Witch in endgame

I've seen a few people suggesting the witch is useless in endgame. While the witch is clearly a better piece with ally rooks, bishops and queen, it's unwise to dismiss the power of the witch in endgame. 

*disclaimer* any resemblance to any live position is purely coincidental, please pm me if there's a problem with a position I post and I'll quickly remove it.

PLEASE DO NOT DISCUSS ANY ONGOING GAMES IN THIS THREAD UNDER ANY CIRCUMSTANCE

Here's a few examples of the witch in endgame...

TEMPO

White to move and win.

Without the witch, this is drawn. But any witch move wins for white, as it wastes a tempo, something black cannot do. 

1. Wa1 Kg7 2. Kxf5 Kf7 3. g6 Kg7 4. Kg5 Kg8 5. Kf6 Kf8...

Now white wastes another tempo! 

6. Wj1 Kg8 7. g7 Kh7 8. Kf7... 1-0

We can also talk about tempo in the context of saving lost endgames.

White would like to play Rh5 to drive the black king to f8, but black has a witch and does not have to move the king. White is unable to force checkmate.

Of course, having the ability to waste a tempo isn't always a good thing.

White to move and win!

If anyone wants to add any positions, feel free, just make sure they are either completed games or arbitrary positions.

Tomorrow I'll talk about blocking.

very nice topic!

Funny you mention  this

I was looking at your game yesterday and noticed a comment you made about the Witch being weaker.

I had already been visiting how to value the Witch and read an old post by @Vickalan have to find again (will edit and link)

<edit> here it is...

https://www.chess.com/forum/view/chess960-chess-variants/comparison-of-material-power-in-variant-chess-games

Not specifically about the Witch, but I concluded the value here to be implied as 5 points (equal to a rook).

Some general thoughts I wrote down just before finding the posts mentioned above:

Piece Mobility (Min/Max)
Rook=16 (from any square)
Queen=30 (from a center square)/ 23 (from a corner square)
Bishop= 7 (from a corner) 14 (from a center square) 9 max from 1st rank, 11 max from 2nd rank, 13 max from 3rd rank or central 4th
Knight= 8 from 24 central squares, 2 from a corner
King= 8, 3 from a corner
Guard= 8, 3 from a corner
Witch= 38 from a center square, 25 from a corner

Power of Pieces in relation to maximum mobility and board size (80 squares)

Knight-
Max global occupancy potential=80/80 (100%)
Max local occupancy potential=8 (10% of board) from 24 central squares =30% of board (any 3rd or greater ranks and files)
Max local occupancy potential=6 (7.5% of board) from 36 squares=30% (any 2nd rank and files c through g)
Max local occupancy potential=4
Majority of squares=60 (75% of board) are 6 or 8 (75% of mobility) and require at least 1 move to achieve.

Bishop-
Max global occupancy potential=40/80 (50%)
Max local occupancy potential=14 (17.5% of board) from 4 center squares = 5% of board

The Witch
It increases actual mobility/range of the slider pieces (5) and pawns (10 from initial position). As an "enabler/disabler", it can increase 3 pieces' abilities to develop from a center 3rd rank without any pawns developed by 21 squares!!! At the same time, it can make enemy pawns/pieces transparent, virtually opening files/diagonals that are otherwise closed.
For example, slider pieces can benefit from the Witch by developing without tempo spent on pawn moves, 2 pieces from a 3rd rank and 3rd/4th file. An enemy Black pawn (on e4) advanced adjacent to the Witch (on e3) could incite a check on the Black King!
Also, castling opportunities are increased with the Witch and an adjacent piece's transparency.
It has no ability to capture, but can sacrifice/self pin (unlike a King) and block a powerful passed pawn (possibly worth 9 points?).
The leaping abilities of the Witch (imo) make it more valuable than a Knight.
For these reasons, the Witch is a very valuable piece. With more slider pieces remaining and in positions of a more closed nature (intial position or all central pawns present), the Witch's value is greatest.
Of the "mobile" pieces (Queen/Rook/Bishop/Knight), the Witch has no effect on the Knight. The Knight's value should increase in closed positions without any (friendly and unfriendly) Witch on the board.

Of course, the opposite also applies...fewer sliding pieces diminishes the Witch's value.

Sorry to bombard your endgame specific topic on the Witch with values concerning all pieces on the board.

Since values are dependent on the positions/situations (like knights and bishops), I thought a range of possible values might be helpful.

1.Ke7 any move other than 1...Kh8 or Kh7

2.Rg5+ Kh8, h7, or h6

No way to walk the Black king to the side?

the only way to win this endgame is to trap the witch and then win K + R endgame

but it's really really hard.

Here's an example of a witch being trapped.

Whoever's turn it is to move, the witch is lost.

If it's white's move, white can simply take the witch with Rxa1+ and be winning the endgame.

