6
[FEN "8/8/8/4N3/4N3/4K3/8/4k3 - - - 0 0 "]

I have this chess problem that I have played with. Logically, there are positions that have the Black King in checkmate. But untill now, I haven’t been able to solve it.

My Houdini returned ‘insufficient material’ when I forced a move.


EDIT

However, if I use infinite mode, Houdini calculates and returns a value approximate ’+1.30’, until ‘+1.42’ at the moment I edited this. This means it is definitely a win for White. [Based on the Houdini guide, ‘+0.89’ means an 80% chance of a win, ‘+0.9’ for a 90% chance, and so on.


Can you solve it?

  • 4
    An evaluation of +1.30 or +1.42 does not mean it is definitely a win for White. And +0.8 doesn't generally translate to an 80% chance of a White win. Statements like "when Houdini 3 shows a +1.00 evaluation in the middle game it has an 80% chance to win the game against an equally strong opponent at blitz time controls" en.chessbase.com/home/TabId/211/PostId/4008591 from creator Robert Houdart might lead to such probabilistic misinterpretation. Even that statement is just a crude observation based on some sample of games between Houdini and other engines, and requires a grain of salt. – ETD Jun 29 '13 at 12:51
  • N.B. As the answers below show, this question rests on a false premise that the endgame in question is a forced win. For more info on this ending, the interested reader should see the highly-related question: chess.stackexchange.com/q/5281/167 – ETD Jul 24 '14 at 23:20
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The position is indeed a draw - but your edit suggests a far more interesting question. Why would Houdini give such an evaluation when the position is a known book draw? @EdDean touched upon the answer, explaining the interpretation of the point evaluation.

Houdini, along with other chess engines, will analyze the position many moves deep. The depth is shown in the engine box and shows you how far ahead the computer is thinking. When Houdini calculates 15 moves ahead, it sees a position where White is up two knights against a lone king. Pure Houdini will not know that White cannot checkmate black without an accompanying Tablebase. However, if enough moves are played, you can "trick" Houdini into realizing that all of its best moves are leading to the exact same evaluation with no end in sight. This will cause Houdini to automatically adjust its evaluation to 0.00 - this is the result of some code that tells it if the position evaluation has not changed for X number of moves, the position must be a draw. Interestingly enough, if you keep playing on after this 0.00 evaluation is suggested and reach a position where the next move is checkmate, Houdini sometimes will still suggest this 0.00 evaluation. I've had this happen to me several times in the past and is likely a bug in the program.

In endgames with 6 pieces or less (including kings but without 5 vs 1), the Nalimov tablebase is a preferred method. This computerized database has a precalculated and exhaustive analysis of all possible scenarios with the aforementioned conditions. It returns the game-theoretical value in any given position - essentially "solving" the position.

If you want to read more about Tablebases, check out the Wikipedia page and an example.

  • 1
    Examining wins using the tablebases is very informative. – Tony Ennis Jun 29 '13 at 14:19
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The position shown is a draw, as Houdini says, because a checkmate with two knights cannot generally be forced, and there is no immediate mate in the position shown.

  • thanks for the answer, I reversed condition.. please looked up the after edit question.. – Ahmad Azwar Anas Jun 29 '13 at 7:13

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