52 ( +1 | -1 ) Quite a nice little study...... by migchess. Here's the diagram:
White to play: what result? Black to play: what result? An interesting feature is that the same position minus the Black e-pawn is a fairly elementary draw. Is the Black e-pawn, then, an asset (making the draw easier, or even leading to a win), or a liability (making the draw harder, or leading to a loss)?
60 ( +1 | -1 ) I would have thought...... People might have had a go at this. Somewhat surprisingly, perhaps, White to play is a win to White; Black to play is a draw.
1) White to play: 1.Kc4 Kd8! 2.Kb5 Kc7 3.Kc5 Kd7 4.Kb6 Kd8 5.Kc6 Ke7 6.Kc7 Ke8 7.Kd6 Kf7 8.Kd7 and Black has to let go the pawn: 8...Kf8 9.Kxe6 Ke8 10.Kd6 Kd8 11.e6 Ke8 12.e7 Kf7 13.Kd7 wins. The e6 pawn turns out to be a liability for Black, as it deprives the BK access to the e6 square. 2) Black to play: 1...Kf7 2.Ke4 Kg6 3.Kf4 Kh5 4.Kf3 Kg5 5.Ke4 Kg4 6.Ke3 Kf5 7.Kd4 Kf4 8.Kd3 Kxe5 Black has won the pawn, and the position looks similar to that in the first line, with colours reversed. But the fact that the Black pawn is so far away from the queening square makes all the difference. White has room to make the "opposition" work for him: 9.Ke3 (the only move) 9...Kd5 10.Kd3 e5 (say) 11.Ke3 e4 12.Ke2 Kd4 13.Kd2 e3ch 14.Ke2 Ke4 15.Ke1 Kd3 16.Kd1 e2ch 17.Ke1 Ke3 Stalemate.
116 ( +1 | -1 ) A quick glance suggests......this position is a draw if Black moves first, in much the same manner as migchess20's study.
My first thought here was that White to move also draws, but a minute or two sufficed to find the win for White. Now if White attacks via the K-side, 1.Ke4 Ke7! 2.Kf5 Kf7 with the "opposition" and White can not progress. 1.Ke4 Kf7? 2.Kf5 wins for White (in a manner analogous to (A) in my earlier posting.
But suppose White heads for the Q-side as being more promising on account of the Black king's distance from it. -1.Kc4 Kf7 2.Kb5 Kf6 3.Kc6?? Ke5 and Black wins! 4.K-any Kxd5 and White has no hope of stopping Black's pawn. White has to be more circumspect: -1.Kc4 Kf7 2.Kb5 Kf6 3.Kb6! Kf5! 4.Kc7! Ke5 5.Kc6 K-any 6.Kxd6 and White wins. Passive defence by Black won't do: -1.Kc4 Kd7 2.Kb5 Kc7 3.Ka6 etc, which we have seen before.
I gather the Soviet School of Chess had a theory of "complementary squares" (of which the "Opposition" forms a part, but only a part). It would be interesting to see some expression of that theory. These sorts of positions call upon such theoretical knowledge in order to spot 3.Kb6 as the winning continuation.
At any rate, it is remarkable how much Chess there is in such simple positions! Cheers, Ion
52 ( +1 | -1 ) Ion ....I know ~ I know~! Coincidentally, I just saw that study this week while thumbing thru my Horowitz (my first) endgame book. Always liked it for being short and sweet book but showing the usual, then the exceptions, pretty well. I go back to it every once in awhile and try again to learn the Square Of the Pawn ... for which I have some sort of mental block :( So my OTB ends up just like he says in the book "I go here, he goes there, I go, he goes, I go he goes I go ... How embarrassing~! }8~/
120 ( +1 | -1 ) Craig...Your Horowitz reminds me of the copy of Irving Chernev's "The Bright Side of Chess" that I used to have. I lent it to someone and never saw it again. Still mourn its loss. Among the games and other stuff, it had several very tasty endgame studies. The thing about the Reti study is, of course, that the Black King is inside the "Square of the pawn", the White king isn't even close, even though White moves first. Possibly my fondness for the ending stems from the revelations I experienced when reading my first chess book Gerald Abrahams's "Pan Book of Chess". Thing like rook- and bishop-pawns on the 7th rank drawing against the queen, where centre- and knight-pawns lose; how to win with K+P vs K; the Lucena Cover in rook endings; two pawns on the 6th rank defeating a rook etc. Or these rather neat ideas: White to play and win w OR w White to play: what result? All pretty exciting stuff - at least, it gave me a big edge in games against my schoolmates... ;-)
87 ( +1 | -1 ) OK, OK ...... I can see everyone is all agog about how the Reti study turns out: White to play: what result w It looks as though that even with the move, White hasn't a prayer. The Black king can catch the White pawn without trouble, the White king isn't even close to catching the Black pawn. So White tries 1.Kg7 ... - makes sense: closer to both pawns. 1...h4 - Bye, bye, sucker! 2.Kf6 ... - Erm... Wait a minute. If now 2...h3 then 3.Ke6 h2 4.c7 Kc7 5.Kd7 will secure the draw! Once the White king can protect the pawn, there's nothing to stop it. We'll see about that! 2...Kb6 -There! White can not protect his own pawn, nor can he catch Black's runner... Can he? 3.Ke5!!... - Bingo! If 3...a3, then 4.Kd6 whereupon White can shepherd his own pawn to queen, with a draw. The alternative is to take... 3...Kxc6 - and... 4.Kf4 reels in the Black pawn.