Tic-tac-toe is a simple turn based strategy game where 2 players, X and O, take turns marking spaces on a 3 x 3 grid. The first player to place 3 of their marks in a horizontal, vertical, or diagonal line is the winner.

Observation Space

The observation is a dictionary which contains an 'obs' element which is the usual RL observation described below, and an 'action_mask' which holds the legal moves, described in the Legal Actions Mask section.

The main observation is 2 planes of the 3x3 board. For player_1, the first plane represents the placement of Xs, and the second plane shows the placement of Os. The possible values for each cell are 0 or 1; in the first plane, 1 indicates that an X has been placed in that cell, and 0 indicates that X is not in that cell. Similarly, in the second plane, 1 indicates that an O has been placed in that cell, while 0 indicates that an O has not been placed. For player_2, the observation is the same, but Xs and Os swap positions, so Os are encoded in plane 1 and Xs in plane 2. This allows for self-play.

Legal Actions Mask

The legal moves available to the current agent are found in the action_mask element of the dictionary observation. The action_mask is a binary vector where each index of the vector represents whether the action is legal or not. The action_mask will be all zeros for any agent except the one whos turn it is. Taking an illegal move ends the game with a reward of -1 for the illegally moving agent and a reward of 0 for all other agents.

Action Space

Each action from 0 to 8 represents placing either an X or O in the corresponding cell. The cells are indexed as follows:

0 | 3 | 6
_________

1 | 4 | 7
_________

2 | 5 | 8

Rewards

If the game ends in a draw, both players will receive a reward of 0.