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As mentioned above, if the last seed sown by a player lands in that player's store, the player gets an extra move. A clever player can take advantage of this rule to chain together many extra turns. Certain configurations of a row of the board can in this way be cleared in a single turn, that is, the
607:
designates the number of seeds that start out in each house. In broad terms, the more seeds, the more challenging is the game. The three-, four-, five- and six-seed Kalah have been solved, with the starting player always winning with perfect play. Thus some web sites have implemented the game with
978:
621:
In the "Seed On" variant, there is no captures when ending in an empty house, but when the last seed ends in a non-empty house on either side of the board, that seed and all seeds from that house are sown, so that the move only ends when the last seed falls in an empty
674:
increases. For example, it can be seen on the right that the unique 5-seed pattern requires only 3 pits, but the 17-seed pattern requires 6 pits. The relationship between the required number of pits and the number of seeds can be described in the following way. Let
215:
their seeds. On a turn, the player removes all seeds from one of the houses under their control. Moving counter-clockwise, the player drops one seed in each house in turn, including the player's own store but not their
838:
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The last seed falls in an empty house on the player's side. The player collects the highlighted seeds from both their own house and the opposite house of their opponent and will move them to the store.
201:
or counters. The board has 6 small pits, called houses, on each side; and a big pit, called an end zone or store, at each end. The object of the game is to capture more seeds than one's opponent.
219:
If the last sown seed lands in an empty house owned by the player, and the opposite house contains seeds, both the last seed and the opposite seeds are captured and placed into the player's store.
618:
The "Empty
Capture" variant: If the last sown seed lands in an empty house owned by the player, even if the opposite house is empty, the last seed is captured and placed into the player's store.
225:
When one player no longer has any seeds in any of their houses, the game ends. The other player moves all remaining seeds to their store, and the player with the most seeds in their store wins.
737:
574:
in the early 1960s, and was able to out-play experienced human players. Since then, there have been myriad Kalah implementations for various operating systems and platforms, including
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to make it fair, or the second player may be allowed to move one seed from any house to any other house before the game begins, resulting in effectively 133 different games.
651:
player can capture all stones on their row, as depicted on the right. The longest possible such chain on a standard Kalah board of 6 pits lasts for 17 moves. On a general
625:
Alternative rules either count the remaining seeds at the end of the game as part of the score of the player who has emptied their houses, or do not count them at all.
646:
This pattern of stones can be captured in a single turn by chaining together 17 consecutive moves. This is the longest such chain possible on a standard 6-pit board.
757:
222:
If the last sown seed lands in the player's store, the player gets an additional move. There is no limit on the number of moves a player can make in their turn.
208:
Each player controls the six houses and their seeds on the player's side of the board. The player's score is the number of seeds in the store to their right.
655:-pit board, the patterns of seeds which can be cleared in a single turn in this way have been the object of mathematical study. One can prove that, for all
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The game may start with a number of seeds in each house different from four. A nomenclature has been developed to describe these variations: Kalah(
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843:
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An alternative rule has players sow in a clockwise direction, requiring more stones to be sowed in a single turn to reach the store.
184:
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162:
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This pattern can be cleared in a single turn by playing pits 1, 3, 1, 2, and 1, in that order, chaining together five moves.
1108:
Broline, Duane M.; Loeb, Daniel E. (1995-02-08). "The combinatorics of
Mancala-type games: Ayo, Tchoukaitlon, and 1/π".
97:
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At the beginning of the game, four seeds are placed in each house. This is the traditional method.
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moves, or equivalently, one and only one clearable pattern consisting of exactly
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in the 1950s. This game is sometimes also called "Kalahari", possibly by false
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101:
1060:"Kalakh" videogame on archive.org, with in-browser DOS emulation gameplay
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120:
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The last seed falls in the store, so the player receives an extra move.
