TEEKO "...is one of the greatest games of all time" said John Scarne, the game's Inventor

About Teeko, from BoardGameGeek:

The game Teko was first released in 1945. Teko is played on a 4x4 grid. The name was changed to Teeko (and the board grid changed to 5x5) for the 1952 release by John Scarne Games. Each player has four pieces. Players start by alternately placing pieces on a 5x5 grid, then alternate moves (moving one piece each turn to an adjacent point on the grid). Object is to get four pieces in a row, or to form a square with your four pieces. Teko Junior rules do not allow diagonal moves. A player can win with the same patterns, but can also win by blocking his opponent's 4 pieces from moving (on a 4x4 grid). In 1998 Guy Steele solved standard Teeko, as well as all variants proposed by the original inventor. The solution was brute force. Standard Teeko (only win with 4 in a row or a 2x2 square) is a draw with perfect play. Advanced Teeko (win with 4 in a row or a square of any size) is a win for the first player. Reimplementations or successors: A fully independently developed successor of the game with similar material and quite close winning conditions is Mondrago. Anyway instead of starting from a clean board Mondrago uses a fixed setup of the player's pawns. Besides winning with squares being parallel to board edges Mondrago uses diagonally and obliquely aligned perfect squares as well.