Lesson
White to move. Main line: 1. Kg7 h4 2. Kf6 h3 3. Ke6 h2 4. c7 h1=Q 5. c8=Q+
The idea is that a king moving diagonally does two jobs at once: it chases the h-pawn AND escorts the c-pawn. 1. Kg7 is the only move that draws — it heads for both at the same time, which a straight-line chase cannot do.
Count the squares and White appears to lose the race by miles. The board does not work that way: on an 8×8 grid the diagonal path is the same length as the straight one, so the king gains a tempo for free every step.
Réti published this in 1921 and it still surprises people. Shown as a replay it is immediate — you can see the king walking toward two things at once.
The position that looks impossible
White’s king is in the corner, miles from Black’s passed h-pawn. Count the squares: the pawn queens comfortably before the king can arrive. The king also cannot support its own c-pawn in time.
Both of those statements are true, and the position is still a draw. Richard Réti published it in 1921, and it is probably the single most famous endgame study ever composed.
One move in two directions
1.Kg7 is the only move that holds, and the engine agrees precisely: it evaluates as 0.00 while 1.Kh7 comes out at around −7, 1.c7 at around −8.6, and 1.Kg8 worse still.
The reason is that the diagonal path towards the pawn also moves the king closer to supporting c-pawn. The king does two jobs with one move, and whichever one Black tries to stop, the other succeeds.
Why the geometry works
On an empty board a king travelling diagonally covers the same number of ranks as one travelling straight. Distance measured in king moves is not distance measured by eye.
That is the whole content of the study, and it is genuinely useful: in king-and-pawn endings, count moves rather than trusting the visual gap.
1.Kg7: 0.00 — the drawing move, and the only one.
1.Kh7: About −7. The king chases the pawn on a straight line and arrives one move too late.
1.c7: About −8.6. Pushing first loses the pawn to 1...Kb7 and leaves nothing.
1.Kg8: About −9.5. Loses the tempo that the whole idea depends on.
Measure king distance in moves, not in visual distance — the diagonal is not slower.
A single move can pursue two goals; look for moves that do, especially when neither goal succeeds alone.
In king-and-pawn endings, count first and evaluate afterwards.
Source: Réti endgame study — https://en.wikipedia.org/wiki/R%C3%A9ti_endgame_study