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# Case Study: 7 Knights vs 3 Queens is a draw!

Hello everyone,
I discovered an interesting case study on Wikipedia about 7 Knights vs 3 Queens game set up according to standard chess:
lichess.org/editor/3qkq2/4q3/8/8/8/8/3NNN2/2NNKNN1_w_-_-_0_1

Here, 3 Queens can't win again 7 Knights and the knight side can force a draw. With computer analysis and also from analysis of Stockfish 13 NNUE, I found that without 50 move rule, the knight side can still force a draw by forming some particular positions on board where Queens can't do anything.

"Chess-variant theorist Betza identified the 'leveling effect', which causes reduction of the value of stronger pieces in the presence of opponent weaker pieces, due to the latter interdicting access to part of the board for the former in order to prevent the value difference from evaporating by 1-for-1 trading. This effect causes 3 queens to badly lose against 7 knights, even though the added piece values predict that the knights player is two knights short of equality."
Courtesy: en.m.wikipedia.org/wiki/Chess_piece_relative_value#Standard_valuations

I played out against Stockfish 8:
https://lichess.org/zKWKKHH4

At analysis board, Black has high advantage but the quoted text from Wikipedia justifies why it's a draw. And if Queen side play poorly, it can even lose!

Running the position at analysis board for enough time after each move to know the best move and playing it, is no different but another experiment that shows how is this a draw.

I found it cool and though to share with chess.com community!

That's a known dtaw

Any database games where it appeared in master play???

Well if white plays the best moves black can force a draw by repetition check or win by checks and forks

Or somthin else

Not always

In fact I just generated 5 random KNNNNNNNKQQQ positions and got SF12 to play them against itself, giving the move to the knights. In each case the queens won, so I suspect OP's assertion is tosh.

That starting position is illegal.

Which?

Here's the first position I posted.

It's double check in the second last diagram.

AussieRookie wrote:

It's double check in the second last diagram.

You're right (I assume you meant third last). The positions were generated randomly subject only to the side not to move not being in check, so a good chance of that happening with the specified material.

@Akbar2thegreat

SF analysis cannot be trusted if the mate is of any depth. This is what it does with a mate in 50 with just 1 queen and 2 knights.

It turns it into a draw on its first move according to the EGTBs. You can assume that it will be considerably less accurate with 3 queens and 7 knights.

The position you say is a draw in your post could well be a deep mate. Similarly my SF win in 27 (second example in the random positions) could actually be a draw.

Nevertheless it seems apparent that the normal result should be a quick win for the queens.

Wow I got into this position 3 times in the last week and didn’t know what the eval was, thanks guys

rychessmaster1 wrote:

Wow I got into this position 3 times in the last week and didn’t know what the eval was, thanks guys

Me too!

@MARattigan

I know that everything depends on position. That's why I wasn't talking about any set up rather I specified one such with the criteria that the queens can't win the knights in few moves and that the knights are near towards it's king.

@morphy1023

It hasn't ever occurred at the top level because of it's complexity and uniqueness though the position can be reached theoretically. The major reason being that before such a position being reached the either player resigns or both agrees to a draw.

@krongabot

No bro! It's a theoretically known draw.

@MARattigan

Two knights can generally draw against a queen if the king is near its knights and they are in a reasonable position by setting up a fortress.

Thus, only in certain positions can a queen win against two knights.

If you don't believe me, see this:

https://en.m.wikipedia.org/wiki/Pawnless_chess_endgame#Queen_versus_two_minor_pieces

Akbar2thegreat wrote:

@MARattigan

Two knights can generally draw against a queen if the king is near its knights and they are in a reasonable position by setting up a fortress.

Thus, only in certain positions can a queen win against two knights.

If you don't believe me, see this:

https://en.m.wikipedia.org/wiki/Pawnless_chess_endgame#Queen_versus_two_minor_pieces

Wikipedia, as is often the case, sums it up so well that it comes to far more than the references ever have said. What Müller and Lamprecht actually say is, "the computer database results show that the ending is generally drawn if the defending king isn’t separated from the knights and they occupy reasonable positions". M&L are referring to practical results taken from the ChessBase Mega Database, not a theoretical evaluation.

In fact, according to the tablebase statistics (either DTM or DTZ50) less than 27% of two knights v. queen positions are drawn, the remainder being won by the queen (except for a negligible percentage that are already mate or mate on the move for the two knights).

The discrepency appears to be mainly due to players (as SF12 in the above example) generally failing to find the wins from winning positions.

I think you might find it difficult to give a convincing proof that the three queens v. seven knights position you gave is actually drawn. Certainly, "This effect causes 3 queens to badly lose against 7 knights, even though the added piece values predict that the knights player is two knights short of equality" appears to be nonsense because most positions  seem to be demonstrably won in a small number of moves by the queens, even if the side with the knights has the advantage of first move.

I imagine very few practical games would involve seven promotions, five of which were under-promotions.