Basic Strategies of Dots-and-Boxes

The three most basic strategies for playing Dots-and-Boxes are given below. Their "level" refers to the number of moves look ahead required to achieve them.

Level 0 - Random Play
The player makes moves at random.

Level 1 - Box Completion
The player will complete a box if possible, and otherwise move randomly.

Level 2 - Third-Side Avoidance
The player will complete a box where possible, otherwise playing randomly but avoiding if possible, completing the third side of a box. This denies the opponent the opportunity to complete a box on their subsequent move.

Winning Proportions for the Basic Strategies

The following figures were determined empirically by playing two million (2*10⁶) games between hand coded players implementing the appropriate strategies. In each case, both the player and the opponent moved first in half of the games.

Proportion of games won by Player against
Opponent.

Game Size 3 x 3		Opponent
Game Size 3 x 3		Level 0	Level 1	Level 2
Player	Level 0	0.5^A	0.003560	0.003255
	Level 1	0.996440	0.5^A	0.159186
	Level 2	0.996745	0.840814	0.5^A

^AThese figures were arrived at by observation,
and checked empirically.

Lex Weaver
October 7, 1996