|Other Names: Kalaha, Kalahar,|
Mankala, Mancala, Mop-up,
Bantumi, Conference, Serata
|Inventor: William Julius Champion|
|Variant of Dakon|
|Sowing: Single laps|
|Region: USA, Germany, Internet|
Kalah was invented by William Julius Champion Jr., a graduate of Yale University, in 1940.
In 1905, he came across an article about a mancala game and it appears that he read many more ethnological works on African and Asian mancala games in later years. W. J. Champion started to sell his game in 1944, patented it in 1952 (design) and 1955 (rules) and then founded in 1958 the Kalah Game Company in Holbrook, Massachusetts (USA). Kalah was produced by them well into the 1970s and the name of the game was a registered trademark from 1970-2002. Champion promoted the game for educational purposes. On August 9, 1961, he organized a tournament at Fiske playground in Wellesley MA. In 1963, there was a Kalah championship with 32 students organized at the Coolidge School in Holbrook MA, which was won on December 12 by Ira Burnim.
In 1959, Kalah became the first remotely played computer game, when it was programmed by MIT students for the DEC’s PDP-1 computer. Many other computerized versions followed. In Germany, Paul Erich Frielinghaus, today a well-known actor, but at this time still a High School student, developped in 1978 a Kalah program (he called the game Serata), which won the first prize in the German Research Competition Jugend forscht (i.e. "youth is doing research"). The game was strongly solved (according to Allis definition) for small instances using full-game databases and weakly for larger instances by Jeroen Donkers et al. in 2001 and by Anders Carstensen in 2011. Starting in 2015 Mark Rawlings (Gaithersburg, Maryland; USA) has written a computer program to extensively analyze both the "standard" version of Kalah and the "empty capture" version, which is the primary variant. If played perfectly, it is usually (it depends on the number of seeds in each hole, the number of holes per row, and the variant) a first players win.
The Swedish Björn Myrvold has written in 2002 a strong Kalah applet.
Although the game was patented, it had been copycatted many times: Conference (Mieg's, 1965), Sahara (Pelikan, 1976) and Bantumi (Nokia, 2000). Kalah is used by the Kellog Electronic Research Academy in Chicago to help students who are suffering under dyscalculia.
Kalah is very popular in the United States, where it is often just called Mancala. In Germany, it is known as Kalaha. Every year there are more than 50 tournaments in the USA, mostly for children.
The game has no African origins despite many claims to the contrary, even by its inventor, because there is no such game in the whole of Africa. However, Kalah suspiciously resembles games played by the Malay people and could be described as single-lap Dakon (Dakon is a Javanese mancala game). Kalah means in Timorese "to defeat". All modern mancala variants, which were commercialized in western countries before 1960, are minor modifications of traditional games. Although they often claim to be ancient, it can be shown that they are, in fact, of rather recent origin. Kalah is for sure not a Sumerian invention, 7,000 years old, as stated by W. J. Champion.
The version called Conference, published in Germany, was inspired by boards kept in Castle Weikersheim.
Kalah is played on a board of two rows, each consisting of six round pits that have a large store at either end called kalah. A player owns the six pits closest to him and the kalah on his right side. Beginners may start with three seeds in each pit, but the game becomes more and more challenging by starting with 4, 5 or up to 6 pieces in each pit. Today, four seeds per hole has become the most common variant, but Champion recommended the expert game
Most Challenging Set-up (Expert Game)
Play is counterclockwise. The seeds are distributed one by one in the pits and the players own kalah, but not into the opponent's store.
If the last seed is dropped into an opponent's pit or a non-empty pit of the player, the move ends without anything being captured.
If the last seed falls into the player's kalah, he must move again.
If the last seed is put into an empty pit owned by the player, he captures all contents of the opposite pit together with the capturing piece and puts them in his kalah. If the opposite pit is empty, nothing is captured. A capture ends the move.
The game ends when one player no longer has any seeds in any of his holes. The remaining pieces are captured by his adversary. The player who has captured most pieces is declared the winner.
