wins), b3 56 Ke4, f2 57 Rb1, b2 58 Kd3, Bc1 59 Ke2, Kd6 60 Kxf2, Ke5 61 Kf3, Kf6=. It's natural to reject this line since we saw that White had a couple opportunities to err in a big way there.

Therefore I was most worried about 44 gxf5, gxf5 45 Kb5, Kc7 (45…e5?? 46 Kb6, e4 47 fxe4, fxe4 48 Kxb7, Ke6 49 a5, Ke5 50 a6, Bc5 51 a7, Bxa7 52 Kxa7 wins) 46 Rg1, e5 47 Rg7+, Kc8 48 Kc4, e4 49 fxe4, fxe4 50 Rg4, e3 51 Re4, b3 52 Kxb3, Bc5 53 Kc4, Ba7 54 Kd5, Kd7 55 a5, Kc8 56 a6 (56 Re7, Kd8 57 Rxb7, e2 58 Rb1, Bf2 59 a6, Kc7 60 a7, Bxa7 61 Re1, Kd7 62 Rxe2 draws), bxa6 57 Kc6, Kd8 58 re5, Bb8 59 Rxe3, a5 60 Ra3, Ke7 61 Rxa5, Ke6 62 Ra8, Bg3 63 Re8+, Kf5 64 Kd5, Kf4 draws.

Since Black draws in this line, you may question why I was worried about playing into it. The reason is that the liquidation of forces seen in this line quickly causes the positions to enter those found on the Fritz 6a's 5-piece endgame tablebases. These tablebases have solved all positions found on them, so Fritz 6a would then play a 100% perfect endgame! My endgame play is not perfect, so clearly I have some apprehension entering a realm where my opponent can not err and where all lines have been solved either to checkmate or a draw.

44. …, e5

Black offers a pawn in order to reach drawn positions by building a fortress that White can't storm. Instead the natural looking 44…Kc6?? 45 Rh1, Be7 46 Rh6, Bxg5 47 Rxg6, Bf5 48 Rxe6+, Bd6 49 Rf6, f4 allows White to win. For example, 50 a5 (50 Rxd6??, Kxd6 51 Kxb4, Kc6 52 a5, b5 53 a6, Kb6 54 a7, Kxa7 55 Kxb5, Kb7 draws because Black maintains the opposition), Kd7 51 Rf7+, Kc6 52 Kb3, Kb5 53 Rxb7+, Kxa5 54 Kc4, Ka6 55 Rd7, Be5 56 Kxb4, Kb6 57 Rd5, Bc7 58 Kc4, Kc6 59 Kd4, Bd6 60 Ke4 (White plans Rxd6+), Bc7 61 Re5!, Kd7 62 Kxf4 wins because White is able to win the opposition after pieces are exchanged.

45. Kd5, b6

Fritz 6a calculated for 20 hours and 50 minutes to a depth of 26/26 ply. It now favors its position by 1.31 pawns. While I think the chess program's assessment is totally wrong, just knowing that its large assessment is growing has a psychologically negative effect upon me; did I miss something obvious? Do I need remedial endgame education classes? I thus start to second-guess my responses, wondering which one of us is in error…the very deeply calculating machine or the master rated human. I'm a little gun shy now after missing the obvious line that allowed Nimzo 7.32 to draw in Ham-Nimzo 7.32. This position requires great precision from both sides, so a mistake for either side can be disastrous.

Black's move is a useful waiting move which prevents 46 a5 (that move minimizes Black's future options to place the King on b6) and also supports a future …Bc5. The alternative waiting move just seems to squander a tempo after 45…Bc7? 46 Rh1, Bd6 47 Rh7+, Be7 48 Kxe5, b3 49 Rh1, Bxg5 50 Rb1 +.

46. Rc1!, …

Fritz 6a calculated for 19 hours and 40 minutes to a depth of 26/26 ply, at an average speed of 432 kilonodes/second. It now favors its position by a whopping 1.47 pawn advantage.

