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When both kings are close to the pawn (and the black king is in front of the pawn, or else he can not reach it), there are two cases :
a)If the pawn is a a-pawn or a h-pawn the result will be a draw. The black king will possess the promotion square and if WHITE persists by advancing the pawn, BLACK will be stalemated.
b)If the pawn is not a a-pawn or a h-pawn, WHITE wins if he can place his king in a square that the pawn can advance to or capture on (a vital square). If he can not do this, it is a draw.
For example :
WHITE : Kc4, Pe4 BLACK : Kf6
WHITE wins if he has the move by playing 1.Kd5 and occupying the vital d5 square (in this example the vital squares are d5, e5 and f5). Play might continue like this : 1.Kd5 Ke7 2.Ke5 (taking the opposition) Kf7 3.Kd6 Ke8 4.Ke6 Kd8 5. Kf7 Kd7 6.e5 and the pawn promotes easily now.
If WHITE fails to play 1.Kd5 and instead plays 1.Kd4, the ending is drawn! BLACK will counter with 1…Ke6, preventing the white king from reaching a vital square.
Advancing the pawn does not help either, since after 2.e5 Ke7! 3.Kd5 Kd7! (taking the opposition again) 4.e6+ Ke7 5.Ke5 Ke8! 6.Kf6 Kf8 7.e7+ Ke8 8.Ke6 BLACK is stalemated. This ending is probably the most commonly arising and needs careful examination.
7. King + 2Bishops vs. King : This ending is winning.
8. King + 2Knights vs. King : This ending is drawn.
9. King + Bishop + Knight vs. King : This ending is winning, but is really difficult.
10. King + Bishop + Pawn vs. King : This ending is winning, except for the case where the pawn is on file a or h and the promotion square can not be controlled by the bishop.
The defending king will occupy the promotion square and will eventually be stalemated.
11. King + Knight + Pawn vs. King : This ending is winning.
Generally speaking, endings with the same material are drawn. Endings where one side has an additional pawn may either be winning or drawn, depending on the position.
Chances that the superior side will win decrease as the number of pawn reduces. For example, in a King + Knight + Pawn vs. King + Knight ending, the defending side will sacrifice the Knight for the Pawn and thus draw. The same action will not suffice if the pawns where 2 to 1 instead, for a pawn would still be left.
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