Many "house rules" exist as there is no governing body, which defines the "official" rules:
- The "Empty Capture" variant permits to capture the last seed when landing in an empty hole on the player's own side even when the opposite hole of the adversary is empty.
- The game ends when a player, at his turn, is unable to move and the remaining pieces are captured by his adversary. The player who has captured most pieces is declared the winner.
- An alternate rule does not count the remaining seeds as part of the score at the end of the game.
The first player has a big advantage. Therefore, a few web sites (igGameCenter, Vying (now defunct)) have implemented the pie rule to make the game fair. After the first turn, the other player may either continue (as if there were no pie rule) or decide to switch sides. This leads to sophisticated game play. Nonetheless the rate of draws in online play is just 9% according to ig Game Center statistics (negotiated draws omitted).
The following game was played between Arty Sandler (Israel) and Ralf Gering (Germany) on June 11, 2008. Each hole contained six seeds at the start. The pie rule was used to make the game fair. Sandler moved first.
1. d(+1)* F(+1) - no pie; 2. e(+1) F-B(+2)
3. f(+1) A(+1); 4. d(+3) D(+3)
5. c(+1) D; 6. f-e-f-b(+4) C(+6)
7. e-c(+2) E-D-E-F(+5); 8. e-d-a(+3) F-A-F-E-F-C-F-D-F-E-F-B(+13)
9. e-b-c-e-d-f(+8) F-E-F-D(+5); 10. e-f-d(+4) C
11. b E-F-D(+2); 12. c E
13. e F(+1).
The two remaining seeds are awarded to Sandler. Gering wins by 6 points.
* a-x(+2) would result in switching as this move gives the first player a too big advantage.
The following game was played between Ralf Gering (Germany) and Olivier Millé (Spain) on May 30, 2009. Each hole contained six seeds at the start. The pie rule was used to make the game fair. Gering moved first.
1. f(+1) C(+1) - no pie; 2. c(+1) E(+1);
3. a(+1) D(+1); 4. c B(+1);
5. b(+1) E(+1); 6. d(+6) D-B(+5);
7. e(+3) F(+2); 8. f(+1) D-C-A(+3);
9. f-e-f-d-f-e(+7) F(+1); 10. d!(+5) D(+11);
11. c-f-b-f-e-f-d(+6) C(+2); 12. f-e(+1) E(+4);
13. a F(+1)
The five remaining seeds are awarded to Gering. Gering wins by 4 points.
The following game was played between Maria do Céu Rodrigues Aguiar Lopes Tavares (Portugal) and Ralf Gering (Germany) on January 24, 2010. The pie rule was used to make the game fair. Tavares moved first. The game was played according to house rule II (that is, it ended when a player was unable to move).
1. b(+1) F(+1); 2. c(+1) C(+1);
3. c F-A(+2); 4. e(+1) B(+1);
5. c D(+3); 6. d(+6) F(+1);
7. b(+1) A; 8. e-a(+2) F-D-F-E-B-E-C-D-E-A(+15)*;
9. e-b(+3) F(+1); 10. a (+33)**
* "Greed ruins gentlemen."
** b, d and e works too.
Tavares wins by 22 points.
Kalah Puzzle 1
South to play and capture 18 seeds.
Kalah Puzzle 2
South to play and to draw.
- Ahl, D. H.
- 101 Basic Computer Games. Digital Equipment Corporation (DEC), Maynard MA (USA) 1973, 19-21.
- Ahlschwede, J.
- Using Genetic Programming to Play Mancala. Doane College, Crete NE (USA) 2000.
- PDP Application Note: Kalah. Digital Equipment Corporation, Maynard MA (USA) 1961.
- Pits & Pebbles. In: Time Magazine June 14, 1963: 67.
- Kalah Recognized as Valuable Educational Aid - 350 Students Participate in Tournament: Kalah Sweeps Coolidge School. In: Melrose Free Press December 19, 1963.
