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Introduction
Diffusion is a two player game which employs a Mancala board and
a set of like-colored stones. Here a 2x6 board with 48 stones will be used. Initially the
board is set up with four stones in each of the small pits and no stones in the large pits,
as shown in Figure 1. Two 2x3 'blocks' are outlined in Figure 2. Each player owns the
block to his left. Numbers indicate the stone count in each pit. Diffusion is a unique,
robust addition to the family of Mancala games. Draws and ties cannot occur in
Diffusion. Mark Steere invented Diffusion on January 20, 2006.
F E D C B A
.---.---.---.---.---.---.---.---.
| | 4 | 4 | 4 | 4 | 4 | 4 | |
| |---+---+---+---+---+---| |
| | 4 | 4 | 4 | 4 | 4 | 4 | |
'---'---'---'---'---'---'---'---'
G H I J K L
Figure 1 -- Diffusion Board - Initial Setup
.-----------.
.-----------| Block B |
.---|---.---.---|---.---.---|---.
| | 4 | 4 | 4 | 4 | 4 | 4 | |
| |---+---+---|---+---+---| |
| | 4 | 4 | 4 | 4 | 4 | 4 | |
'---|---'---'---|---'---'---|---'
| Block A |-----------'
'-----------'
Figure 2 -- Blocks A and B
Object of the Game If, at the conclusion of a turn, one of the two blocks is
completely vacated, the owner of that block wins.
Moves Players take turns making moves. You begin your turn by scooping all of the
stones out of any one of the 12 small pits which contains stones. (There will never be
more than five stones in a small pit.) You conclude your turn by distributing those
stones into pits adjacent to and surrounding the newly emptied pit, as described in
the following sections. Players cannot pass on their turn. There will always be at least
one move available.
Stone Distribution for Edge Small Pits Having scooped all of the
stones out of one of the four non-corner small pits in your near row, you must distribute
those stones into small pits which are orthogonally or diagonally adjacent to the newly
emptied pit as follows: Place one stone into the small pit immediately to the right of the
emptied pit, and proceed counterclockwise around the emptied pit, depositing all of the
remaining stones, one stone per small pit, in a continuous sequence (no gaps).Figure 3
shows such an example.
.---.---.---.---.---.---.---.---.
| | 4 | 4 | 4 | 4 | 4 | 4 | |
| |---+---+---+---+---+---| |
| | 4 | 4 | 4 | 4 | 4 | 4 | |
'---'---'---'---'---'---'---'---'
Figure 3a -- Starting Position
.---.---.---.---.---.---.---.---.
| | 4 | 4 | 4 | 4 | 4 | 4 | |
| |---+---+---+---+---+---| |
| | 4 | 4 | 0 | 4 | 4 | 4 | |
'---'---'---'---'---'---'---'---'
Figure 3b -- Scoop All Stones out of Edge Small Pit
.---.---.---.---.---.---.---.---.
| | 4 | 5 | 5 | 5 | 4 | 4 | |
| |---+---+---+---+---+---| |
| | 4 | 4 | 0 | 5 | 4 | 4 | |
'---'---'---'---'---'---'---'---'
Figure 3c -- Distribute Stones Counter-Clockwise Around Emptied Small Pit
Stone Distribution for Corner Small Pits Having scooped all of the
stones out of one of the four corner small pits, treat the adjacent large pit as two empty
small pits, and follow the distribution rules described in the preceding section. Figure 4
shows such an example.
.---.---.---.---.---.---.---.---.
| | 3 | 0 | 2 | 0 | 0 | 2 | |
|20 |---+---+---+---+---+---| 20|
| | 0 | 0 | 0 | 0 | 1 | 0 | |
'---'---'---'---'---'---'---'---'
Figure 4a -- Starting Position
.---.---.---.---.---.---.---.---.
| 0 | 0 | 0 | 2 | 0 | 0 | 2 | |
|---|---+---+---+---+---+---| 20|
| 0 | 0 | 0 | 0 | 0 | 1 | 0 | |
'---'---'---'---'---'---'---'---'
Figure 4b -- Scoop All Three Stones out of Corner Small Pit
.---.---.---.---.---.---.---.---.
| | 0 | 0 | 2 | 0 | 0 | 2 | |
|22 |---+---+---+---+---+---| 20|
| | 1 | 0 | 0 | 0 | 1 | 0 | |
'---'---'---'---'---'---'---'---'
Figure 4c -- Distribute Stones Counter-Clockwise Around Emptied Small Pit
No Six-Count Small Pits If the addition of a stone to a small pit would increase
the number of stones in that small pit to six, you must add that stone to one of the large
pits instead. Then resume distributing the remaining stones, starting with the next
small pit in the counterclockwise direction around the emptied pit. Figure 5 shows
such an example. As noted earlier, a small pit should never contain more than five stones.
.---.---.---.---.---.---.---.---.
| | 2 | 0 | 1 | 4 | 0 | 1 | |
|20 |---+---+---+---+---+---| 10|
| | 0 | 0 | 5 | 5 | 0 | 0 | |
'---'---'---'---'---'---'---'---'
Figure 5a -- Starting Position
.---.---.---.---.---.---.---.---.
| | 2 | 0 | 1 | 0 | 0 | 1 | |
|20 |---+---+---+---+---+---| 10|
| | 0 | 0 | 5 | 5 | 0 | 0 | |
'---'---'---'---'---'---'---'---'
Figure 5b -- Scoop All Four Stones out of Edge Small Pit
.---.---.---.---.---.---.---.---.
| | 2 | 0 | 2 | 0 | 0 | 1 | |
|20 |---+---+---+---+---+---| 12|
| | 0 | 0 | 5 | 5 | 1 | 0 | |
'---'---'---'---'---'---'---'---'
Figure 5c -- No Six-Count Pits - Large Pit Increases by Two
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