## Mar 31 Reti's Position

Here's a classic endgame puzzle called the Reti Endgame Study from 1921. It features an apparently lost position for White, but there is a way to force a draw. White is heading up the board (the white marker indicates White’s home turf). White to play and draw.

Solution below.

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It just looks so hopeless at first. White could try chasing the black pawn on h5, but the King would be too slow. Similarly White can't get the King over to help its own pawn on c6 before Black's King gobbles it up.

However White can threaten to do both of these things by moving along the main diagonal to g7. This closes some distance on both the white pawn and the black pawn. At this point Black can choose to head to b6 to threaten the White pawn, or they can advance their own pawn, but crucially they can't do both.

Let's say they advance their pawn forwards slightly, we get this position:

Now the same sort of logic applies. If the white King tries to chase the black pawn they are still not going to catch it. Similarly, if they head towards the white pawn then Black can move its king to b6 to get there first. But once again we can do both of those things at the same time by moving the white king to f6 which gives us the position below:

What can Black do here? Pushing the pawn again is tempting, but it enables White to draw by getting its king in to protect the queening square of c8 with a check. This means that both players will have a queen and a king and so it will be a draw.

Instead Black could move its king to b6 to attack the white pawn. In which case once again White can move the king along the main diagonal as below:

The logic is the same for the third time in a row: White is threatening to catch up with the Black pawn or protect its own pawn. Black can stop one but not both. Either both players get queens or neither do, so drawn.