19

Although top players are extremely good at finding checkmate, the number of permutations of moves in just 3 moves can be hundreds of thousands, and the farther out the possible mate (e.g. mate in 4, mate in 5), the more permutations are possible; so it is understandable that a checkmate will sometimes be missed by top players.

Engine analysis of past grandmaster games would reveal missed checkmates - what percent of classical games did/does a grandmaster miss a checkmate?

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    Is a # in 2 consider missed if the player takes 2 or three move longer ( without losing the forced mate ) – AKP2002 Jul 3 at 6:46
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    @AKP2002 good question. I don’t think so, I am very much interested in when a forced mate is possible (but missed), and the very next move a forced mate is no longer possible – stevec Jul 3 at 6:50
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    Theoretically, each position is either a draw or a forced checkmate for one side. – Carsten S Jul 3 at 12:10
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    @Jeffrey I think it should count as a missed mate if Player 1 has a forced mate but takes a line which would allow Player 2 to draw, but Player 2 then makes an error and Player 1 does win in the end. – Philip Kendall Jul 3 at 21:54
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    I asked a more specific version of this question at chess.stackexchange.com/questions/30243/… . Thanks, Steve, for bringing up the idea. I wondered if I should leave it for you, but the answers here talk about the vagueness of the definition, so I felt there should be a more specific question. – Bit Chaser Jul 3 at 22:43
24

Probably more often than people realize.

There have been several notable instances where GMs (even world champions) have missed simple mates in one.

From my own experience, when I analyze my games the engine frequently will point out some ridiculous 25 move forced mate. In a game, I'm not going to take the time to calculate something like that out if I have a very clear, simple and direct win. Maybe it takes a couple of moves longer but who cares?

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  • IOW, you're seeing a forced mate in even more moves, which just happens to involve first removing so many enemy pieces that they're sure to resign before it actually comes to pass. – leftaroundabout Jul 4 at 12:11
18

It really depends on what counts as a missed checkmate. In Blitz we occasionally see a missed mate in 1. In slower games, mates in a few moves are rarelly missed. But the problem is that sometimes long mate sequences will be "intentionally missed", as the player will go for a solid advatange that guarantees victory rather than calculate a 15-move long line that leads to mate but could be wrong. Does this really count? You're probably mating anyway but 20 moves further down the line.

If we refer exclusively to missing forced mates that lead to not winning the game, I'd say they're few and far between

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7

I agree with the answers above, however, there are actually some cases where GMs missed mate-in-ones in classical chess while not in time trouble. If memory servers right, I have read about that a few years back on chess.com's news page, but I cannot find the article right now.

The main reason is the following: Player A only needs a draw (to outright win the tournament or advance in a knockout tournament, for instance) and has calculated a quite long forced line leading to a perpetual or stalement. Then these forced moves are blitzed out and the mate-in-one is missed.

Of course, this still happens only rarely, but the percentage of easy mates missed by GMs while having lots of time is probably farther away from 0 than one might first expect.

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6

This depends entirely your horizon for what you consider a missed mate. Is there any upper bounds on the number of moves required? Would you consider a "mate in 53" to be a missed mate, even if no one, human or computer, had the computational power to actually find such a mate (but maybe in 100 years a computer could show a forced mating sequence from that position)?

Assuming that you would consider a missed "mate in 53" to be a missed mate, then the answer is that no one can give you a precise number, for the simple reason that no one can determine which situations contain such a mate. There does, however, exist a theoretical answer: the number of missed mates by a player in any game is precisely the number of instances in which that player had a winning position at one time but later the position became drawn or lost. The key insight is that a forced mate exists if and only if one of the players has a won position, even if the horizon for that forced mate is so far out as to be effectively impossible to compute.

You could probably get a reasonable estimate for the number of missed mates in a given game by running the game through a good chess engine and setting an appropriate cutoff evaluation, where any evaluation above that score is considered a won position for that player and any evaluation below that score is considered a draw or a loss. Since a pawn is generally considered enough to win, a score like 1.0 or 1.1 might be a reasonable choice. The number of missed mates would then be the number of times the computer evaluation crossed that cutoff line from high to low -- e.g., if the evaluation was 1.4 one move and .6 the next, quite probably the player moved from a won position to a drawn position, missing a theoretical forced mate. The downside to this method is that it is sensitive to the cutoff evaluation chosen, the engine accuracy, and the engine stability. Possible very sensitive, as it is quite possible to imagine a situation where a sequence of player moves or engine analysis at different depths fluctuate frequently over the chosen value in a narrow range, leading to large uncertainty as to whether the current move does in fact represent a change from won to drawn or vice-versa. Similarly it is quite possible that one engine evaluates a position as above the cutoff while a different engine deems it below.

A precise answer is clearly impossible, but if people are interested and time permits, I might try running a grandmaster game or two through my engine and see what results come out.

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  • Along these lines, one might argue that 100% of games might contain a missed mate because its still unknown whether white or black can force a win. If they can, every game which doesn't go down that route qualifies as a mised mate. – Cort Ammon Jul 3 at 19:44
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    @CortAmmon Yes, although most strongly believe that the starting position is drawn, if it instead turns out to be a won position for white (or even black), then every game that does not end in a win for white (or black) contains by definition at least one missed mate. – Galendo Jul 3 at 19:53
  • @Galendo I had been wondering what is meant by this, but I understand the reasoning now – stevec Jul 12 at 3:14

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