Hans Niemann and the Fifth Endgame of the Apocalypse

I’ve written before about the Four Endgames of the Apocalypse — the four rare endgames that all chess players dread, which occur just often enough (like once or twice a lifetime) that you really ought to know them. They are:

1. K+Q vs. K+R
2. K+B+N vs. K
3. K+Q+RP vs. K+Q
4. K+R+B vs. K+R

There is one other head-breaking endgame I didn’t mention because I thought it was too unlikely to come up in a real game:

5. K+2N vs. K+P.

But I was wrong! A couple weeks ago, two California juniors played a game in Chicago (!) that went down to this ultra-rare endgame. Even more flabbergasting the player with the two knights, Hans Niemann, actually won the game without exceeding the 50-move rule, a feat that many grandmasters have failed to do. In so doing, he may even have rewritten endgame theory (see below).

First, let me say something about Niemann. A year ago he was just your typical 10-year-old expert. His rating even dropped t0 2099 last July. But since then what he has done has been a-MA-zing. He moved to the East Coast, played more than 300 games in the past year, and his rating has shot up from 2099 to 2322. He is now the top-rated 11-year-old in the country.

His opponent in this game, Vignesh Panchanatham, is no slouch either. At 2363, he is the number six 15-year-old in the country, although since he isn’t an IM already he’s probably washed up as a chess player. (Sigh.)

Panchanatham won a pawn early, but then messed up in various ways and they finally got to this position:

Position after 51. Nxg5. Black to move.

FEN: 8/8/8/3N2Np/5p2/k3p3/P6K/8 b – – 0 51

This is probably where Black missed his last clear shot at a draw. He should eliminate the last White pawn right away, with 51. … Kxa2. I’m sure Panchanatham didn’t do this because White can play 52. Nxf4, but he failed to realize this is a good thing for Black. We have now entered the Bizarro World of the 2N’s versus P’s endgame, where Black wants White to take all of his pawns (because that leads to a book draw). White, on the other hand, wants to leave one Black pawn on the board. The strategy then is to blockade the last pawn with one knight, use the other knight to maneuver Black’s king into a corner, then bring in the second knight to deliver checkmate. (This has to be timed very carefully because as soon as the blockade is released, it will be a race between the Black pawn and the White knight.)

So Black should have been thinking very hard about two questions — how do I get rid of all of my pawns, and failing that, what pawn do I want to be left with? Even without knowing any theory, I would have said that the best pawns to be left with are the e3 pawn, because it’s only two steps away from queening, and the h-pawn, because it’s so far away from my king and this makes it harder for White to win the checkmate race at the end. The one pawn I do not want to be left with if I’m Black is the f-pawn. So Black should be happy for White to take on f4.

In fact, after 51. … Kxa2 52. Nxf4 the Nalimov tablebases say that the position is drawn. (Incidentally, if it were White to move, White would have mate in 93 moves!) The drawing move is 52. … h4! Without giving you a lot of analysis, the reason is that if the pawn gets to h3 it’s a theoretical draw. So White must blockade it immediately. The king is never a good blockader — White’s king’s function in this endgame is to herd Black’s king around. So the h-pawn has to be blockaded with a knight. But after 53. Ngh3 Kb2 Black’s king gets to d2 in time to defend the e3-pawn and he cannot be driven away.

Instead, Panchanatham played 51. … e2?? 52. Nf3 (blockading the f-pawn!) Kxa2 53. Nc3+ Kb3 54. Nxe2 h4 55. Kh3 Kc4 56. Kxh4 Kd3 and we have now entered the Fifth Endgame of the Apocalypse.

Position after 56. … Kd3. White to move.

FEN: 8/8/8/8/5p1K/3k1N2/4N3/8 w – – 0 57

OK, now let’s talk a little bit about theory. These endgames were exhaustively studied by a Russian problem composer named A. A. Troitzky, who discovered the “Troitzky line.” This is not really a line but a set of squares: a4, b6, c5, d4, e4, f5, g6, h4. If the Black pawn has not advanced past one of those squares the game is always won for White. If the Black pawn has advanced farther, then Black can draw in some cases.

Looking at this position, we can see that the f-pawn is past the Troitzky line. However, Black cannot draw! In fact, according to the Nalimov tablebase, with perfect play by both sides White mates in 62 moves.

What?! Does this mean that Troitzky was wrong? No! This is where we get to the fine print, the ultra-ultra-refined endgame knowledge that even grandmasters don’t know. In fact, it’s quite possible that Troitzky is the only one who knew this (and maybe even he didn’t — I haven’t seen his book.) With the pawn blockaded on f4, Black can draw if he can get his king to g2. Otherwise, he loses.

This was completely amazing to me, because I figured the right idea for Black was to run as far away from the pawn as possible. But in fact, he wants to run to the h1 corner because there the pawn actually helps the defense. The f4 pawn takes away the square g3 from White’s king and knight, which is critical both for constraining Black’s king and for delivering checkmate.

