Value of the Witch

There are discussions about the value of the Witch, and here is a good place to have the discussion. I have a thought about the Witch in the end game. She can block a lone pawn and stop a passed pawn. She has many legal moves where without a Witch you may be confronted with zugzwang. This makes her still worth more than a pawn in the end game. 

In the middle game, of course, her  value depends on the presence of allied long range pieces.

Did any one consider end games W K against K R, or W K against K B N? Must be draw. I am not sure about W K against K Q.

If we have an endgame with very little material, then the witch could be worth less than a pawn.

If black had pretty much any piece other than the witch here, he would quite easily at least draw this. All he would have to do is sacrifice his piece on the pawn. However, the witch can not do this and when whites pawn and king comes closer the witch will be unable to stop the pawn from promoting. Eventually this position is reached:

Black is in zugzwang. If black moves his witch white promotes. If black moves his king, blacks witch is hanging. If it was white to move white could play Ke8 and black is once again in zugzwang.

Queen + king is enough to win against King + witch, so white wins this.

This said, in most pawn endgames with many pawns I agree the witch is (usually) worth more than a pawn.

About King + Queen vs King + Witch, the witch can't really help much when the side with the queen uses both his king and queen to force the opponents king to the edge of the board. Once on the edge the queen just needs protection by the king to mate.

Interesting example Martin0 

thanks

K+N+N vs K+W is probably losing for K+W, while without the witch it's drawing.

K+R vs K+W is a draw.

K+G vs K+W is winning for the guard.

K+P vs K+W endgames will vary depending on which king wins the race to promotion square.

I think K+G vs K+W is winning, might be wrong though.

K+B+N vs K+W?

I must confess, I don't know the classic K+B+N technique without the witch, so not sure if zugzwang is a key tactic. If it is, then the witch will be enough to draw.

Perhaps it comes above the 50 moves limit of the 50 moves rule

It shouldn't, assuming perfect play. All that matters is zugzwang.

I think I could finish K+B+N vs K, assuming I have time to analyse, I just don't know it by heart. I suspect it's brute force rather than zugzwang, so I don't think the witch will save, but I'm not very confident about that.

K+W andvK+W+P?

It will depend on the position of the kings, but assuming the defending king is well positioned, then it's a draw, since he can move the witch and therefore avoid zugzwang.  In K+P vs K, the attacking side makes progress by forcing the defending king to move away from squares it wants to control. If the defender has a witch, the king doesn't have to move.

Surely the queen wins. Pin the rook, advance the king. The witch is powerless.

Hmm maybe not actually, the witch can block check while the rook guards it. Draw.

I'm sure what you mean is Q+K vs Q+G+G+K

Nice analysis going on here

https://www.chess.com/clubs/forum/view/witch-in-endgame