Dots and Boxes
Draw, close the boxes, play again: beware of the long chain.
The game of dots and squares. Whoever closes a box wins it and plays again; the whole art lies in forcing your opponent to open the long chains.
- Players
- 1 or 2 players
- Length
- 5 to 15 min
- Against the AI
- Two players on one device
15 days of full access, no account · No download
How to play
Goal
On a grid of dots, players take turns drawing a horizontal or vertical line between two neighbouring dots. Whoever draws the fourth side of a box wins it. The player who owns the most boxes at the end wins.
How it works
- One line per turn. If your line closes at least one box, you claim that box (or boxes) and you must play again.
- A chain is a run of boxes with two sides drawn: as soon as a line is drawn in it, the opponent can take all of them in a row.
- The game ends when all the boxes are taken.
Strategy
- Safe lines: as long as any remain, never draw the third side of a box.
- Double-dealing: when taking a long chain, keep control by leaving the last two boxes to your opponent (four for a loop); they will then have to open the next chain.
- Long chain rule: the first player aims for the number of dots in the grid added to the number of long chains (three boxes or more) to be even; the second player, odd.
About the AI
The AI reasons in “strings and coins”. It always takes a free box, and at the end of a chain it chooses between taking everything and the double-deal. Endgames made of independent chains and loops are evaluated exactly by dynamic programming; an alpha-beta solver with a transposition table calculates the last lines perfectly (up to 30 at Master level, which is the whole game on 3 × 3 from the second line). In the middle game, it simulates thousands of sequences of safe lines to win the chain parity battle.
AI levels
- BeginnerOften takes the boxes offered, but sometimes draws the third side of a box.
- AmateurTakes every box and avoids giving gifts, with no chain strategy.
- IntermediatePlays safe, calculates the last twelve lines exactly and masters the double-deal.
- ExpertAnticipates the chain battle by simulation and calculates the endgame exactly.
- MasterLong chain rule, double-dealing sacrifices and a perfectly calculated endgame.