Those of you who don't believe computer programs can play endgames well had better look at this. Fritz found the best move. I expected 46 Rh1, e4 47 fxe4, fxe4 48 Kxe4, Be7 49 Rd1+, Kc6 50 Rd5, Bd6 51 Rb5, Bd6 51 Rb5, Be7 52 Ke5, Bxg5 53 Rxb4, Bd2 54 Rc4+, Kb7 55 Rc2, Bb4 56 Ke6, Ka6 57 Kf6, Ka5 which draws. Now I can hear you say, but Steve, 46 Rc1!, e4 47 fxe4, fxe4 48 Kxe4, Be7 49 Rd1+ just transposes back to the above line, so where's the problem? The problem is that the point of Fritz 6a's fiendishly clever move order is that 48 Rc6!, Bc5 49 Rxg6, b3 50 Rh6, e3 (50…Be3 51 Rh7+, Ke8 52 Rh4, b2 53 Rxe4+, Kf7 54 Rb4, Kg6 5 Rxb2, Kxg5 56 Kc6 wins) wins for White. I didn't see this at first because my notes only had 51 Rh2, Ba3, which draws. This is a correct conclusion. But after reviewing my notes, I saw that the natural 51 Rh2?? should be replaced with 51 Rh1, a move that's harder to find during late-night analysis.

Now 51 Rh1, Bb4 (51…b2 52 g6, Bf8 53 Rg1, Bg7 54 Ke4, e2 55 Kd3, Kd6 56 Kxe2 wins) 52 Kc4, Bd2 53 Kd3, b2 54 Kc2, Ke7 55 Rh2! (White prepares Kxb2 by first preventing …e2), Bc1 56 g6, Kf8 57 Re2!, Kg7 58 Rg2, Kh8 59 g7+, Kg8 60 Kb1, Bd2 (60…e2 61 Rxe2, Kxg7 62 Re6, Kf8 63 Rxb6, Be3 64 a5, Ke7 65 Rb7+, Kd8 66 a6, Kc8 67 Re7, Bg1 68 a7 wins) 61 Kxb2, Bb4 62 Kb2, Bd6 63 Kc3, Be5+ 64 Kd3, Bxg7 65 Rg6, e2 66 Kxe2, Kf7 67 Rxb6, Bd4 68 Rb7+, Ke8 69 Kd3, Bf2 70 a5, Kd8 71 a6, Kc8 72 Kc4, Bg1 73 Rg7 wins.

How much of the above analysis did Fritz 6a calculate? We won't know until a "post-mortem" is done, but it is conceivable that it followed the above notes to the 59th move (26 ply). A "post-mortem" will be conducted with the chess program's assistance after all 4 games end, so stay tuned for developments.

46…, Bc7!

Given the discovery that my original analysis was flawed, I can no longer play my planned 46…e4?? line. Fortunately, Black seems to have another drawing line. I just hope I calculated this one correctly during late-night analysis. The text line, like the 46…e4?? plan, offers up a Black pawn and envisages liquidation of more pawns to reach what seems to be a drawn endgame. Even if all pawns are liquidated, Rook versus Bishop endgames are usually drawn. The rule of thumb is that even if Black's King is pushed into a corner, Black can still draw if that corner square is the opposite color of his Bishop. My King will therefore stay near the light colored a8 square. Most endgame books will provide adequate coverage of Rook versus Bishop endings, but my inadequate library of three endgame books, provides no help in those positions where both sides have multiple pawns.

Black does have another choice, but it loses. Namely 46…Bc5?? 47 a5, e4 48 a6, Kc7 49 a7, Kb7 50 Ra1, Ka8 51 fxe4, fxe4 52 Kxe4, b3 53 Rb1, Kxa7 54 Rxb3, Be7 55 Rb5, Kb7 56 Re5, Bd8 57 Kd5, b5 58 Ke6, b4 59 Kf7, Kc6 60 Kxg6, b3 61 Re3 wins.

47. Rc4, e4

Fritz 6a calculated for 19 hours and 40 minutes to a depth of 26/26 ply, at an average speed of 432 kilonodes/second. It has now increased its evaluation to a 2.09 pawn advantage for White.

I suspect that these endgames are difficult for top-level computer programs to assess. While Fritz 6a's endgame performance to date has been really fine, due in part to being mated to a fast Pentium III computer and being allowed 18-20 hours to compute, it's ability to understand whether an advantage exists is poor. It correctly calculates that Black will cough up a couple pawns and therefore believes that this future material surplus will lead to an advantage.

But unless I'm sadly mistaken, Black has a draw here. Therefore, my conclusion is this: chess computer programs can calculate beautifully when calculation is called for when the result is within its search horizon. But their ability to assess positions correctly is often very poor. In fact, certain positions are known to be very difficult for chess engines to assess (i.e. positions where material is compensated for by pawn structure or development or other general positional considerations, closed middle games, and technical endgames). But to be fair, there are positions where we more intuitive humans struggle to both accurately calculate and assess (i.e. positions where many pieces remain on the board with plenty of open lines available to them).

