Here is a full explanation
https://en.wikipedia.org/wiki/Two_knights_endgame#Troitzky_line
Can you mate with two knights?
You can force a mate with king and two knights versus king, as noted many times in this forum. Such mates cannot be forced from positions with king and two knights versus king, however, assuming the convention that a mate is called forced only if the mating sequence is longer than one ply. In any forced mate with king and two knights versus king, the mating move must be a capture of a piece previously owned by the lone king.
So Black cannot escape mate here for example
but, by convention, the mate is not referred to as a forced mate in 1.
Here are a few examples of forced mates with king and two knights versus king.
The last is shown as the first diagram in @tygxc's Wikipedia link above, with the comment, "Checkmate position, but it cannot be forced (Seirawan 2003:17)", though I have managed the mate position numerous times in practice against the Nalimov EGTB.
There is some justification for that, in that the alternatives shown for Black on his last move in my example allow him to choose different mate positions, but they also say (unattributed)
Although there are checkmate positions with two knights against a king, they cannot be forced
which is simply incorrect.
It is however impossible to correct because the link is controlled by a small group of users, sock puppets and special ids who delete any corrections by people outside the group, but who don't bother to make the corrections themselves.
Except in very specific conditions, it can't be forced. Of course positions can be set up where mate is forced, but it doesn't generalize into the material in and of itself can force mate. If the material is randomly placed on the board, unlesss you get into one of those edge cases, mate can't be forced.
Except in very specific conditions, it can't be forced. Of course positions can be set up where mate is forced, but it doesn't generalize into the material in and of itself can force mate. If the material is randomly placed on the board, unlesss you get into one of those edge cases, mate can't be forced.
If you do enough practice with two knights v.pawn against an EGTB from general positions, you will encounter my third example quite often and checkmate positions with two knights against a king can be forced from many positions.
I did say any mate of depth greater than one would require extra material prior to the mate to force, so I agree that king and two knights cannot force mate against a lone king (with the conventional meaning in chess literature of 'force') but
Although there are checkmate positions with two knights against a king, they cannot be forced
is simply not true. I have previously attempted to correct the Wikipedia statement with, essentially, what you say in your post, but without success.
In fact OP asks only,
Can you mate with two knights?
so this would also do as an answer.
Understood. When I see the question, I almost always assume it's being asked in the context of KNN vs K and most of the time that's been a correct assumption.
It is interesting to note that while 2 knights cannot force mate vs K, if the opponent is unlucky enough to have a pawn (thus K and 2 N vs K and P) then things become interesting as the option of stalemate is no longer available to him and the two knights can in many cases force mate.
Not always unlucky. The pawn can in many cases force mate instead.
(But that's another thing you can't mention on Wikipedia.)
If the side with the pawn has the move he wins about as many positions as the side with the knights (or more under competition rules) but his winning chances are significantly reduced if the side with the knights has the move.
Overall in KNNKP assuming FIDE basic rules (no 50 move rule)
White wins 21.80 % of positions
Black wins 7.94 % of positions
70.26 % of positions are drawn.
Under competition rules (50 move rule in effect) some of the winning positions for both sides included above are actually draws, but mainly for White. The draw percentage rises to 77.5 % and White wins drop to 14.6 %. Black's change is negligible.
That being said, it's questionable whether anyone could actually reliably play the Black wins successfully against a tablebase (even though the maximum mate depth is only 74 compared with 115 for the White mates).
E.g. this is how SF14 plays a Black to play and mate in 60 against Syzygy
Losing to two knights with nothing else left on the board apart from opposing king is existingly possible IF the losing king deliberately allows the checkmate to happen!
You could evidently call it "suicide mate"!
The player with the bare king must know the exact moves to make to lose in this position and it's so hard for any inexperienced player to do, you could almost call it a skill!
I'm pretty damn sure however in any face to face tournament, both players and even the tournament supervisor would deem N+N+K v K a draw "by insufficient material"
However, in many software programs including those bot character programs on this website, will force a N+N+K v K endgame to proceed to the 50 move rule or stalemate because of the technical possibility of the suicide mate!
You mean king and two knights against lone king? Only if your opponent is dumb enough because it is not theoretically possible to force a win.
Paradoxically, although the king and two knights cannot force checkmate of the lone king, there are positions in which the king and two knights can force checkmate against a king and some additional material. The extra material of the defending side provides moves that prevent the defending king from being stalemated. The winning chances with two knights are insignificant except against a few pawns. These positions were studied extensively by A. A. Troitsky.
If the side with the knights carelessly captures the other side's extra material, the game devolves to the basic two knights endgame, and the opportunity to force checkmate may be lost. When the defender has a single pawn, the technique (when it is possible) is to block the pawn with one knight, and use the king and the other knight to force the opposing king into a corner or nearby the blocking knight. Then, when the block on the pawn is removed, the knight that was used to block the pawn can be used to checkmate.
Well I just got off the phone with a national master and he told me it is impossible to mate with just two knights. There would have to be at least one other pawn on the board in order for the mating sequence to work.
I have a book that has the mating sequence for two knights, though I do not want to give it to you
No it is possible, but you cannot force it.
But that is with a king’s help and the opponent foolishly backed into the corner, otherwise it is impossible to checkmate with a king jumping around the center or sides.