deutsche Version

Richard Réti's chess problem




White to move. White can achieve a draw.


The position seems to be favourable for Black. The white king cannot prevent the black pawn reaching the bottom row and becoming a queen. On the other hand, the black king can prevent the white pawn reaching the top row. But there is a solution for White to achieve a draw.

This problem was composed by Richard Réti whose portrait and biography can be found on a stamp page of this website. I think it appeals to mathematicians because it is like "minimal art".

Solution

The key move is  1. Kh8-g7 ... , followed by  2. Kg7-f6 ... . (We will show that the other three possible start moves lead to a winning position for Black.) If the black pawn tries to reach the bottom row the white king can protect his own pawn; then both sides will get a queen. If the black king attacks the white pawn the white king can catch up with the black pawn.

Let us first check three plausible move sequences which show how White can indeed reach a draw:

1.  Kg7  h4
2.  Kf6  h3
3.  Ke7

1.  Kg7  Kb6 or h4
2.  Kf6  h4 or Kb6
3.  Ke5  h3
4.  Kd6

1.  Kg7  Kb6 or h4
2.  Kf6  h4 or Kb6
3.  Ke5  K×c6
4.  Kf4

Now a complete analysis will be given. For every possible black move the optimal white move leads to a draw. There is no way for White to win (it should be understood that Black makes no mistakes) as the black king is able to take the white pawn in the second move. Only those move sequences will be checked in which Black tries to win as long as possible.




K...  is any move of the king.

means: A black pawn move is followed by a white pawn move. An attack of the black king against the the white pawn is followed by an assisting move of the white king.

means: The white king follows the black pawn and takes it.



Kg7 is the only white start move to reach a draw. Here are the black answers to other white start moves: