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Consider a normal game of chess with one change. As soon as you put the opposing king in check you have won.

If both players play optimally, how long is the game?

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  • $\begingroup$ Is this a question that has a known answer? Or is it unsolved as far as you know? $\endgroup$ Dec 3, 2023 at 23:52
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    $\begingroup$ @pmacfarlane I believe I know the answer but I haven’t seen anyone else solve it. $\endgroup$
    – Simd
    Dec 4, 2023 at 0:03
  • $\begingroup$ I wonder how long it takes for the black to give check. On the first glance it seems there are too many possible moves, making this unsolvable. $\endgroup$ Dec 4, 2023 at 19:48
  • $\begingroup$ @ZizyArcher Do you mean ignoring that white will already have won? $\endgroup$
    – Simd
    Dec 4, 2023 at 21:09
  • $\begingroup$ @Simd Yes - the game would be that white check is not a win (black still needs to move king or defend) while black check is. But as said, I guess there are tons of moves that need to be checked (eg white making checks to delay?), making this unsolvable by hand. $\endgroup$ Dec 5, 2023 at 7:43

1 Answer 1

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White can force a check in

5 moves.

White starts with the move

1. Nc3.
White is now threatening 2. Nb5, 2. Nd5, 2. Ne4.
After any of these moves, white will be threatening to give a knight check. There's no way that Black can prevent all three threats - for instance, after 1. ... c6, 2. Nb5 and 2. Nb5 are prevented, but 2. Ne4 still works.

As a result, to extend the game, Black needs to

Prepare to move the king on move 2, to get out of the way of the knight. This can be accomplished by moving the d7, e7, or f7 pawn.
A play of 1. ... d6 fails to 2. Ne4, after which black cannot escape 3. Nf6+.
Similarly, 1. ... f6 and 1. ... f5 fail to 2. Nb5 and 3. Nd6+.
After 1. ... e5, 2. Nd5 prevents the Black king from escaping, allowing 3. Nf6+ to win.

As a result, Black's only remaining options are

1. ... e6 and 1. ... d5. In fact, these are the only moves which extend the game past move 3.
If black plays 1. ... d5, white can respond with 2. Nb5, after which black's only move to prolong the game is 2. ... Kd7. White then plays 3. Nf3, after which 4. Ne5+ will win, unless black moves their king on move 3, at which point the other white knight can check on move 4.

Thus, we have narrowed Black's options down to

1. ... e6. This is Black's only option which extends the game past move 4.
Now, White can play 2. Ne4, forcing 2. ... Ke7. White now plays 3. Nf3, threatening 4. Nh4, Ne5, and Nd4, each followed by a check on move 5. No move by black prevents more than two of these (e.g. 3. ... Nc6), so black again needs to look to move their King.
Moving to a light square fails to a check by the e4 knight, and black's only other option is to move their Queen to prepare 4. ... Kd8. However, white can then play 4. Ne5, and 5. Nc6+ even if the black king retreats to d8.

In conclusion, against best play, white wins in

Five moves, with the main line variation
1. Nc3 e6
2. Ne4 Ke7
3. Nf3 Qe8
4. Ne5 Kd8
5. Nc6+

Here's a Lichess study showing many of the variations.


This puzzle is described on the chess variants website, where it is claimed that

a forced mate in four for White is known.

That site cites the Classified Encyclopedia of Chess Variants, which in Chapter 10, page 82, says that a solution to this puzzle was given in July 1916, in the British Chess Magazine, Volume 36, page 201, quoting the Brooklyn Eagle, with the claimed solution:

"White could win by 1 Nc3 followed by an attack by the other knight"

given by Marshall, but does not give a specific number of moves.

A more detailed solution, matching the solution I gave above, is given in the site's other, broken citation, which I believe was intended to point at WGR10 by Michael Keller, in section Cx5, which gives the solution:

"Frank Marshall, however, found a forced win for White using only his two knights. One way is 1 Nc3 e6 (1...d5 2 Nb5 Kd7 3 Nf3) 2 Ne4 Ke7 3 Nf3, winning with the threat of either 4 Ne5 or 4 Nh4. 1...e5 and 1...d6 are met by 2 Nd5, while 1...f6 or 1...f5 are met by 2 Nb5."

Thus, the correct answer is

a win for white in 5 moves.

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    $\begingroup$ 5. Nf6+ should be 5. Nc6+. $\endgroup$
    – Allure
    Dec 4, 2023 at 9:55
  • $\begingroup$ This is a great answer. Do you have a way of working out which first moves by white lead to a victory by black? Or shall I ask that as a separate question? $\endgroup$
    – Simd
    Dec 4, 2023 at 16:43
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    $\begingroup$ @Simd That sounds like a separate question - I did this all by hand, I don't have a generic technique or a solver or anything. $\endgroup$
    – isaacg
    Dec 4, 2023 at 18:40

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