This game is played on an $8 \times 8$ chessboard with two kings. The columns are numbered from $A$ to $H$ from left to right, and the rows are numbered from 1 to 8 from bottom to top. The white king plays first and starts at the bottom left (at $A 1$), the black king starts at $A8$. The goal of the white king is to reach one of the squares $F 8, G 8$ or $H 8$, the goal of the black king is to prevent this. (The kings follow the movement rules of chess: on their turn, a king moves one square in any of the eight directions, and is not allowed to move into the range of the enemy king).
The crucial idea is that of opposition. If a king finds itself on the same column as its enemy, separated by an odd number of squares, then it can block the enemy indefinitely: no matter what move the opponent makes, it can always regain the opposition on the next move (this is an invariant). White has therefore lost as soon as Black manages to take the opposition. However, White can take the opposition from the start, keep it until reaching column $G$. Once in $G$, Black will move either to $F$ or to $H$, and then White moves in the opposite direction, advancing one row. If Black returns to column $G$, then White can always regain the opposition. White can always win in less than 17 moves; here is an example of a game where Black manages to block White for 17 moves: $1 . A 2 B 8,2 . B 2 C 8,3 . C 2 D 8$, 4.D2E8, 5.E2F8, 6.F2G8, 7.G2F8, 8.H3G7, 9.G3F7, 10.H4G6, 11.G4F6, 12.H5F7, 13.G5F7, 14.H6G8, 15.G6F8, 16.H7F7, 17.H8.