All I can say is that it would have taken a heck of a lot of guts for Black to move his king toward g2. Panchanatham did what any sensible human player would do, and tried to keep his king in the center.

Playing over the next part of the game, I was blown away by the precision with which Niemann maneuvered Panchanatham’s king to the side of the board. I would not have known how to do this. But Niemann had to figure it out, over the board, with his clock ticking! (By the way, he had about an hour to play and Panchanatham had 15 minutes, with a 30-second-per-move time increment I believe.) I’m going to fast-forward through this part, because neither side made any big mistakes, so we can get to the most important positions.

The game continued: 57. Ned4 Ke4 58. Kg5 Kd5 59. Kf5 Kc4 60. Ke4 Kc5 61. Ne2 Kc4 62. Kf5 Kd3 63. Ned4 Kc4 64. Ke4 Kc5 65. Kd3 Kd5 66. Nb3 Kd6 67. Kd4 Ke6 68. Ke4 Kd6 69. Kd4 Ke6 70. Nbd2 Kd6 71. Kc4 Ke6 72. Nf1 Kd6 73. N1h2 Ke6 74. Kc5 Kd7 75. Ng4 Ke6 76. Nf2 Kd7 77. Ne4 Ke6 78. Nd6 Kd7 79. Nb5 Ke6 80. Nbd4+ Kd7 81. Kd5 Kc7 82. Ke6 Kb6 83. Kd6 …

Let’s come up for breath.

Position after 83. Kd6. Black to move.

FEN: 8/8/1k1K4/8/3N1p2/5N2/8/8 b – – 0 83

White has made more progress than I would have believed possible. Black’s King shoulders are starting to press against the edge of the board, and he has what appears to be an important decision to make: to run toward the a8 corner or the a1 corner?

The answer is, it doesn’t matter. The winning procedure is essentially the same for White in any of the three corners, a1, a8, or h8. The story would be different only if Black’s king could get to the h1 corner, but it can’t: the knight on f3 controls the critical square e1 (as well as the other critical square, h4, as we’ll see later).

Let’s take a look at what would happen if Black attempted to run toward a1 (and onward to h1 if possible). The game might continue something like this:

83. … Ka5 84. Kc5 Ka4 85. Nc6 Kb3 86. Kd4 Ka4 87. Kc4 Ka3 88. Ncd4 Ka4 89. Nb3 Ka3 90. Nc5 Kb2 91. Kd3 Kc1 (diagram)

Position after 91. … Kc1 (analysis). White to move.

FEN: 8/8/8/2N5/5p2/3K1N2/8/2k5 w – – 0 92

Even though this position didn’t happen in the game, I think that it is absolutely critical for understanding this endgame — how the White king cooperates with the mobile knight, the role of the static knight, and finally how White delivers checkmate.

The first thing to notice is that White gets nowhere if he tries to maintain the opposition: 92. Kc3? Kd1 and White must play 93. Kd3 to keep Black’s king from escaping to e2 and reaching the “good” corner of the board. After 93. … Kc1, we have a repetition of position.

The key concept for White is to use the knight to do some of the king’s work. The only winning move is 92. Na4! Notice how the king and knight together become like a super-king, controlling four adjacent squares on the second rank.

Black’s king has two different directions it could run, but the most thematic one is 92. … Kd1. Now White plays 93. Nb2+! Note how White’s knights take away one square at a time. The static knight takes away e1 (remember how I mentioned this earlier?). The mobile knight takes away d1, and then in a couple more moves it will take away c1. In that way, Black’s king will be trapped in the corner. Play will continue 93. … Kc1 94. Kc3 Kb1 95. Nd3 Ka2 and reach another turning point.

Position after 95. … Ka2 (analysis). White to move.

FEN: 8/8/8/8/5p2/2KN1N2/k7/8 w – – 0 96

Once again we have a position where the “normal” move, 96. Kc2?, claiming the opposition, does not work. Black plays 96. … Ka3 and the king starts high-tailing it toward the other side of the board. Once again, White must use the knight to do part of the king’s job, and therefore he plays 96. Kb4! Notice how the knight keeps Black’s king from moving to b2. Therefore he must play the retreat 96. … Kb1 and now 97. Kb3! locks the king in the corner (a1-b1) for good. It is now time to bring in the other knight. The game ends 97. … Ka1 98. Nd2 f3 99. Nb4 f2 100. Nc2 mate.

I’m going to call this maneuver the “Niemann maneuver,” where White’s knight goes to a4 (controlling a flight square), b2 (with check), d3 (controlling two flight squares, b2 and c1) and the king goes to c3, b4(!) and b3. As we’ll see, it can be executed in any of the three corners of the board Black’s king can get to. And I reiterate that the knight on f3 prevents the king from ever getting to the safe corner.

Now, back to the game! Let’s go back to diagram three, where White has just played 83. Kd6. In the actual game, Panchanatham played 83. … Kb7 and the game continued 84. Nb5 Kb6 85. Nc3 Ka5 86. Kc5 Ka6 87. Nd5 Ka5 88. Nb6 Ka6 89. Nc4 Kb7 90. Kd6 Kc8 (diagram).

