24

According to the Lomonosov tablebases, it's mate in 40 for black. While the queen can't force mate by herself, she can force a zugzwang. In this case, when the bishop is forced to move to e8. Then, it's a matter of giving checks until the queen forks the king and bishop. One of the longest variations given is as follows: [FEN "7k/5BpP/3K2P1/8/8/8/8/4q3 w -...


22

Here's a simpler way to see why it's winning for black: You're right that the queen cannot checkmate the king by itself, but it can stalemate the king [*] (an example pointed out by Ionut Deaconu) and that's all we need here as that would force the bishop to move. Once the bishop moves it's clear that material loss is unavoidable as either the bishop [**] or ...


16

A fortress in chess is a position in where the weaker side defends by making waiting moves, and where the stronger side cannot make any progress as long as the defender does not make a crazy move. A very well-known fortress position is the following: [fen "6k1/6p1/5r1p/8/Q7/8/7P/6K1 w - - 0 1"] It is impossible for white to make any progress if black just ...


15

Depth 64 means 64 half moves, it includes moves both by white and black. It isn't close to being able detect draws by means of the 50 move rule (100 plies). Especially since that is only the depth of the deepest line in the search, and to conclude it was certainly a draw, Stockfish would have to look at a huge number of lines that all eventually draw by the ...


12

You're right, at the first sight it looks like a draw: Black's king is kept out of play and the Queen cannot checkmate alone. Black's only idea for a win would be to sac the Queen on h2 and try to promote the other pawn, but that's obviously impossible because of the White Bishop still in play. However, there's a trick: White can be put in zugzwang by Black'...


10

White defends, but it is really a pain to hold this position. It took me few minutes to formulate correct plan since Stockfish found some strong ideas for Black. Below is the image of the fortress we are aiming for: If Black king tries to penetrate through queenside, he must aim for c3 square in order to create double attack on c2 pawn (using king and ...


9

The key here is zugzwang - White has an ideal defensive position at the moment, his king stops yours penetrating, his bishop covers the weak pawns on g4 and c4, and the pawn on a5 you can't easily get at is it is on a black square. BUT when white has to move he will either have to move his king (letting your king in), or move his bishop (leaving a pawn ...


6

I took the liberty of consulting with the Syzygy tablebases for a while, and came to the following conclusion: the endgame is drawn. This is far from obvious, but it has to do with the following fortress: [fen "4Q3/5pk1/7r/6KP/8/8/8/8 w - - 0 1"] Black draws this by shuffling the rook between e6 and h6. Bizarrely enough, as long as the h-pawn ...


5

This is a great question and a fun problem to mull over. Indeed the way it's written on wikipedia one gets the impression that amazon-vs-empress fortresses are trivial and easily attainable for the weaker side, where in fact it's very difficult to even come up with dummy examples where the empress stands any chance of holding (so not surprising not to see a ...


4

This is an easy position for Stockfish with tablebase, but very hard without it. The only way Stockfish can work out it's a draw is search all the way through 50-move draw. Otherwise, it'd think the position is winning for Black because Black has a knight up. Your browser may not have the capability to search such high depth. That's exactly the reason why we ...


4

It does look like a fortress. After 1...Qe2+ 2.Bb2 Qd2 White can wait with Ka2-b1-a2 or Bb2-a1-b2 depending on where the queen sits. Black cannot bring the king to d4 because of discovered checks, so the best try seems to be to travel to d5 and play a3 when the pieces are Qd2, Bb2, wKb1. Then Rxa3 Kc4 prevents the rook from coming back to c3 because of Qxc3 ...


3

It's a position with a big material disadvantage that still can be held. Eg. White: Kg1 Pg2 Black: Kd2 Pg3 + Bishop anywhere You are piece down but the opponent still can't win. Your position is a fortress.


3

The key to tackling these kind of positions in a game is to imagine where you would like to put your pieces and then see how you could achieve that. In this position for white the first aim would be to get the king to e5 to attack the e6 weakness and at the same time threaten to infiltrate on either f6 or d6. The problem is that black will have no problem ...


3

Try the TCEC adjudication rules, adapted for your situation. You can use more aggressive (or less aggressive) adjudication rules if you need them, e.g. by changing the threshold eval needed for adjudication. Win adjudication: Game ends in a win if there is a mate, engine resigns, time runs out, there is a crash, illegal move, by 6-men TB adjudication, or by ...


3

In this question the formation is referred to as a "turtle formation", although that's in the context of Bughouse. I've also personally heard it referred to that way in the context of Bughouse when playing over the board (although not with the rooks moved to those squares.) Bughouse aside, there's a lot wrong with doing things this way. The bishops are ...


2

This has definitely happened in endgames, e.g.: Queen and a minor piece versus two rooks: this is usually a draw for a knight and a win for a bishop, although the win takes up to eighty-five moves. The best method of defense is to double the rooks on the third rank with the opposing king on the other side and keep the king behind the rooks. This case with a ...


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