Note that this information has been copied directly from the T2 wiki, and lightly edited. If you find information that is false or innacurate, please update it!
Heket's Rake is based on the game "Philosopher's Football" or "phutball".
The game is played on a 15x9 board. There are two types of piece on the board: the rake, and mushrooms. The goal is to move the rake to your side of the board. Play alternates starting with the 'west' player moving first; to compensate for the first-move advantage, the rake starts offset one square in east's direction.
On each turn, a player may either place a mushroom or move the rake. Mushrooms may be placed in any open square on the board. The rake moves by jumping over one or more mushrooms vertically, horizontally, or diagonally to an empty space. The jumped mushrooms are removed from play. It is possible to chain multiple jumps together.
For example, consider the following board ('R' indicates the rake, 'M' a mushroom):
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . M M R M . . . . . . . . . M . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
West may jump the two mushrooms to the left of the rake, followed by a jump over the lower-left mushroom, resulting in this board:
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . M . . . . . . . . . . . . . . . . . . . . . . . R . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
It is not possible to jump off the north or south edges of the board. It is possible to jump off the east or west edges, resulting in a win for that side, unless that move would also take it off the north or south edges. (Note that it is sufficient for the rake to reach the final east or west row for that side to claim a win.)
Akhet wrote a fantastic program for recording and studying rake games. It is available here. It is extremely useful for planning ahead. Most good rake players will plan at least 4 or 5 moves ahead.