2 Bishops vs Knight Endgame

From a practical point of view, would any of these longer, more esoteric positions result in checkmate even though a computer analysis says it will.  A computer may be able to calculate these positions, but humans might have some trouble.  There may be some players out there who can memorize all of the variations that might occur, but there wouldn't be many.  The result would be games that drag on while players make a futile attempt to checkmate their opponent because some computer analysis shows that it is possible.

I agree with Endgame. Why have the increment in these cases? It would just drag the game on. Since these kinds of endgames where there is a win, but it might take 100 moves, are so rare why not just have a set time limit to do it in no matter how many moves it takes. If someone is able to make 150 moves in 5 or 10 minutes, what's the harm?. It's probably way less than 1% of the time they would even happen, so I dont see how it would hurt anyone. But it would help those rare cases where someone is not allowed to win. Every other competitive activity has rules that cover the less than 1% occurances, I dont see why chess can't figure it out.

Chess does have a rule that covers those instances. You mate in 50 moves or if neither of you claim a draw, 75.

One thing that has not been mentioned.  In the position shown in #1, does checkmate occur without the knight being captured?  If it requires the knight capture (as shown in Wayne_Thomas' examples), then the 50-move count starts after the capture, and it's possible to mate with two bishops within 50 moves.

In all of the examples I've seen, the knight gets captured first.  In post #13, I posted one possible line starting from the diagram in post #1.

I checked the tablebase, and with best play on both sides it takes 51 moves to capture the knight (assuming that I counted correctly) and 16 moves to checkmate.  There were numerous instances were alternate Black moves would have shortened the game.

Also, as I went through the endgame, there were several white moves that would have resulted in a draw, so checkmate wasn't forced.  White had several opportunities to blunder.

Not if you play them right they can't.

Here is one pitfall.  During a game a player is not allowed to use reference material.  So players would be required to memorize all of the positions that may require more than 50 moves.  If they did recognize the position, they would have to contact the TD (or arbiter) who would have to verify that the position was one of the exceptions.  Is it really worth the effort?  Even in the Post #1 position, White is not guaranteed a win.  It's just highly probable that White will win (I've done a cursory check, and White would have to do something pretty stupid for the game to be drawn other than by the 50-move rule.  It's just a matter of how many moves will it take).

woton wrote:

"I checked the tablebase, and with best play on both sides it takes 51 moves to capture the knight (assuming that I counted correctly) and 16 moves to checkmate."

In my diagram in post #13, White would capture the knight on move 53.  Are you saying that White misplayed at some point?

I put the position into the tablebase (see link Post #4).  At the start, it said mate in 67.  When the knight was captured, it said mate in 16.  Subtracting, I get the Knight capture on move 51.

For anyone who has some time to spare, go to the link in Post #4, input the Post #1 position, and run through a non-best-move variation.  I composed  a 30-move variation using non-best moves and gave up when the program noted that White would win in 70 more moves (if you choose the wrong move, the number of moves to mate increases).  Since it's highly unlikely that both players would choose the best move every time, this game could drag on forever.

Can someone show me a tablebase calculated game that actually shows the 100 moves or whatever. I'm curious what it looks like.

My diagram in post #13 should be correct.

EndgameStudy

Go to the link in Post #4, input the position in Post #1.

You will see a list of all the possible moves together with the number of moves to mate associated with each move.  With White to move, if you choose the top move each time, mate will occur in 67 moves (or so the program says).  Instead of choosing the top move, choose Bc1-f4 where mate occurs in 73 moves.  You have now increased the number of moves to mate from 67 to 73.  Next choose the best move for Black.  Continue the process and at almost every White move, you will have a choice that increases the number of moves to mate.  It will go on forever.

Note:  The program does not calculate a sequence of moves.  You have to choose the move that you want to play.  The program just tells you that if you make the top move each time, mate will occur in 67 moves.  I created a series of moves using the poorest move for White and the best move for Black (I excluded White moves that led to draws).  That sequence would probably not occur in normal play, but neither would a sequence of moves where each player made the best move.

wayne_thomas

The only suggestion that I can make is go to the tablebase and compare your moves against the programs.  The program doesn't keep a count of the moves, it just gives the number of moves to mate following your move.  I didn't actually count the moves, I just assumed that the number of moves to mate was continually decreasing.  There may have been a move or two where there was no decrease.  The important point is that the Knight capture required more than 50 moves, so whether it was 51 or 53 is incidental.

My diagram seems to line up with the tablebase I checked.

wayne_thomas

Move 9 for Black

Your move Nh5

Tablebase   Ne8