109:
93:
17:
976:, William J Champion, "Game Counter", published 1955-10-11
96:. The Kalah board was first patented and sold in the United States by
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1057:
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50:
997:. Digital Equipment Computer Users Society (DECUS). 31 March 1961
833:{\displaystyle \lim _{n\to \infty }{\frac {s(n)}{n^{2}/\pi }}=1}
119:
with a first-player win if both players play perfect games. The
900:{\displaystyle \lim _{n\to \infty }{\frac {n^{2}}{s(n)}}=\pi }
575:
130:
659:, there exists one and only one pattern clearable in exactly
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345:
236:
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670:
These patterns require arbitrarily long rows of pits and
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Nokia 3310 gameplay of "Bantumi", a kalah-identical game
1083:
by
Geoffrey Irving, Jeroen Donkers and Jos Uiterwijk.
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The player begins sowing from the highlighted house.
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can be used to balance the first-player's advantage.
683:) denote the minimum number of seeds which requires
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43:
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832:
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603:designates the number of houses on each side, and
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197:The game provides a Kalah board and a number of
732:{\displaystyle s(n)\sim {\frac {n^{2}}{\pi }},}
229:It is possible for the game to end in a draw.
8:
942:"Kalah: A Commercial Count and Capture Game"
165:. Unsourced material may be challenged and
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185:Learn how and when to remove this message
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115:For most of its variations, Kalah is a
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92:is a modern variation in the ancient
7:
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163:adding citations to reliable sources
1058:https://archive.org/details/Kalakh
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27:Board game in the mancala family
954:from the original on 5 Feb 2024
1152:Board games introduced in 1940
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1:
570:Kalah was implemented on the
30:For the village in Iran, see
98:William Julius Champion, Jr.
1017:"Games: Pits & Pebbles"
994:PDP Application Note: Kalah
1178:
1043:: CS1 maint: url-status (
29:
566:Video game implementation
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974:US Expired 2720362A
94:Mancala family of games
947:University of Waterloo
901:
834:
761:asymptotic equivalence
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34:. For other uses, see
1095:by Anders Carstensen.
902:
835:
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752:{\displaystyle \sim }
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630:Mathematical analysis
36:Kala (disambiguation)
1093:Solving (6,6)-Kalaha
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687:pits to clear. Then
159:improve this section
840:, or equivalently,
211:Players take turns
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739:where the symbol
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127:Standard gameplay
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16:(Redirected from
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1025:. June 14, 1963
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106:Kalahari desert
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1081:Solving Kalah
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1039:cite magazine
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144:This section
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78:United States
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19:
1162:Solved games
1136:Games portal
1115:math/9502225
1088:
1076:
1065:
1053:
1027:. Retrieved
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999:. Retrieved
993:
987:
968:
956:. Retrieved
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604:
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596:
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342:
233:Example turn
228:
212:
198:
196:
181:
172:
157:Please help
145:
114:
89:
88:
917:Pallanguzhi
763:, that is,
216:opponent's.
117:solved game
32:Kalah, Iran
1146:Categories
928:References
586:Variations
580:Nokia 3310
578:, and the
69:Single lap
895:π
859:∞
856:→
819:π
782:∞
779:→
747:∼
722:π
707:∼
599:), where
146:does not
104:from the
102:etymology
952:Archived
911:See also
759:denotes
610:pie rule
175:May 2024
121:pie rule
1157:Mancala
1029:May 28,
1001:May 28,
958:May 27,
667:seeds.
167:removed
152:sources
110:Namibia
18:Bantumi
980:
622:house.
213:sowing
74:Region
66:Sowing
1110:arXiv
922:Oware
572:PDP-1
199:seeds
90:Kalah
58:Ranks
44:Kalah
1045:link
1031:2024
1022:TIME
1003:2024
960:2024
608:the
150:any
148:cite
849:lim
772:lim
576:DOS
161:by
108:in
61:Two
1148::
1100:^
1041:}}
1037:{{
1019:.
950:.
944:.
907:.
582:.
112:.
80:,
1118:.
1112::
1047:)
1033:.
1005:.
962:.
892:=
886:)
883:n
880:(
877:s
871:2
867:n
853:n
828:1
825:=
815:/
809:2
805:n
799:)
796:n
793:(
790:s
776:n
727:,
717:2
713:n
704:)
701:n
698:(
695:s
685:n
681:n
679:(
677:s
672:n
665:n
661:n
657:n
653:n
605:s
601:h
597:s
595:,
593:h
188:)
182:(
177:)
173:(
169:.
155:.
38:.
20:)
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.
