the first one white could win 
Endgames in fog of war:king+bishop vs king,king vs king e.t.c
Sort:
the second one is actually very rough,you do not know what your opponent's move is so you do not know where their king is,you might just sac your king.
the third one white will have a hard time trying to win,the king might be on the left,right,2 squares up,2 squares up and left/right,so black can to go to the left/right of the pawn and hope that the white king will go to the back of the pawn which will win if white goes behind the pawn.
Basically black can be at anywhere and if white move he will just take his pawn and form endgame 1 or his king and win
the last one should be a win by black if he had the luck
(basically fog of war endgame is luck based)
in #2, i think the best strategy is to shuffle back and forth on e2 and d2
in reality it would be draw accepted
I think it's impossible, or at least really hard to form a strategy unless you have more information. I would say that all of these are draws unless you get really lucky
in #1, there's a higher chance of luckiness.
in #3, you would know where the black king is because your pawn can't move to e5.
i would do Ke3, forcing the king back. Since the king is back i'll do Kd4. Now, e5.
If e6 is dark, the thing blocking the pawn from moving is the king, so repeat strategy. Otherwise the king is not in the square squares directly in front of your pawn, but I still don't know where the king is, and the possibilities of c6 and f4 zugzwang me. Hmm.
#4 Both the bishop and knight can get lucky, the white king will stay on the dark squares. Maybe white can do Kf2, and then shuffle the knight around his king.
Contrary to tacticspotter's comments, position-1 is drawn and in position-4 I would prefer the knight.
King + bishop vs. king:
The lone king can always stay on the opposite color of the bishop, and then it becomes a luck game of which king approaches the other by mistake.
White can secure a draw by keeping the king on the opposite-color of the bishop, and the bishop dancing around it.
King + bishop vs. king + knight:
I think it is mostly luck-based, but I would take the knight.
In short, since King + bishop vs. king is a draw, the side with an extra knight is not worse by having it...
The longer explanation is that the player with a bishop has no visibility of one color. While the range of a knight is smaller, it can see both colors, and help the king move around.
In your example, a knight on d1 can tell the king whether it is safe to move to d2 if you know that the black king is not on c1.
And in general, with a little dancing around near the king (so the bishop don't capture you for free), you are likely to get more board-information.
Bottom line, I think it is a draw but would prefer the side with the knight. Since even if you lose it, then by position-1 we know it becomes a draw.
Per qfcbv's question:
King + rook vs. king:
This is a likely-winning position, with slight chance of a draw.
If you have a slight idea where the enemy king is, you can cut the board "in half" so that the rook separates the kings so you can't lose. Then, move the rook and king together, scanning files such that the rook is always protected. Eventually you will see the enemy king, which probably won't see your rook. It can see the rook only if it is too close, but then you should try to back away the scanning, but the opponent will be risking coming closer to stay in sight.
If you are lucky, the opponent will remain in the line-of-sight and lose. Otherwise, keep scanning. Since the lone king has no information at all where you move, assuming you keep at a distance, while this scan doesn't guarantee a win, I find it likely to win within the 50-moves limitation.
About the single pawn endgame:
Surprisingly (or not) - a pawn on b or g file is a forced-win: a pawn sees the three squares in front of it, so it is possible to advance the king on the a or h file (respectively) while pushing the pawn.
In any other file, the lone king must choose one of two strategies:
(1) assume that white protects its pawn, which means that the king also moves forward, so it should try to ambush it by waiting on the side. For example, if the pawn is on the d file, the lone king should try to stay on the b or f files, such that: there is 50% on which side the king advances, times 50% who approaches first, so 25% chance to win if this is what the attacker does. If the pawn is on the a or h file, then there is only 1 side so we get 50% chance to win/lose.
(2) Assume that the pawn pushes alone at some point, and just take it. If this assumption was correct, the position is a draw (or a luck-game).
In both cases, if the assumption is wrong, the defender loses (either due to queening or to recapture of their king). Which choice is played is likely to depend on style/psychology as well as the "feel" of what is more common by other players. I would guess that most players will try to advance their pawn with the king's protection.
ys302 写道:
Contrary to tacticspotter's comments, position-1 is drawn and in position-4 I would prefer the knight.
alright then:
or
what is black's plan?
PS: stalemate is actually win because of capture the king
King + bishop vs. king + knight:
I think it is mostly luck-based, but I would take the knight.
In short, since King + bishop vs. king is a draw, the side with an extra knight is not worse by having it...
The longer explanation is that the player with a bishop has no visibility of one color. While the range of a knight is smaller, it can see both colors, and help the king move around.
In your example, a knight on d1 can tell the king whether it is safe to move to d2 if you know that the black king is not on c1.
And in general, with a little dancing around near the king (so the bishop don't capture you for free), you are likely to get more board-information.
Bottom line, I think it is a draw but would prefer the side with the knight. Since even if you lose it, then by position-1 we know it becomes a draw.
no really:
You constructed very specific cases. It is like claiming that in regular chess a queen-up endgame is "not a win" because you can set up a stalemate position. In Fog-of-War you can even place the kings near each other and claim one side loses, but you are missing the point.
In a typical end-game, the starting positions of the pieces are more chaotic, and not known to both sides.
And finally, in your last post (#12), assuming I play with your weird idea that both players know the exact board position, white can sacrifice the knight by playing "2.Kd2" ("2. Nd2" is a mistake) and running away, and hiding somewhere while shuffling on 2 specific dark squares. This will guarantee a 50% chance of winning, if that is not a draw.
And if the position is not known, after Nb1 I would have played Kb2, and then assuming the black king was still on b4 (afraid to approach if the knight didn't move), then I can shuffle my knight a3-b1-c3.
same idea
th3re4lalpH4z3r0 写道:
same idea
what do you mean?
Discuss strategies for fog of war Endgames here.
Examples:1.white to move,black knows colour of white bishop,neither player knows any position of opponents pieces in fog of war
2.White to move,neither player knows any position of opponents pieces in fog of war.There shouldn't be any strategy involved here...,should it?
3.white to move,neither player knows any position of opponents pieces in fog of war.as stalemate is a win in this mode the standard approach by black wouldnt work here.
4.white to move,white knows colour of black bishop,neither player knows any position of opponents pieces in fog of war