THE HORIZON EFFECT

Wikipedia defines the horizon effect as: a problem in artificial intelligence whereby, in many games, the number of possible states or positions is immense and computers can only feasibly search a small portion of them, typically a few plies down the game tree. Thus, for a computer searching only five plies, there is a possibility that it will make a detrimental move, but the effect is not visible because the computer does not search to the depth of the error (i.e., beyond its “horizon”).

 

What it means, in more understandable words, is that when a chess computer finds a move, or a series of moves, that loses material, or some other advantage, it stops analyzing that move or series of moves. This can lose the game, or at least the advantage, as it fails to see a strong reply or the continuation of play that will allow it to retain or increase its advantage.

 
An early example of the horizon effect can be found in this game.

 
De Legal-Saint Brie?
France, 1750
1.e4 e5 2.Nf3 d6 3.Bc4 Bg4 4.Nc3 Nc6

De_Legal
5.Nxe5 Bxd1?? (There were many computers in the early 1980’s would simply take the offered queen, as it was taught that being up a queen would lead to victory and would therefore stop analyzing. This simple trap caused consternation and scorn by some players as they wanted a “serious” chess computer. By the way, this trap is known as De Legal’s mate.) 6.Bxf7+ Ke7 7.Nd5mate 1-0

 
A more recent example can be found in this game:

 

Escalante-“andersonwillians” (1511)
Najdorf Thematic Tournment
Chess.com, July-August 2019
1.e4 c5 2.Nf3 d6 3.d4 cxd4 4.Nxd4 Nf6 5.Nc3 a6 6.Bc4 g6 7.f3 Bg7 8.Be3 O-O 9.Qd2 Nc6 10.O-O-O Bd7 (The Najdorf has transposed into a Dragon, B77 to be exact.) 11.g4 Rc8 12.Be2 Ne5 13.h4 Nc4 14.Bxc4 Rxc4 15.h5 Qc7 16.Kb1 Rc8 17.hxg6 hxg6 18.Nde2 (This is an important move as it provides another piece to guard c3 and puts a stop to Black’s attack.) 18…Be6 19.Bh6 Bh8?
2019_08_08_A
20.Bf8! (This keeps the Black’s king from escaping to the center.) 20…Kxf8 (Not 20…Rxf8 21.Qh6! +-. Best for Black is 20…Nh5 21.Rxh5 gxh5 22.Qh6 Rxf8 23.Rh1 Bg7 24.Qxh5, and now if 24…f5 25.Nf4! wins on the spot.) 21.Rxh8+ Ng8

2019_08_08_B
22.Rxg8+! (The chess.com computer recommends 22.Qh6+ Ke8 23.Rxg8+ Kd7 24.Rxc8 Qxc8 25.e5 Kc7 26.exd6+ exd6, when White is obviously winning. But the text move is better as it leads to a forced mate. So why did chess.com computer miss this move? Probably because it saw that White loses the exchange and concluded that’s not a good way to proceed. So it stopped analyzing.) 22…Kxg8 23.Qh6! f6 (Black is in Zugzwang, as his king is paralyzed and he can’t get help in time. 23…d5 24.Rh1 +-) 24.Qxg6+ Kf8 25.Rh1 1-0 (25…Bg8 26.Rh8 e6 and now either 27.Qxg8+ or 27.Rxg8+ mates.)

 

 

Self-Destruction or the Big “Z”

ZUGZWANG is the compulsion to move in chess, where any move would result in loss of position, material, or game.

 

A player who is forced into this type of position does not want to move as any move by that player only makes winning the game easier for his opponent. In other words, he is forced to self-destruct, literally move by move.

Here are a few (simple) examples.
“abdo10000”-Escalante
Blitz Game
chess.com, Feb. 4 2019
[White made a miscalculation in the middlegame enabling Black to win a bishop. White could resign, but chooses to play on.]

2019_02_14_A46.Kh1 (White puts his king in a stalemate position. Unfortunately for him, he still has pawns he can move.) 46…Kf3 (Black can achieve the same result by …Kg3 or …Kh3. The important thing is to keep the white king trapped in the corner, when he must move his pawns.) 47.a3 bxa3 48.c4 a2 49.c5 a1=Qmate 0-1

 

Here two more examples, slightly more sophisticated.