- Computer Recreations. In: Software: Practice and Experience 1971; 1 (3): 297–300.
- Kalah: A Commercial Count and Capture Game. Museum of Waterloo, London (Ontario, Canada) July 30, 2001.
- TAG Students Finish Tournament. In: Blanco County News March 16, 2011.
- Bell, A. G.
- Kalah on Atlas. In: Mitchie, D. (Ed.). Machine Intelligence 3. University Press, Edinburgh (Scotland) 1968, 181-193.
- Betten, D.
- Kalahari and the Sequence "Sloane No. 377". In: Annals of Discrete Mathematics 1988; 37: 51-58.
- Brill, R. L.
- A Project for the Low-Budget Mathematics Laboratory: The Game of Kalah. In: Arithmetic Teacher 1974; 21 (February): 659-661.
- Ceceri, K.
- Hands-on Learning: Mancala Board Game (Column). In: Home Education Review 2008 (July-August); 32: 44-45.
- Champion, W. J.
- Game Board (US D165,634). United States Patent Office, Washington DC (USA) January 8, 1952.
- Champion, W. J.
- Game Counter (US 2,720,362). United States Patent Office, Washington DC (USA) October 11, 1955.
- Champion, W. J.
- New or Old (Letter). Kalah Game Company, Holbrook MA (USA) 1970.
- Ching, W. E.
- Analysis of Kalah. Department of Mathematics, National University of Singapore 2000/2001.
- Christensen, B. M.
- Kalaha - Nu med endnu flere kugler og huller. In: Famøs 2012 (22); 1: 34-36.
- Cofer, A.
- Mancala in Java: An Experiment in Artificial Intelligence and Game Playing. Department Honor Thesis. The University of Tennessee at Chattanooga, Department of Computer Science, April 1, 2003.
- De La Cruz, R. E., Cage, C. E. & Lian, M.-G. J.
- Let's Play Mancala and Sungka: Learning Math and Social Skills through Ancient Multicultural Games. In: Teaching Exceptional Children 2000; 32 (3)38-42.
- Donkers, J., Uiterwijk, J. & Irving, G.
- Solving Kalah. In: ICGA Journal 2000; 23 (3): 139-147.
- Fesser, M.
- Entwicklung von Spielstrategien mittels evolutionärer Algorithmen am Beispiel von Kalaha. Diplomarbeit Nr. 2184. (Final Diploma Thesis). Fakultät Informatik, Elektrotechnik und Informatik, Universität Stuttgart, Stuttgart (Germany) 2004.
- Haggerty, J. B.
- Kalah — An Ancient Game of Mathematical Skill. In: Arithmetic Teacher 1964; 11 (5): 326-330.
- Henriksen, R. C.
- Game Faces. In: Columbia Daily Tribune July 1, 2011, A10.
- Jader, G. H.
- Tournament Marks Mancala Revival. In: Daily Herald February 26, 1996.
- Lehmann, E. Hicke, K. & Juhre, V.
- Projekt Kalaha: Gesamtdokumentation. Rückert-Oberschule, Berlin (Germany) 2000.
- Lemaire, B.
- Tutoring Systems Based on Latent Semantic Analysis. In: Lajoie, S. & Vivet, M. (Ed.). Artificial Intelligence in Education. IOS Press, Amsterdam (Netherlands) 1999, 527-534.
- Lipovec, A.
- How Do Children Play Kalah? In: Duh, M. & Seebauer, R. Beiträge zum "Internationalen Jahr der Hugend". LIT Verlag, Münster (Germany) 2011, 118-124.
- Lipovec, A.
- Children's Strategic Thinking While Playing Mathematical Games In: A. Juryeviy Lozanyiy (Ed.). Expectations, Achievements and Prospects in Theory and Practice of Early and Primary Education: Collected Papers of Special Focus Symposium 11th Days of Mate Demann. Zagreb (Croatia) 2010, 245-256.
- Machatscheck, H.