48. fxe4, fxe4 49. Rxb4, …

Had I been White, I would have played 49 Rxe4! Black is forced to be ever so careful in order to draw. My analysis continued with 49…Bd6 50 Re6, Bc6 51 Rxg6, b3 52 Rf6, b2 53 Rf1, Bb4 54 g6, Bc3 55 Rg1, Bg7 56 Rb1, Ke7 57 Kc6, Bd4 58 Rd1, Kf6 59 Kd5, Bc3 (59…Be3?? 60 Rb1, Bc1 61 Kc6 wins) 60 Kc4, Be5 61 Rg1, Kg7 62 Kb3, Bf6 63 Kc2 (White's King keeps guard on the b-pawn in order to free his Rook). Now after 63…Be5 64 Re1, Bf6 doesn't it seem Black draws? Wrong! White scores with 65 Re4!, Kxg6 66 Re6, Kf5 67 Rxb6 and wins. Black must look a little harder to find 63…Bd4! 64 Rd1, Bc5 65 Rd5 (White threatens 66 Rxc5 when Black's King can't stop White's a-pawn), Be3 66 Rd6, Bc5 67 Re6, Bd4 68 Kb1, Kh6 and now Black draws.

So the above analysis is pretty clever, right? Wrong! Computer chess enthusiast, Jouni Uski, from Finland, and fellow computer chess enthusiast, Paolo Soares, from Brazil, found a very clever win for White with 51 Rf6! Surprisingly White finds it best not to take the pawn immediately because his Rook is now able to capture Black's b-pawn. Then, 51…b3 (I should add that 51…Kc7 52 Kc4 wins for White since 53 Rxg6 now works) 52 Rf3, b2 53 Rb3. My analysis continues with 53…Kc7 (53…Be3 [53…Ba3 54 Rxb6 wins] 54 Rxb2, Bxg5 [54…Kc7 transposes into the 53…Kc7 line] 55 Rxb6, Bd2 56 Rxg6 wins) 54 Rxb2, Be3 55 Rc2+, Kb7 56 Rg2, Ka6 57 Ke6, Ka5 58 Rg4 wins for White. Good job, Jouni and Paolo! Their concept is really very simple once it is shown to you, but finding this simple concept is difficult since 51 Rxg6?? just seems so natural. I wonder, could you have seen this during a late night analysis session, my dear readers?

Apparently Fritz 6a could not. It calculated for 10 hours and 15 minutes to a depth of 25/47 ply, at an average speed of 458 kilonodes/second to find a different move. It now values its position by 2.69 pawns.

49. …, e3 50. Re4, Bd8

Fritz 6a calculated for 17 hours and 15 minutes to a depth of 26/44 ply, at an average speed of 464 kilonodes/second. It still favors its position by 2.69 pawns.

51. Rxe3, Bxg5

Fritz 6a does not see that Black can build an endgame "fortress" which I think draws by hanging onto the b-pawn. Instead, after a 13 hour and 30 minute search to a depth of 26/49 ply, it favored its position by 2.66 pawns. Fritz 6a calculated at an average speed of 468 kilonodes/second.

52.Re6, Kc7 53. Kc4, …

White's last move came as a surprise to me since I expected the materialistic machine to grab the free pawn with 53 Rxg6, Be3 54 Rg7+, Kb8 55 Kc6, Bd4 56 Rb7+, Ka8 (56…Kc8?? 57 Rd7, Bc5 58 a5, bxa5 59 Rg7 wins) 57 Rh7, Kb8 58 Rf7, Be3 when Black draws in this "fortress" defense. Still, the game line is likely to either transpose into this line or one very similar to it.

Fritz 6a

53…, Bh4

Black can obtain a "fortress" defense in this fashion too. In fact, now 54 Kb5, g5!? creates a second "fortress" possibility where Black offers up the b-pawn in order to grimly hold onto the g-pawn. A probable continuation would be 55 Rxb6, Bf2 56 Rg6, Be3 57 a5, Kb7 58 a6+, Ka6 59 Rg7+, Ka8 60 Kc6, Bd2 when Black may draw too. Instead, I would play the more orthodox fortress with 54…Bf2 55 Rxg6, Bd4 which transposes back to the game line.

Black had another option in 53…Bd2, but after 54 Kb5 (54 Rxg6 should transpose back into the game line or a very similar position), Ba5 55 Rxg6, Kb7 56 Rg7+, Kc8 Black can probably draw here too. However this position is too confining since I now have no options to move my Bishop as long as White's King attacks my b-pawn.

