@SelfmateMan Huge thanks for the FENs and explanations. Many will learn from what you've written. I'll go over your work more than once to make sure that I fully absorb it.
@WarOverABoard im happy that you like it :)
@blackzombie #8 see de.lichess.org/forum/game-analysis/dont-understand. Stockfish sees a move repetition and therefore gives the eval 0.0
@Vinvin #14 that article has a good, precise definition of what a keysquare is: A square which wins the game when the king is placed there, no matter where the opponents king is and no matter which side to move. I mixed this up a bit in my first example from #6 ( 2k5/8/p1P5/P2K4/8/8/8/8 w - - 0 1 ). I will try to explain this example again, using the articles more precise definition. Its for my own learning purpose, and because its fun, but maybe this is also helpful for anyone else.
The (interesting) Key Squares (alias KS) are d7 and b6 (another KS is b7, but not d8, b8, a8, a7, because a bkd6 could take pawn c6). If the white king is there, it is won, no matter where the black king is or which side to move. One has not to calculate deeper (btw, a software which calculates such key squares in pawn endgames would be a nice thing to have).
White will not be able to get to d7 with his king from the right side, as black will play Kc7xc6. So lets see if we can work with KS b6.
The only route to b6 is c5. and the only square for black to protect b6 is c7. it is not a7 because then white reaches KS d7.
This brings us to another type of squares which i would call 'dynamic key squares' (alias DKS). White is won if his king is on one of such squares, but only if it is blacks move and if the black king is on one or more specific 'twin squares' (alias TS).
The first DKS is c5, and its TS is c7. Black then has to retreat and white is able to enter KS b6 and wins.
Another DKS is d6 and the TS are d8 and b8. Then, after ..Ke8 c7 white 'silently' (alias 'without checking', a well know motif) moves his pawn to the seventh rank. Then Black has to go to b7 and White reaches KS d7.
So now we know that all squares around the black king are TS (b8, d8, c7) or squares he can not enter (b7, d7).
From this follows that d5 is also a DKS and c8 is its TS. Because then black has to enter one of the TS b8, d8, c7 and white, from d5, can enter the related DKS c5 or d6.
We also see that if the white king is on b4/c4/d4 the black king is not allowed to move to TS c7 because then white can enter DKS c5.
Therefore white can go to DKS d5 from c4 and d4, black can go to the related TS c8 from b8 and d8. But c4 and d4 are connected, and b8/d8 are not. This means that white can go to d5 in two OR in three moves, black can only go to c8 in two moves. So white can 'lose' one tempo and black can not. This is a Zugzwang motif and it allows the triangle manoevre: 1.Kc4 Kb8 2.Kd4! (or 1.Kd4 Kb8 2.Kc4!) Ke8 and now White enters DKS d5 and wins.
That was fun :)
The (interesting) Key Squares (alias KS) are d7 and b6 (another KS is b7, but not d8, b8, a8, a7, because a bkd6 could take pawn c6). If the white king is there, it is won, no matter where the black king is or which side to move. One has not to calculate deeper (btw, a software which calculates such key squares in pawn endgames would be a nice thing to have).
White will not be able to get to d7 with his king from the right side, as black will play Kc7xc6. So lets see if we can work with KS b6.
The only route to b6 is c5. and the only square for black to protect b6 is c7. it is not a7 because then white reaches KS d7.
This brings us to another type of squares which i would call 'dynamic key squares' (alias DKS). White is won if his king is on one of such squares, but only if it is blacks move and if the black king is on one or more specific 'twin squares' (alias TS).
The first DKS is c5, and its TS is c7. Black then has to retreat and white is able to enter KS b6 and wins.
Another DKS is d6 and the TS are d8 and b8. Then, after ..Ke8 c7 white 'silently' (alias 'without checking', a well know motif) moves his pawn to the seventh rank. Then Black has to go to b7 and White reaches KS d7.
So now we know that all squares around the black king are TS (b8, d8, c7) or squares he can not enter (b7, d7).
From this follows that d5 is also a DKS and c8 is its TS. Because then black has to enter one of the TS b8, d8, c7 and white, from d5, can enter the related DKS c5 or d6.
We also see that if the white king is on b4/c4/d4 the black king is not allowed to move to TS c7 because then white can enter DKS c5.
Therefore white can go to DKS d5 from c4 and d4, black can go to the related TS c8 from b8 and d8. But c4 and d4 are connected, and b8/d8 are not. This means that white can go to d5 in two OR in three moves, black can only go to c8 in two moves. So white can 'lose' one tempo and black can not. This is a Zugzwang motif and it allows the triangle manoevre: 1.Kc4 Kb8 2.Kd4! (or 1.Kd4 Kb8 2.Kc4!) Ke8 and now White enters DKS d5 and wins.
That was fun :)
Oh my. I have just read #6 again and i see that i posted the wrong fen in paragraph 5! Here is the correct position, #6 and #15 are referring to it.
de.lichess.org/6zPC8Yx2
de.lichess.org/6zPC8Yx2
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