- Stein um Stein: Exotik der Brettspiele. Verlag Neues Leben, Berlin (Germany) 1984, 69 & 84-87.
- Missawa, D. D. A. & Rossetti, C. B.
- Desempenho de crianças com e sem dificuldades de atenção no jogo Mancala. In: Arquivos Brasileiros de Psicologia 2008; 60 (2).
- Mohammad, J. H.
- The Kalah Game System [Master Thesis (M.S.)]. California State University, Northridge CA (USA) 1999.
- Musumbu, K.
- Kalah Game: An Application of Artificial Intelligence. In: Sveti, S. Proceedings of the International IPSI-2003 Conference. Montenegro (Yugoslavia), November 2003.
- Musumbu, K.
- The Semantics of Kalah Game. In: 4th International Symposium on Information and Communication Technologies Volume 2005. ACM, 2005, 191-197.
- Neumeister, M.
- Fallbasiertes Lernen von Bewertungsfunktionen (Diplomarbeit) . Universität Leipzig, Leipzig (Germany), 9. November 1998.
- Nielsen, H. S.
- Studerende løser gåden om Kalaha. In: Jyllands-Posten June 3, 2011.
- Noe, T.
- A Comparison of the Alpha-Beta and Scout Algorithms Using the Game of Kalah. UCLA-ENG-CSL-8017, University of California, Los Angeles (USA), 1980.
- Oon, W.-C. & Lim, Y.-J.
- An Investigation on Piece Differential Information in Co-Evolution on Games Using Kalah]. In: Proceedings of Congress on Evolutionary Computation 2003; 3: 1632-1638.
- Pence-Lanctot, I.
- Students Learn About Traditional African Game of Mancala. In: James River Journal March 9, 2012.
- Pok Ai Ling, I.
- The Game of Kalah. Department of Mathematics, National University of Singapore 2000/2001.
- Rechenberg, P.
- Ein rekursives Programm fuer das Kalah-Spiel. In: Elektronische Rechenanlagen 1970; 12 (1): 11-19.
- Reutter, H.
- African Game Teaches Math Strategies to Students. In: Grand Island Independent January 31, 2004.
- Ridder, J.
- More Than Just a Game. In: Post-Tribune December 13, 2002.
- Ridder, J.
- Mancala Helps Students to Meet State Standards. In: Post-Tribune December 20, 2002.
- Russel, R.
- Kalah: The Game and the Program. In: Stanford Artificial Intelligence Project, Memo. University of Stanford, Stanford (USA) 1964 (Nr. 22).
- Russel, R.
- Improvements to the Kalah Program. In: Stanford Artificial Intelligence Project, Memo. University of Stanford, Stanford (USA) 1964.
- Simister, J. L.
- Learning an Evaluation Function Using a Connectionist Network: A Project in Machine Learning Based on the Game of Kalah. University of Utah, Salt Lake City UT (USA) 2004.
- Silver, R.
- The "Kalah" Game Playing Program (Interoffice Memorandum M-1098). Maynard MA (USA) March 31, 1961.
- Slagle, J. R. & Dixon, J. K.
- Experiments with the M & N Tree-Searching Program. Communications of the ACM 1970; 13 (3): 147-154.
- Torrey, V.
- Mancala. In: Popular Mechanics 1962; 61 (11); 151.
- Weicker, K. & Weicker, N.
- Evolving Strategies for Non-player Characters in Unsteady Environments. In: Giacobini, M. et al (Ed.). Applications of Evolutionary Computing. Springer Verlag, Berlin & Heidelberg (Germany) 2009, 313-322.
- Zaslavsky, C.
- Africa Counts: Number and Pattern in African Culture. Prindle, Weber & Schmidt, Boston (USA) 1974, 328.
- Kalah – the first remotely played computer game
- First prize in the German Research Competition Jugend forscht
- Solving (6,6)-Kalaha
Solutions to Kalah Problems
1. 5(x2) 2
2. 3 3
3. 2(x2) - Each player has got 36 points.