Though it's certain that this game will not attract as astoundingly in-depth analysis as
Conway's Game of Life, it does have the difference that it actually is a
game, the type you can play against someone.
It turns out that the proper name of the game is Philosophers' Football.
Setup
Draw a rectangular grid of 15 lines by 19 lines on a sheet of
posterboard. Be sure to count lines and not the spaces in between. Put a dot on the middle intersection of lines.
You will need a bunch of coins and something about the same size which isn't a coin, and perhaps which stands upright - one of those generic plastic "men" which might resemble men if the men are radially symmetric and have shrunken heads would work. This object is the football.
Gameplay
Play alternates between two players. A turn consists of doing one of the following:
- Placing a coin on one of the grid intersections
- Jumping the football over a coin or line of coins, either horizontally, vertically, or diagonally, and possibly continuing with more jumps. The player may then optionally remove any number of the coins which were jumped over.
An example:
. = grid intersection
o = coin
@ = football
In this board position...
....@...
...o....
........
...o....
...o....
........
a player may make jumps to the spaces numbered 1, 2, and 3 in order:
....@...
...o....
..1.....
...o....
..3o2...
........
However, if the player wants to stop the other player from getting
to that position, he can place a coin like this:
....@...
...o.... The football can still jump over those 2 coins, but it will
..o..... end up away from the line of coins. This may be advantageous
...o.... if there are more coins set up down the line. However, the
...o.... other player could get back with a well-placed coin.
Winning
The object of the game is to get the football into your "endzone" - the last grid row of the board on your side, or to jump over that row and off the board.
There's a lot of strategy to the game, as you would expect from John Conway, a pinnacle of game theory.
I learned this game at Mathcamp, where Conway spent a week. He was good at it, of course, but sometimes lost - at which point he would let out his characteristic bellow.