Mancala World

Cups → German.

Other Names: BohnDuell,
BohnenDuell, Schalen-Spiel
Inventors: Arthur & Wald
Amberstone, 1965
Variant of Kalah
Ranks: Two
Sowing: Single laps
Region: USA, Germany,

Cups, a mancala game, was invented in 1965 by father and son Arthur Amberstone and Wald Amberstone who were both cofounders of the New York Gamers Association (N.Y.G.A.). They also invented Power, and High Deck, a card game based on medieval society. At the time both were working as basket makers as well as game designers in New York City. This game was first published in A Gamut of Games by Sid Sackson in 1969. Wald Amberstone co-founded the Tarot School in 1995 along with his wife Ruth Amberstone.

In Germany, 2x4 Cups is known as BohnDuell, Bohnenduell ("bean duel") or Schalen-Spiel ("game of cups"). BohnDuell is played at Brettspielwelt, where tournaments were organized in the years 2003-2007.

There was a BohnDuell Guild from 2003-2007, which kept an Elo list ranking the best players. The strongest player according to the game's Elo list was "racingphil" (*12/31/1982) who lived in the town of Schongau (Bavaria), Germany.

Another mancala game which was invented by the Amberstones is Coin Duel.


Cups is played with 2x3=6 - 2x10=20 cups and a bigger pot at the right end of each row. 2x4 is the size of BohnDuell in Brettspielwelt and the size recommended by Sid Sackson "for initially becoming acquainted with the beauties of Cups". Later the players can experiment with greater numbers of cups or can play with just three cups, making a "delightful miniature" (Sackson).

There must be always 10 beans per hole, so each player has 100 seeds when playing on a 2x10 board. These beans are kept in reserve, until they enter the game. At the start the board is empty.


Initial Position (Maximum Size)

Each player only plays on his/her side of the board. Play is from left to right.

If it's your turn, you must do one and only one of the following actions:

  • Take some beans (from on to the number of cups) from your reserve and distribute them to the right, one by one, by starting in your leftmost hole. If the last bean is dropped into an empty hole and the opponent's hole opposite of you contains beans, these are captured and put into your pot. Only the opponent's beans are captured.
  • Empty one of your cups which contains as many beans as needed to reach your pot with the last bean. You distribute these beans, again one by one, to the right and capture the last bean, which is dropped into your pot. You may only empty a cup if you reach with the last seed your pot.

There is the possibility of a "blocked cup", that is a cup containing more beans than needed to reach the pot. It is not possible to play from an overloaded cup, which therefore becomes an easy target for the opponent.

You must move, if you can. The game ends when no player is able to move. The seeds which are remaining in the cups are not counted. The winner is the player who captured more beans.

The game is particularly suited for retrograde analysis. It is very easy to construct from a given "perfect" endgame position other positions which are more than 50 steps "away". These problems appear to be unsolvable even for the most experienced human player.

A perfect endgame position has the following characteristics:

  • every seed can eventually be played into the pot
  • the leftmost hole (called 1) is filled
  • it must number as few seeds as possible
  • no seeds are left in the reserve
  • you must have at least one seed in your cups
  • the opponent has no seeds left which can interfere with your steps

Table 1

n(h) || n(s) || seeds in holes 1 - n(h)
1 || 1 || 1
2 || 2 || 2 0
3 || 4 || 3 1 0
4 || 6 || 4 2 0 0
5 || 10 || 5 3 1 1 0
6 || 12 || 6 4 2 0 0 0
7 || 18 || 7 5 3 1 2 0 0
8 || 22 || 8 6 4 2 0 1 1 0
9 || 30 || 9 7 5 3 1 3 2 0 0
10 || 34 || 10 8 6 4 2 0 2 1 1 0
n(h) = number of holes
n(s) = number of seeds

The position 10 8 6 4 2 5 1 0 0 1, for instance, can be transferred into the perfect position in three steps.

The rather artificial position 3 1 0 0 4 3 0 0 0 1 (88 seeds in reserve) takes more than 80 steps to transfer.

See also


Amberstone, W. 
Personal Communication (E-Mail to Ralf Gering). New York (USA) 05/16/2005.
Sackson, S.
A Gamut of Games. Pantheon, New York (USA) 1969, 40-45.
Schneider, A. 
BohnDuell goes online. Bonn (Germany) 2003.
Schwagereit, J.
Cupa: A Program to play Cups, also known as BohnDuell or Schalen-Spiel. Krefeld (Germany) 2005.

External Links

BohnDuell becomes a game of caution and brinkmanship. You need to be careful how you place and move your stones because it can be very easy to freeze one of your pits. One wrong move and you can hand your game to your opponent. At the same time, you have to be prepared to take advantage of every mistake your opponent makes.

Lowell Kempf (2006)


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