Tripples

Trippples is a 1972 William T. Powers' race game, where the board is constructed with a set of pieces marked with their possible moves.

According to BBG:

Trippples is played on a 8×8 board as opponents race from one corner to the other. On the board are placed, in a pre-movement round, tiles with three arrows which point to three of the eight surrounding spaces. Each player plays these tiles alternatively until they have all been played. Movement is made by following the arrows, and avoiding the neutral zone in the middle. The game ends when one player reaches his goal or when both players cannot make legal moves.

The key game mechanism is that your move options are determined not by the three arrows on the tile under your (transparent) game piece, but by those under your opponent's piece. Thus, each move is chosen to try and limit your opponent's next as well as to try and guarantee yourself a good selection of choices. This adds an element of bluff and second-guessing to the game.

The rulesheet:

The game does not have the property of converging to the endgame, it seems possible to walk on circles, never be able to reach your final corner. That's why the rules have two extra winning conditions for these types of situation. To slightly reduce this problem, it's better to consider that empty tiles allow for unrestricted moves.

There's a version using hidden information, where all tiles start upside down, and are only revealed when a piece stops there. It's also possible to add an element of luck, by shuffling the tiles and placing them on the board at random.

This game has patent US3820791. When searching this game I came by the blog The Dreams of Gerontius, which has a post about Tripples, and mentions an much older 1894 patent (US519326) for a game with some board design similarities, 

This is a game for two or four players, with capture and scoring themes.