Chomp - Rules, History & Strategy Guide

Chomp was invented by mathematician David Gale in 1974 and reached the world through Martin Gardner’s legendary Mathematical Games column in Scientific American. The setup is disarming, a chocolate bar with one poisoned corner, but the game encodes a deep result: by the strategy-stealing argument, the first player always possesses a winning strategy on any bar larger than a single square, yet no general rule for finding it is known.

The game is a dressed-up version of a 1952 number-theory game by Fred Schuh played with divisors, and it remains a staple of combinatorial game theory courses: easy to state, fully solvable by computer on small boards, and stubbornly unsolved in general, with research papers still probing three-dimensional and infinite bars today.

Chomp is a two-minute duel of permanent decisions: every bite removes a rectangle of chocolate forever, and the whole game funnels toward one poisoned square.

1. Start with a rectangular chocolate bar (Arcadia uses 4x7); the top-left square is poisoned.
2. On your turn, choose any remaining square and eat it together with every square below and to its right.
3. Alternate bites; there is no passing and no undo.
4. Never bite the poison while other chocolate remains.
5. The player left with only the poisoned square must eat it and loses.

• Read positions as staircases: after any bite the bar’s rows are non-increasing going down, and every staircase is either winning or lost.
• Memorize the lost shapes: the 2x2 block is lost for the mover, and handing it over wins the game.
• Use the 2-row rule: with two rows left, keep the top row exactly one square longer than the bottom.
• Prefer small corrective nibbles over big dramatic bites; tempo control beats material greed.
• Against a perfect opponent, plan the full line before your first bite: one inaccuracy is fatal, but the opening position is always winning for you.

Chomp scales in every direction: different bar sizes change the solved lines but not the theory, three-dimensional Chomp bites boxes out of chocolate bricks, and infinite ordinal Chomp is a genuine research topic. Its ancestor, Schuh’s divisor game, plays the identical structure with the divisors of a number, where the number 1 is the poison.