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Diffusion

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Diffusion
Inventor: Mark Steere, 2006
Variant of Kalah
Ranks: Two
Sowing: Single laps
Region: USA, Internet

Diffusion, a variant of Kalah, was invented on January 20, 2006 by Mark Steere, USA. He also designed many other abstract strategy games; e.g. Quadrature (1992), Tanbo (1993), Impasse (2003), Byte (2005), and Cephalopod (2006). Diffusion can be played at SuperDuperGames. The strongest player is Scott Stubbs ("Lexicon") who won the Diffusion Subtournament of the MSG Triathlon 2006.

Rules

Diffusion employs a 2x6 mancala board and a set of 48 like-colored stones. Initially the board is set-up with four stones in each of the small pits and no stones in the large pits. The board is divided into two 2x3 blocks as highlighted in the first diagram. Each player owns the block to his left.

Diffusionini

Initial Position

Players take turns making moves.

You begin your turn by scooping out 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.

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 continous sequence (no gaps).

Having scooped all of the stones out of one of the four non-corner small pits in your far row, you must distribute those stone in the following manner: Place one stone into the small pit to the left of the emptied pit, and proceed counterclockwise around the emptied pit, depositing all of the remaining stones.

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 (one of the two small pits in your near row and the other in your far row) and follow the distribution rules as described.

In summary, start at the clockwise limit and distribute the stones in sequence, counterclockwise around the emptied pit.

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. A small pit should never contain more than five stones.

Players cannot pass on their turn. There will always be at least one move available.

If, at the conclusion of a turn, one of the two blocks is completely vacated, the owner of that block wins. Draws and ties cannot occur.

Variants

Several variants exist:

  • Diffusion can be generalized to larger boards such as 2x8 or 2x10 as suggested by Mark Steere on January 29th, 2006. He even composed an endgame problem for "Generalized Diffusion" (see Problem 2 below).
  • games.wtanaka.com has implemented variants with one, two or three stones per pit for learning the game
  • On November 30, 2009, Mark Steere published Diffusion v2. In this variant two 1x6 blocks are used instead of two 2x3 blocks. In other words each player owns the row on his side (as usual in two-row mancala games) and tries to empty his row first. This game, which has been implemented on games.wtanaka.com, resembles Waurie even more.
  • Mark Steere also suggested a variant that is played on a 4x8 board (Four-rank Diffusion).
  • Different scoring: After the first player (the player who started the game) has vacated his sphere of influence, his opponent may play at least one stone back into the first player's camp or to vacate his own camp right afterwards. In the first case, the game continues, in the latter case the game should be counted as a draw. This variant was proposed by Ralf Gering on March 26, 2006 who called it "Balanced Diffusion", although it is neither known that the original game is unfair nor that the "balanced" version is truly balanced. A logical extension of this variant is point-scoring: The winner gets as many points as his opponent still needs moves to vacate his holes as well. The loser gets zero points. This variant leads to different endgames (see Problem 3 below).

Endgame Problems

Problem 1

Diffusionprob1

Player A (Left) to move and win the game.

A tricky endgame composed by Mark Steere on February 12, 2006.

Problem 2

Diffusionprob2

Left (A) to move and win the game.

This endgame on a 2x8 board was composed by Mark Steere on January 29, 2006.

Problem 3

Diffusionprob3

Right (B) to move. Compare the standard rules to the balanced rules!

This endgame was created by Ralf Gering on March 26, 2006.

References

Anonymous.
Diffusion (2006). BoardGameGeek, Dallas, TX (USA) 2006.
Huang, W.-H.
Game Reviews: Diffusion. Mountain View, CA (USA) 2006.
Luca, C.
La semina e il raccolto: Diffusion, Reaping Mancala e Hus. In: Il Fogliaccio degli Astratti 2006; 31 (March): 1-2.
Steere, M.
Diffusion Rules. Palo Alto, CA (USA) 2006.
Steere, M.
Diffusion Addendum (4x8). Palo Alto, CA (USA) 2006.
Steere, M.
Diffusion. Palo Alto, CA (USA) November 30, 2009.


Solutions to the problems

1. c! (but not: d??, D, e, E, f (:1), F (:1), B, c Right wins), D, d, E, C!, F (:1), e, D, B, E, C!, F (:1), f (:1) +

2. G!, H (:2), e, a, f, b, g, c, h (:1) +

3. a) Standard Diffusion: D, e, b, f, c, C, E, d, D, e, E, f and Left wins! --

b) Balanced Diffusion: D, e, b, f, C, E, d, D, e, E, f, F and Draw!; or C!, e, D, f, c, d, E, e, b, f, c, d, F and Right wins!

(capital letters = lower row; small letters = upper row)

External Links

Copyright

© Wikimanqala.
By: Ralf Gering
Under the CC by-sa 2.5 license.

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