 

Jonny Hector (2465)-Sergei Tiviakov (2490)
Stockholm, 1990
1.e4 c5 2.Nf3 d6 3.d4 cxd4 4.Nxd4 Nf6 5.Nc3 g6 6.Bc4 Bg7 7.h3 (A waiting move. More common is 7.Bb3.) 7…a6 8.O-O b5 9.Bb3 Bb7 10.Re1 O-O 11.Bg5 Nbd7 12.Nd5! (White usually does well if he can get this move in.) 12…Rc8 13.Qd2 Rc5 14.Nf3 Re8 15.c3 Qa8 16.Rad1 Nxd5 17.exd5 Nf6 18.Be3 Rxd5 19.Bxd5 Bxd5 20.Nh4 Bxa2 21.Bh6 Bh8 22.f4 Bb3 23.Ra1 Ne4 24.Qe3 Bd5 25.Qb6 Bb7 26.Re3 Bf6 27.Nf3 Ng3 28.Bg5 Nf5 29.Ree1 Bg7 30.Nh4 f6 31.Nxf5 gxf5 32.Bh4 Kf7 33.Re2 Bh6 34.Bg3 Qc8 35.Kh2 Qc4 36.Rf2 Qe4 37.Rf3 Qc6 38.Rxa6 Qxb6 39.Rxb6 Bxf3 40.gxf3 Ra8 41.Rxb5 Ra2 42.Kg1 Bf8 43.c4 Ra1+ 44.Kf2 Rc1 45.b3 Rc2+ 46.Kf1 h5 47.Rxf5 Rc3 48.Rb5 h4 49.Bf2 Bh6 50.f5 Rc1+ 51.Kg2 Rc2 52.f4 Bxf4 53.Kf3 Bg3 54.Be3 (White is still winning after 54.Bxg3 hxg3 55.Kxg3 Rc3+ 56.Kg4. The text move keeps the tension on the board.) 54…Be1 55.Rb8 Rh2 56.Bh6 e5 57.Rb7+ Ke8 58.Bg7 Rxh3+ 59.Ke4 Kd8 60.Bxf6+ Kc8 61.Rh7 Rxb3 62.Kd5 Rb7 63.Rh8+ Kd7 64.Bxh4! Bxh4 65.Rh7+ Be7 66.f6 Ke8 67.Ke6 d5 68.c5 Rc7 69.Rxe7+ Rxe7+ 70.fxe7
2019_02_14_B
1-0

 

 

Of course, such self-destruction is not limited to pawns only endgames.

 

GM Spassky-GM Fischer
World Ch.
Reykjavik, July 11 1972
Game 1
1.d4 Nf6 2.c4 e6 3.Nf3 d5 4.Nc3 Bb4 5.e3 O-O 6.Bd3 c5 7.O-O Nc6 8.a3 Ba5 9.Ne2 dxc4 10.Bxc4 Bb6 11.dxc5 Qxd1 12.Rxd1 Bxc5 13.b4 Be7 (This position is more or less drawish. Mariotti-Tatai, Match, Rome, 1972 continued with 14.Nfd4 Bd7 15.Bb2 Nxd4 16.Nxd4 Rac8 17.Rac1 Rfd8 18.Bb3 Kf8 19.Rxc8 Rxc8 20.Rc1 Rxc1+ 21.Bxc1 1/2-1/2. Spassky’s move is more dynamic.) 14.Bb2!? Bd7 15.Rac1 Rfd8 16.Ned4 Nxd4 17.Nxd4 Ba4 18.Bb3 Bxb3 19.Nxb3 Rxd1+ 20.Rxd1 Rc8 21.Kf1 Kf8 22.Ke2 Ne4 23.Rc1 Rxc1 24.Bxc1 f6 25.Na5 Nd6 26.Kd3 Bd8 27.Nc4 Bc7 28.Nxd6 Bxd6 29.b5 Bxh2?? (Black, who is the aspiring to be the next world champion, makes a horrible beginner’s move. Black never recovered in this game. And didn’t show up for the next one. Only two games into the match and Bobby was down 0-2. The fact that he won this match, and the world championship, is simply incredible.) 30.g3 h5 31.Ke2 h4 32.Kf3 Ke7 33.Kg2 hxg3 34.fxg3 Bxg3 35.Kxg3 Kd6 36.a4 Kd5 37.Ba3 Ke4 38.Bc5 a6 39.b6 f5 40.Kh4 f4 41.exf4 Kxf4 42.Kh5 Kf5 43.Be3 Ke4 44.Bf2 Kf5 45.Bh4 e5 46.Bg5! e4 47.Be3 Kf6 48.Kg4 Ke5 49.Kg5 Kd5 50.Kf5 a5 51.Bf2 g5 52.Kxg5 Kc4 53.Kf5 Kb4 54.Kxe4 Kxa4 55.Kd5 Kb5 56.Kd6

2019_02_14_C

(White can play Kc7 protecting his pawn while attacking Black’s. Black has no choice but to play 56..Ka6. White will reply with Bd4 and Black can either give up protecting his pawn. or run his pawn down the a-file, and wait for White to play an eventual Bxa1. And then Black has to give up the a6 square.)