The general rule of thumb for the fortress position I'm creating is that Black needs to avoid the following position: White's King is at b5 or c6 and his Rook is also attacking the Black b-pawn while Black's Bishop is posted on c5. The reason being that a White advance with a5 drops material and the game. Therefore I'll generally keep my Bishop away from c5.

54. Rxg6, Bf2

Fritz 6a finally takes the offered pawn. The alternative was 54 Kb5, Bf2 (54…g5!? was analyzed in the previous comment) 55 Rxg6, Bd4 when we transpose to the expected game line.

Fritz 6a calculated for 18 hours and 30 minutes to a depth of 26/42 ply, at an average speed of 487 kilonodes/second. At first, I was impressed by Fritz 6a's ability to probe some line extensions as deeply as 42 ply. But when I saw that it still favors its position by 2.69 pawns, I knew that it "knows" very little about this endgame. Most humans know that this position is drawn. I offered to help matters along with a conditional, "if 55 Kb5, then 55…Bd4".

55. Kb5, Bd4

Initially Fritz 6a selected 55 Rg2 after 19 hours and 20 minutes. It had searched to a depth of 26/42 ply and favored its position by 2.69 pawns. However, that move looked like a mindless reshuffling of pieces. Franklin then installed the Turbo 5-piece endgame tablebases to his computer and replayed the position. He wrote, "When I fired up the computer (last night) to analyze the 6-piece endgame, I could hear the hard-drive really working. So it must have been analyzing the various lines with exchanges leading to 5 or fewer pieces. This morning the hard-drive accesses were no longer firing away and the evaluation looked much as it did before the endgame module was installed. It appears to me that the additional endgame knowledge helped in evaluating obviously bad lines where one side or the other gave up material or made unfavorable exchanges.

Therefore, by avoiding exchanges, Fritz 6a continues to believe it is up big". Franklin went on to speculate that the 5-piece endgame tablebases, "may enable the computer to go to a slightly greater depth within the same amount of time". The final result was that the chess engine searched to the same depth as before but now selected the more logical looking text move. This is confirmation that the 5-piece endgame tablebase affects the chess engine's assessment even prior to reaching a 5-piece endgame. Fritz 6a still favors its position by 2.69 pawns though.

56. Rc6+, …

After 12 hours Franklin wrote, "The evaluation of +2.72 was given for two moves (55 Rc6+ and 55 Rg4)." For the record, it had searched to a depth of 27/45 ply, at a speed of 397 kilonodes/second. Franklin wrote, "It looks to me like it doesn't know what to do. It might be interesting to have it evaluate multiple lines, instead of finding just the 'best' line. Maybe all lines would be evaluated as +2.72".

Finally after 18 hours of calculating, Fritz 6a played the move I expected many moves ago. It searched to a depth of 27/51 ply, at the reduced speed of 381 kilonodes/second. It downgraded its evaluation to a 2.69 pawn advantage. Fritz's second choice looked like a typical pointless computer endgame move, merely pushing my Bishop back and forth.

Now dear reader, you are entitled to some much needed humor. As you see from my previous commentary, I've written that the position is drawn and many strong masters agreed with me. In fact, several OTB and Correspondence Masters heaped sympathy upon me for the following dilemma. How do I explain to weaker players that the position is a draw and that White can't make progress, in spite of the chess engine's evaluation of a win? I don't want to spend the rest of my life playing this endgame out with Fritz 6a while it exhausts every possible move until it agrees the position is a draw. So the other masters advised me to play just a few more moves until it is evident that the chess engine has no plan other than forcing

So do you, dear reader, see that the position is drawn? Do you understand that if the pawns are exchanged that Black has a book draw by putting his King on a8? Do you see that Black's King and Bishop hold the b-pawn so White can make no headway? If you agree with me about this, then we are totallyWRONG! At least that's what Bobby Fischer says.

Simon Finn wrote that a nearly identical position arose with colors reversed in Reshevsky-Fischer, 11th match game, Los Angeles 1961. This is covered in Fischer's My 60 Memorable Games, as game 28 (see notes to Black's 53rd) and note that the colors are reversed. Both grandmasters agreed to a draw, but Fischer later claimed he found an endgame study-like win for the side with the Rook! Simon Finn, after reviewing Fischer's notes saw that there are 5 steps that must be followed in order to win.

This all sounded far too theoretical the first few times I read it through. But, even those of you who hate endgame studies will surely enjoy this one. Let's move through this process of discovery together with the analysis I did late at night.

