Chomp
The two-player game of Chomp was published by David Gale in 1974.1 The rules are very simple, yet a
perfect general play strategy is still unknown.
Materials: Pencil and graph paper (or paper with a small hand-drawn grid). Or marker and
markerboard. Or square tiles (e.g. from Scrabble or Qwirkle). Or sugar/sweetener packets at a
restaurant. There are many possible ways to play.
Setup: Begin by creating a rectangular segmented “chocolate bar” where we pretend a corner piece is
“poisoned”. If drawing the board, either outline on graph paper or draw a rectangular grid2, and mark a
corner (e.g. the lower-left) as poisoned. If using tiles, form a rectangle of tiles, with one corner being
distinct.3
Rules: Players alternate taking rectangular “chomps” of the candy bar. The object of the game is to
avoid chomping the poisoned last square of the candy bar.
For each chomp, the player chooses an unchomped square. In addition to chomping that square, the
player also chomps all unchomped squares in the rectangle of squares from that chosen square to the
corner square farthest from the poison.
This is easiest to understand with an example. Suppose we play a game on a 3 row, 4 column board
with the poison in the bottom-left corner, which we’ll call (0, 0). Position (x, y) will be x columns to the
right of the poison and y rows up from the poison. In this game, we show nine turns in sequence:
The first player (who fills with diagonal lines for this illustration) chomps only (3,2), the farthest corner
from the poison. The second player (horizontal lines) chomps (2,1) and thus along with it the
unchomped squares of the rectangle from (2,1) to the farthest corner (3,2). This includes (2,2) and (3,1).
1
David Gale’s Chomp is based on Fred Schuh’s game of Divisors published in 1952.
It is best to have a different number of rows and columns. Otherwise, there is a trivial winning strategy. Can you
find a way to win easily as first player with a square board?
3
For example, place all scrabble/Quirkle tiles face-down, but leave one corner tile face-up, or use all sugar packets
except for a single, questionable artificial sweetener packet in one corner.
2
Play in this example continues through the ninth turn where the first player is forced to chomp the final
poisoned square and so the second player wins.
Strategy
Certain shapes of remaining chocolate bar tiles are “losing shapes”. When a player is presented with a
losing shape on their turn, they must either (1) chomp the last remaining poisoned square, or (2) chomp
to make a “winning shape”. A player presented with a winning shape can always make a chomp that
leaves the opponent with a losing shape. Thus, the player with a winning shape on their turn can (with
perfect play) herd the opponent towards chomping the poisoned square.
Questions for the curious:

For the 3-by-4 board, there are 7 losing shapes. One is the shape with only the poisoned corner.
What are the other 6 shapes?
 With perfect players, does the first player win or lose? That is, is the whole 3-by-4 board a
winning or losing shape?
 For which size boards is the whole board a winning shape for the first player?
Neller Variants: Add multiple poisoned squares anywhere in the board. (Variant 1) Avoid eating the first
poisoned square, or (Variant 2) eat the fewest poisoned squares. Chomp direction is decided before
play, or can be towards any corner.4
Play Grids
4
Play ends in variant 1 after the first poisoned chomp. In variant 2, play ends when a win/draw/loss is determined.