If it's black to move, it's a little more complicated. The witch can't travel through the white nor black kings. If the witch stays on the a file, it's gone. If black moves Wb1 (only move delaying loss of witch), it's still lost.

1... Wb1
2. Ra1 Kc1
3. Kb3!

Zugzwang and black has to lose the witch and it is a lost endgame.

In this topic Martin0 gave a nice endgame position

https://www.chess.com/clubs/forum/view/value-of-the-witch

I can't imagine white can force this. Black can obviously blunder to lose, and certain positions are not good for black either, for example...

1. Ra2+ Kbx 2. Rb2+... and white forks the king and witch. Black cannot be complacent, he can't just move the witch to any unprotected square, but in this position the only bad squares, other than direct attack, are a1 and b1.

In the position you post, black has made the mistake (presumably) of putting his king in the same corner as the witch. Best is for black to head towards j8. Of course, maybe black's last move was Kxd1, in which case he was already lost.

Eventually the position will reach a similar one to the one I posted. Zugzwang is an essential tool in a K+R vs K endgame, but if black has a witch then he can simply move it instead of the king. So long as the witch and king have sufficient distance then black is fine. 

Any endgame that requires zugzwang to finish, the witch will save in all but extreme examples.

For clarity, zugzwang is the obligation to move causing one's downfall. It literally means "move compulsion", in my K+R + K+W endgame, Rh5 would put black in zugzwang if not for the witch because black has no choice but to play Kf8, which allows mate. If black's king can stay on g8, there is no checkmate, which is why the witch is important in this endgame.

The witch may not be completely useless but in most endgames where there are still plenty of pawns and minor pieces, I would rather have a minor piece than a witch.

Of course, but we nearly always prefer to have a minor piece rather than a pawn, too. We would not then assume the pawn is of no value to us though.

There will be some endgames where a witch is actually better than a minor piece, but they will be rare. However, the witch can still be a minor piece in its own right, better than a pawn or two, and perhaps make the difference between a win and a loss when facing a rook, for example G+W vs R. There are some things I'll have to wait to talk about, but I wanted to get on to the subject of blocking.

First of all, there's the obvious...

White to move and draw.

Obviously, white is losing if he doesn't have the witch, as he can't get to a1 fast enough, But after 1. Wa1, black now has to take a1 with the king, and then move out of the way of the pawn. He doesn't have time though.

1. Wa1 Kb5 2. Kg2 Kb4 3. Kf3 Kb3 4. Ke2 Kb2 5. Kd2 Kxa1 6. Kc1/Kc2 and black blocks his own advance.

The witch can also block checks, which frees up other pieces to attack.

Here, black has a very advanced pawn, and a bishop for witch. White has a resource though...

1. Rxc1 Rxc1+ 2. Wi1!... black is powerless to stop Bf4, which either mates or wins the rook, while also controlling black's promotion square. Black's best play is 2... Bf5 3. Bf4+ Ki8 4. Bxc1 Bxg4... white is the only one with winning chances, but perhaps black can blockade this position. I doubt it, but this position certainly demonstrates that blocking with the witch was far better than with the bishop. The witch proved to be better than black's bishops.

And we can block files and ranks...

Black is threatening to infiltrate with Rf2, but white can draw this endgame.

1. Wf4! Rd8 2. Wd4... black has no way through. RxW is never an option as white is able to stop either the c- or g-pawn, and should even be able to push for a win with a passed e-pawn. 

Of course, these endgames are unlikely, but the basic principles will apply a lot more often than you might think. The witch can be a valuable endgame piece, even without supporting pieces like rooks, and if your opponent has forced you to give up a rook for his witch, for example, and has you in trouble, the endgame power of the witch might be a saving resource and form your defensive strategy. A witch can hold off a rook in many situations. That's not a useless piece.

That last position, black might be able to win it actually, he has time to centralise his king before giving up his rook. That might be enough. But it doesn't really matter, I just wanted the basic idea to be obvious.

I n practice I would say you're right, but assuming perfect play I'm gonna say it can be done.

Why did you quote my entire post? Yes you're right, but I don't care enough to fix it. 

Just like I'm too lazy to properly analyse these positions! The witch position is a bit sloppy on my part, but I'm simply trying to make the point that it's a useful endgame piece that can defend the king, which in turn allows a better minor piece to attack. I'm pretty sure the rook and pawns position is winning for black, too. That's easy to fix, just get rid of the a6 pawn.

https://musketeerchess.net/tools/boardpainter/

you gave me the idea to make an endgame manual

I'm happy about that panda. Link me when it's ready please.

Cool topic. I've seen the witch used in some games simply to stop a pawn from promoting. Example is here:

58.c7...Wc8
59.Bh8...b3
60.Kh4...Nb4
61.Ki5...Kg6
62.Kj6...Nd3

(Black eventually wins).

Complete game is here: (Tomato vs Ry).