And now we don't even need steps 4-5 because 64 Kb7, Be3 65 Rc6+, Kd7 66 Rc3, Bg1 (66Bc5 12 a5 wins, as in Step 4) 67 Rd3+, Ke6 68 Kc6, Bf2 69 Rb3, Bd4 70 Rxb6 wins. Amazing! So now dear reader, are you prepared to jump on board Bobby Fischer's bandwagon and claim that White has a win here? Then I say you are totallyWRONG AGAIN!

With all due respect to Bobby Fischer and his claims to have no errors in his published analysis, there is an error in his published analysis. We can transpose directly into his analysis from My 60 Memorable Games but with colors reversed via 58Bc5 59 Rb5, Bf2. We are now following his line which runs 60 Ka7, Bd4 61 Ka8 (remember the steps above), Kc6 62 Rb1, Bc5 63 Rc1, Kc7 (63Kd6?? 64 Kb7 wins) 64 a5, Kc6 65 a6, Kc7 66 a7, Kc8 67 Rh1, Kc7 68 Rh7+, Kc8 69 Rh6!, Kc7 70 Rc6+!!, Kxc6 71 Kb8, Bd6+ 72 Kc8 "and the pawn queens". This is really beautiful indeed. But instead 67Bd6!! 68 Rh6, Be5 69 Rxb6, Kc7 70 Re6, Bf4 71 Re2, Bd6 72 Rc2+, Kb6 draws because Black traps White's King on a8. How about that for a little endgame magic? Now that the drawing scheme has now been revealed, Helmut Froeyman of Belgium subsequently demonstrated a simpler way to draw with 63b5 64 a4, b4 65 a6, Kb6 66 Rxc5 (66 a7, Bd6 draws), Kxc5 67 a7, b3 68 Kb7, b2 69 a8/Q, b1/Q+, which draws.

So, now that we've made history by busting Fischer's printed analysis and dug deeply into this position, we can safely conclude that this entire line is a safe draw for Black. If we accept that, then we areyou guessed it, TOTALLY WRONG!

Dan Andersson of Sweden and Helmut Froeyman of Belgium both subsequently showed that White's winning process begins with 63 Kb8!, instead of 63 Rc1. Now, please follow along for some head-spinning endgame magic. After 63 Kb8!, Bd4 64 Kc8! (this tempo loser forces Black into zugzwang, as will soon be evident), Bf2 65 Rc1+, Bc5 66 Kb8, b5 (allowing the White King to reach b7 is tantamount to resignation) 67 a5, b4 68 a6, b3 (68Kb5 69 Rxc5 wins) 69 a7 wins. If Black instead tries to prevent White's Rc1+ with 64Be3, then 65 Rb2, Bd4 66 Rc2+, Bc5 67 Rc1 transposes to the winning line already given.

Now I hear you cry out that since this winning mechanism is known, Black should then play 62Kc7, instead of 62Bc5, in order to transpose back into my Fischer busting drawing line. For example 62Bc5 63 Rc1+, Bc5 64 a5, Kc6 reaches the drawing line I gave earlier. So in conclusion, Black finally reaches the safe haven afforded by the drawn position, right? WRONG AGAIN! Helmut Froeyman discovered the brilliant 64 Ka7!!, Kc6 (64, Kc8 65 a5 wins) 65 Kb8 which transposes back into his bust of my bust of Fischer's line. Given this knowledge, that means White also can win with 62 Kb8 in addition to 62 Rb1. Can we thus conclude that this endgame's magical mystery tour been totally solved? I think so!

Now here's the big question. How much of this did Fritz 6a calculate? Given the machine's subsequent play, it's clear that even if it saw all these moves (highly doubtful, I think), it has no clue about how to evaluate the resulting positions. Instead, it's only evaluating the material difference rather than "understanding" the position on the board.

56…, Kb7

This move looks forced. A nice side note is that it also prevents White's King from advancing to a6 as in Step 1.

57. Re6, …

Now it is difficult for me to predict Fritz's moves because it totally lacks a plan. Apparently it wants to back my King up to the back rank. A related but equally futile plan is to kick my Bishop around a few times before trying to squeeze my King with 57 Rc4, Bf2 58 Rf4, Be3 59 Rf7+, Kc8 60 Kc6, Kb8 61 Rf8+, Ka7, which draws. Regardless, Fritz 6a calculated for 17 hours and 50 minutes to a depth of 26/40 ply, at an average speed of 368 kilonodes/second. It still favors its position by 2.69 pawns.