Position after 90. … Kc8. White to move.

FEN: 2k5/8/3K4/8/2N2p2/5N2/8/8 w – – 0 91

Recognize this position? If we ignore the static knight and pawn on f3 and f4, it’s just diagram 4 flipped upside down! So Niemann applied the Niemann maneuver:

91. Na5! Kd8 (In this position … Kd8 is not so thematic because h8 is not a safe corner. The Nalimov tablebase says that Black can hold out several moves longer with 91. … Kb8.) 92. Nb7+! Ke8.

Of course, this move was not available to Black on the other side of the board. Here White feels the absence of his static knight, which controlled e1 but doesn’t control e8. However, there are no worries — now that Black’s king has made his choice, we will chase him to the h8 corner and apply the Niemann maneuver one more time!

Just for the sake of pedagogy, if Black had played 92. … Kc8 then we could apply the full Niemann maneuver: 93. Kc6 Kb8 94. Nd6 Ka7 95. Kb5! Kb8 96. Kb6 Ka8 97. Ne5 f3 98. Nd7 f2 99. Nb5 f1Q 100. Nc7 mate. This is so pretty that I’ve got to put in a diagram.

Successful completion of the Niemann maneuver.

FEN: k7/2NN4/1K6/8/8/8/8/5q2 b – – 0 100

Back to the game! After Panchanatham’s 92. … Ke8 the game went 93. Ke6 Kf8 94. Nd6 Kg7 95. Kf5 and now Panchanatham made his one and only big mistake since move 51.

Position after 95. Kd6. Black to move.

FEN: 8/6k1/3N4/5K2/5p2/5N2/8/8 b – – 0 95

Here Black played 95. … Kh6? Do you see why this is a blunder? Hint: If you’ve been paying attention, you should get the answer almost immediately.

While you’re thinking about it, let me digress briefly to an issue that I haven’t talked about before: the 50-move rule. Back on move 57, I told you that the Nalimov tablebase says that White has mate in 62 (i.e., move 119) with perfect play. Unfortunately, he would never get to that point because Black would claim a draw on move 107. According to Wikipedia, FIDE briefly changed the 50-move rule to a 100-move rule and then a 75-move rule for problematic endgames like this one, but by 2001 they changed it back to a 50-move rule for all positions. Ironically, for at least a little while they tried to list all the endgames where 75 moves would be allowed, and one of them was the 2N vs. P endgame where the pawn is behind the Troitzky line. Under that version of the rules, Niemann would not have been allowed to play 75 moves because Black’s pawn is in front of the Troitzky line!

This shows the futility of the case-by-case approach to the rules. Clearly the rules makers could not have further subdivided the endgame into subcases: “pawn at f4, Black king can reach g2,” “pawn at f4, Black king can’t reach g2,” etc. Then the rules would be telling the players how to play! Ultimately I think there had to be a uniform rule for all endgames. Whether it should be 50 moves or 75 could be debated, but 50 is traditional.

For this game, the difference was crucial. After Black’s best move, 95. … Kh7!, the Nalimov tablebase says that it’s mate in 24 with perfect play. In other words, we’re right back where we started, where White can mate on move 119 but Black will claim a draw long before then, on move 107. But after 95. … Kh6??, the position drops all the way down to a mate-in-ten, so the 50-move rule does not come into play. So even though in a theoretical sense 95. … Kh7 and 95. … Kh6 are both losing, in a practical sense 95. … Kh7 would have drawn.

Now, have you figured out why 95. … Kh6? is so bad? The answer is that it walks straight into the Niemann position! Check it out: the two kings and the active knight are in exactly the same positions as in diagrams 4 and 6, only with the board rotated by one more quarter turn. We’ve seen twice before that this is a loss for Black. Not surprisingly, Niemann executed the Niemann maneuver to perfection: 96. Ne8! Kh5 97. Ng7+! Kh6 98. Kf6 Kh7 99. Nf5 Kg8 100. Ke7! Kh7 101. Kf7 (locking the king in) Kh8 102. Ng5 f3 103. Ne7 f2 104. Ng6 mate.

That leaves one more loose end. Suppose Panchanatham had played 95. … Kh7!, and suppose we suspended the 50-move rule. How could Niemann have forced a mate?

I’ll leave this as a question for readers to investigate. I doubt that I could have figured it out — certainly not with my clock ticking. I had to look it up in the Nalimov tablebase. It turns out that you need one more endgame trick, of a type that is fairly well known, but needless to say I have never seen it in a position like this. If readers are interested, perhaps I will answer this question in my next post.

P.S. One other thing. With all these 11-year-old and 15-year-old wunderkinds showing the way, it should be hardly a surprise that the tournament was won by a 14-year-old: Jeffery Xiong. I apologize for giving more attention to Niemann than to the winner of the tournament! You can read more about the tournament at the USCF website, and by the way they have photos of both Xiong and Niemann.