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Tricks in the K+P ending.

This is a nice ending ... a good thing to know in any K+P endgame.

pwn-eg2_pos1.jpg, 20 KB

8/ppp5/8/PPP3k1/8/6K1/8/8 w - - 0 1

It is White to move in this position. {See above.}

Can the first player win ... ... ... or is this just a draw?

This is a neat trick ... especially if you have never seen it before.
1.b6!, (Maybe - '!!')
The only correct way to proceed.

Why? The answers are simple:
# 1.) The Black King is far away from the Pawns.
# 2.) White's Pawns are far advanced.
# 3.) In such situations, a breakthrough is imminent.

[ Many students try to win by simply marching the King over ... here that does not work at all.

For example: </= 1.Kf3?! Kf5; 2.Ke3? Ke5; 3.Kd3?! Kd5; 4.Kc3?? Kxc5; {Diag?}
... and now Black is winning ("-/+") easily from this position.

(In this line, White could probably draw with 4.b6.) ]

1...axb6;
There are not a lot of choices for Black in this position.

[ </= 1...a6?; 2.bxc7 Kf5; 3.c8Q+ Kf6; 4.Qxb7, "+/-"

*************************************************************

        Or 1...cxb6; 2.a6!! bxa6; 3.c6 Kf6; 4.c7 Ke7;
        5.c8Q a5; 6.Qb7+ Kd6; 7.Qxa7 Kc5; 8.Kf4 Kb5;
        9.Ke4 a4; 10.Kd4, "+/-" with an easy win. ]

2.c6!! bxc6; {Box?}
This is pretty much forced.

[ </= 2...bxa5?; 3.cxb7 a4; 4.b8Q a3; 5.Qxc7 a2; 6.Qa5+ Kf6; 7.Qxa2, "+/-" ]

3.a6 Kf6; 4.a7, "+/-" {See the diagram below.}
White wins easily.

pwn-eg2_pos2.jpg, 19 KB

8/P1p5/1pp2k2/8/8/6K1/8/8 b

[ Also good is: 4.Kf4!?, winning.

*** *** *** *** ***

       If you need to see the proof, (that White is winning in this position); then here it is:
       4.a7 Ke7; 5.a8Q Kd7; 6.Kf4! b5; 7.Ke5 b4; 8.Qb7 c5; 9.Qb5+ Kc8; 10.Qxc5 b3;
       11.Qc3, "+/-"   White has a completely obvious and decisive advantage here. ]