57…, Kb8 58. Rd6, …

Fritz 6a calculated for 17 hours and 30 minutes to a depth of 28/42 ply, at an average speed of 443 kilonodes/second. It still favors its position by 2.69 pawns. Franklin was kind enough to record that 58 Re8+ and 58 Rg6 were assessed to be favorable by 2.66 pawns while 58 Re1 was valued at 2.63 pawns. His message was, "Fritz doesn't know what to do. Four moves got practically identical evaluations". Yes, it's clear that this mechanical beast lacks the human ability to plan, so it just aimlessly pushes my pieces around. Unfortunately, it will examine nearly every piece pushing line until it sees that it can make no progress and the position is drawn.

58…, Be3 59. Rd8+, Kb7

Fritz 6a calculated for 20 hours to a depth of 29/48 ply, at an average speed of 388 kilonodes/second. It still favors its position by static evaluation of 2.69 pawns. Since Fritz has no plan, it aimlessly chases my pieces around.

Black's choices were between the text move and 59… Kc7, which forces the Rook to move. As a comparison between them, let's examine a sample line with 59… Kb7 60 Rd7+, Kc8 61 Kc6, Kb8 62 Re7, Bd4 63 Re8+, Ka7 64 Kb5, Kb7 when no progress has been made compared to the position at the 59th move. Similarly 59… Kc7 60 Re8, Bd4 61 Re7+, Kc8 62 Kc6, Kb8 transposes into the above line. I chose 59… Kb7 because it's instinctive to maintain the opposition; but my point is, Black draws regardless of his choice, since White can make no progress.

60. Rd7+, Kc8

Fritz 6a plays into the line forecast in my previous note. It calculated for 16 hours and 30 minutes to a depth of 29/29 ply, and still favors its position by 2.69 pawns. This computation was done at an average speed of 433 kilonodes/second.

61. Re7, Bd4

Fritz 6a continues to merely chase my pieces around without any plan in sight. The chess engine calculated for 21 hours and 30 minutes to a depth of 28/46 ply, at an average speed of 387 kilonodes/second. Unfortunately, it favors its position by 2.66 pawns.

The computer operator, Franklin Campbell, set the chess engine to display only the best line. Given its alpha-beta algorithms, this is its most efficient mode. However, Fritz 6a recently began to display two or more moves with almost identical evaluations. Franklin wrote that it's "as though it couldn't make up its 'mind' about what was best". Franklin also noted that while it's set to find the best single line, it sometimes displays 7-8 lines, usually with the same starting move.

My guess is that this phenomenon is caused by the fact that many lines transpose. If transpositions are involved they would have the same evaluation if the transpositional line were the main line, and a slightly lesser evaluation if the transposition were a slight deviation from the main line. For example, Franklin noted that another line that was displayed was 61 Kc6 evaluated at 2.63 pawns. Thus it perhaps saw 61 Kc6, Kb8 62 Re7, Bd4 (see my commentary to Black's 59th move for more on this line) and 61 Re7, Bd4 62 Kc6, Kb8 reaching the same position. It may have given this line a lesser evaluation due to its alpha-beta algorithm, or because in the former line this was a small deviation from its main line. Of course this is all speculation on my part. I am far from a knowledgeable source on anything involving computers.

After this comment was written, Franklin received several helpful responses. One example is from Robin Smith, who will soon be the clear winner of the 13th United States Correspondence Chess Championship. "This is normal in ChessBase. When you set it to display only the best move, it gives you a history of it's thinking. The last move displayed (the one on the bottom) will always be it's latest 'thinking', the move selected after the longest and deepest search. This should be the move selected for the Stephen Ham game(s), even if the evaluation is slightly worse than the moves displayed above it. By the way, the Fritz 6a - Stephen Ham game has become pretty absurd. It is quite clear that Fritz 6a both has not and will not make any progress in the position. If you or Steve would like to have the position adjudicated by me, I would be happy to oblige. In fact I will do it without even being asked ... draw. The other game (Steve-Fritz) is still quite fascinating. Go Steve!" Thank you, Robin.

62. Kc6, Kb8

Prior to the receipt of Robin Smith's input (See previous comment) and that of others, the computer operator, Franklin Campbell wrote the following. "I noticed once again this morning that Fritz showed three different moves with nearly the same evaluation. It's possible that it will have sorted it out by tonight and settled on one move, but I won't be surprised if it hasn't. Perhaps this is a ChessBase thing, and not a Fritz thing. If I specify 3 best lines, ChessBase displays exactly three lines. If I specify four, then four lines are listed. But if I specify only one line, then it fills the analysis box with lines, usually with the same initial move(s) after a very short time. In some cases, though, different first moves are shown with nearly the same evaluation. I just tried an experiment with ChessBase. I only have the Crafty chess engine at work, but I set up the initial board position and fired up Crafty, specifying only the best line. I then made the analysis window as large as possible. In a few seconds it had displayed 16 lines in this box."

The position has just transposed back to the line I gave to Black's 59th move. Fritz 6a calculated for 18 hours and 15 minutes to a depth of 25/39 ply, at an average speed of 367 kilonodes/second. It upgraded its assessment to a 2.72 pawn advantage. Its two other candidates were 62 Rf7 (2.69 pawns) and 62 Rh7 (2.62).

63. Kd5, Bc5

Fritz 6a continues to merely chase my pieces with no sign of any "plan" in sight. This is all the more evident in light of 63Bf2 64 Kc6, Bd4, which repeats the position. The chess engine calculated for 22 hours and 10 minutes to a depth of 26/38 ply, at an average speed of 373 kilonodes/second. Its assessment has now been downgraded to 2.66 pawns.

We've already seen that White's only winning motif is reached by getting his King to b7 or b8, then repositioning his Rook to the c-file to pin Black's Bishop to his King, and then advancing his a-pawn at the appropriate time. But in Fritz's desire to chase my pieces around, it's moving its pieces in the wrong directions. Meanwhile my King is firmly planted near the important b7 and a8 squares.

In conclusion, it's apparent that Fritz 6a will not find any win here. Since this is not a rated game and is played only for educational purposes, there is no reason to continue the game much longer. Both Franklin Campbell, the computer operator, and I wish to bring this long game to a conclusion without exercising the 50-move rule (taking the game to 105 moves). Those of you who are curious regarding whether Fritz 6a will EVER find a win are invited to do so on your own computers. Therefore I propose a reasoned conclusion: if there is no evidence of Fritz 6a making any attempt to maneuver into a winning position by move 70 (Fritz need not reach a won position, merely maneuver toward it), the game will be adjudicated as drawn. This is in accordance with the purposes set forth for this match. After all, even a weak chess player operating the chess engine would see by move 70 whether or not any progress is being made toward victory. If not, it is reasonable to conclude that a draw would be accepted.

64. Rd7, Bf2

The computer operator, Franklin Campbell, wrote that there is, "still no sign of a higher computer intelligence." Fritz 6a calculated for 17 hours and 30 minutes to a depth of 28/46 ply, at an average speed of 385 kilonodes/second. Its evaluation continues to decline and is now evaluated at 2.63 pawns.

I read into this declining evaluation that the chess engine realizes its winning prospects seem to diminish with each move. Further, it is unable to plan. Worse yet, its pieces continue to move away from the established winning motif for this endgame (see the commentary to White's 56th move). My guess is the chess engine chose its last move due to the following logic. It realizes that its King needs to maneuver into the area of the b7-square. But, 65 Kc6, Bd5 merely repeats the position. This is unacceptable if it is to maintain its 2+ pawn advantage evaluation. Therefore 64 Rd7 prevents …Bd5.

65. Rf7, Bg1

It's amazing that the chess engine really has no capacity to play anything of value. Instead, it continues to merely force a piece to move back and forth. More confirmation that it realizes there is no victory in sight is that its assessment has now dropped to 2.59 pawns. That's the third consecutive evaluation downgrade. This assessment was made after calculating for 19 hours and 30 minutes to a depth of 28/44 ply, at an average speed of 389 kilonodes/second.

66. Rd7, Bf2

We have now just repeated the position that was on the board after Black's 64th move. This is yet further corroboration for my theory that Fritz 6a is beginning to acknowledge that it can't find anything. I’m really curious to see what Fritz does next, both for a move and an evaluation.

Fritz 6a calculated for 20 hours and 15 minutes to a depth of 28/45 ply. This was done at an average speed of 387 kilonodes/second. However, it maintained its evaluation of a 2.59 pawn advantage.

There is a little trick that Black needs to watch out for here. After 66…Bc5?? 67 a5, Bf2 68 a6, Ka8 69 Kc6, Be3 70 Kb5, Bg1 71 a7, Be3 72 Ka6, Bg5 73 Rc7, Bf4 74 Rc8+, Bb8 75 axb8/Q is checkmate.

67. Kc4, Kc8

The chess engine calculated for 21 hours and 30 minutes to a depth of 29/29 ply, at an average speed of 389 kilonodes/second. To my surprise, Fritz 6a increased its evaluation to 2.63 pawns.

68. Re7, …

What's this? The chess engine has given up chasing my pieces around…at least for this move. What does this mean? Has it developed a plan for progress? Let's find out.

Fritz 6a calculated for 16 hours and 50 minutes to a depth of 29/29 ply, at an average speed of 389 kilonodes/second. Once again Fritz increased its evaluation, now favoring itself by 2.66 pawns.

68…, Bc5 69. Re5, Kb7

Fritz 6a calculated for 17 hours and 45 minutes to a depth of 24/39 ply, at an average speed of 392 kilonodes/second. It still evaluates the position as 2.66 pawns in its favor.

Black had a choice between the text move and 69…Kc7, both of which transpose. I selected the text move though to discourage an immediate White attempt to play Kb5-a6-b7. Another point of Black's King move is that we can repeat positions that have already occurred. Here's a sample of what I examined.

69…Kb7 70 Kb5, Bd4 71 Re7+, Kc8 72 Ka6 (72 Kc6 repeats the position of the 62nd move), Bc5 73 Re2, Bg1 (Both 73…Kb8 and 73…Bd4 seem satisfactory too) 74 Rc2+, Kb8 (74…Bc5?? 75 a5 wins for White) when White has yet to demonstrate any progress.

69…Kc7 70 Kb5, Bf2 (70…Kb7?? 71 a5, Bd6 72 Re6 wins) 71 Re7+, Kc8 72 Ka6 transposes into the above line.

70. Kb5, Bd4

Fritz 6a calculated for 17 hours and 45 minutes to a depth of 29/45 ply, at an average speed of 392 kilonodes/second. To my total surprise, the chess engine has now raised its assessment to 2.69 pawns in its favor.

Given my statement after the 63rd move, of adjudicating this position as a draw if Fritz makes no progress, we could justifiably end the game now as a draw. However, since Fritz 6a now evaluates this position as being more favorable than at any previous stage, I think we owe it to the machine and to the readers just to play on for a few more moves to see what, if anything, it has really got.

71. Re7+, Kc8

Well, it may not have much after all, since we have now returned to the position after Black's 61st move. I wonder if Fritz 6a is programmed to note all repeated positions.

Regardless, it calculated for 20 hours and 55 minutes to a depth of 26/41 ply, at an average speed of 374 kilonodes/second. It still favors its position by 2.69 pawns, so let's see if it deviates from its previous line now.

72. Re8+, Kb7

Now I know Fritz has no plan. It can not advance or improve the position of its King. It can't advance its pawn without having it removed from the board. So, the only constructive move remaining is a Rook move. But if Fritz 6a drives my King to the back rank with 73. Re7+, Kc8, we then will have a draw due to a three-fold repetition of the position after Black's 61st move. Perhaps there's a "bug" in Fritz' program that doesn't allow it to detect this three-fold repetition. The support for my supposition is because Fritz 6a now increased its assessed advantage to 2.72 pawns! It came to this conclusion after calculating for 24 hours to a depth of 23/37 ply, at an average speed of 334

Master Dan Heisman wrote in confirmation of my suspicion regarding a bug in Fritz 6a, “This is definitely true. I have seen it dozens of times. Of course, the programmers don't believe me. Fritz often detects 3-fold repetitions with one side to move, but then goes back to +3, or whatever, on the other player's ply.”

73. Re7+, Kc8

1/2-1/2

This three-fold repetition of the position has occurred. This position occurred after Black's 61st move, 71st move and 73rd move. As such, it is proof of a "bug" in Fritz 6a. This position is now legally drawn in spite of the fact that Fritz still favors its position by 2.66 pawns after 17 hours and 25 minutes of calculations. So while we have further evidence that chess engine assessments are not reliable, the chess engine did play some very strong chess, even in the endgame where computers are relatively weak in OTB chess at much shorter time controls.

The game was exciting. At one stage, I had a chance to enter a superior endgame by grabbing a pawn. Instead, I made the all too-human decision to stick to my strategy of exchanging Queens. Fritz 6a then demonstrated a fine defense for White, one that I had overlooked. Black subsequently pushed too hard and reached an objectively lost endgame, albeit one that most Masters and even some Grandmasters misjudged. Fritz 6a misjudged it too and then failed to demonstrate that it could utilize its material advantage in a greatly simplified position, even with the benefit of 5-piece tablebases and very deep searches.

Last Updated: 2001.01.31