Mancala World
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These statistics give mathematical values characterizing the game.

Games ONLY With Shared Sowing Area

(A) No accumulation holes:

Name of the Game k(1) k(2) k(3) m (+) m n (+) n (-) n
55Stones n/a 110 n/a 90 ? ≥30 ≤11 19
Adji-boto 5 25 100 5 ? ? ? ?
Afrika 8 64 383 8 2.6 ≥108 ≤50 74
Alemungula 3 18 107 6 4.35 ≥150 ≤11 42
Al-manqala 7 49 328 7 ? ? ? ?
Azigo [Aro Chuku] 16 256 4,409 ? ? ? ? ?
Anywoli 12 116 1,223 12 ? ≥162 ≤73 109
Aw-li On-nam Ot-tjin (2x9;5) 9 73 596 9 ? ? ? ?
Bohnenspiel 6 36 206 6 ? ≥94 ≤17 40
Boola 3 9 25 11 2.5 ? ? 50
Canicas (1x11 (3x6=1)) 6 726 7,986 121 ? ? ? ?
Catch 31 (2x6;5) 6 36 206 6 ? ≥59 ≤15 49
Cirk (1x7;4+8) 7 49 294 7 ? ? ? ?
Gulek (long game) 1 8 112 ? ? ? 41 ?
En Gehé (2x50;4) 50 1,964 ? 50 ? ? ? ?
Giuthi (2x10;8) 27 930 ? 10 ? ? ? ?
Hoyito (2x12;4) 12 116 ? 12 ? ? ? ?
Kauri 6 36 206 6 ? ≥170 ≤13 40
Kay 6 29 124 6 ? ? ? ?
Kiothi 2,613,660 ? ? ? ? ? ? ?
Lamlameta 12 98 925 12 4.1 ≥168 ≤33 97
Manji 7 106 ? 16 ? ? ? ?
Mbothe 1 7 57 9 ? ? ? ?
Numercy (2x13;7) 13 152 ? 13 ? ? ? ?
Oware 6 36 190 6 3.5 ≥221 ≤12 60
Atomic Wari (1x36;4) 33 1,056 ? 34 ? ? ? ?
Bao Arabica (2-p) 3 36 412 12 ? ≥53 ≤23 40
Cross-Wari (2x6;6) 6 36 216 6 ? ? ? ?
Dogon gagara 6 77 ? 16 ? ? ? ?
Glass Bead Game 10 115 1,414 ? ? ≥157 ≤150 153
Orancala (2-p) 1 11 114 11 ? ? ? ?
Ouri 6 36 180 6 ? ? ? ?
Pas de Deux 64 4,096 ? 64 ? ≥173 ≤85 112
Rondell (partisan, expert) 8 n/a n/a 8 ? ? ? ?
Songo Ewondo 7 49 309 7 ? ≥168 14 100
The Colony 103 ? ? ? ? ? ? ?
Tuca Tuca 6 30 141 6 ? ? ? ?
Um ed-Dyar (2x12;12) 12 144 1,717 12 ? ? ? ?
Unee Tugaluulach 3 9 27 3 ? ? ? ?
Vai Lung Thlan 6 36 186 6 ? ≥106 ≤50 75
Widdershins 1 n/a n/a 10 ? ? ? ?


(B) With accumulation holes:

Name of the Game k(1) k(2) k(3) m (+) m n (+) n (-) n
Bulto 10 67 473 10 ? ? ? ?
Embeli 10 80 584 11 ? ≥49 ≤34 41
Imbelece 8 51 345 8 ? ? ? ?
Kalah (2x6;6) 10 60 325 1,258 4.75 ≥62 ≤15 49
Banan-Cala 5,460 29,811,600 ? ? ? ? ? ?
Cross-Kalah (2x6;6) 10 100 792 ? ? ≥72 ≤13 34
Da Vinci's Mancala 168 ? ? ? ? ? ? ?
Diffusion (2x6) 12 132 ? 12 ? ≥91 ≤37 70
Geisterfahrer 5 25 101 ? ? ? ? ?
Kariba 109 11,881 ? ? ? ? ? ?
Pass It On (2-p) 7 47 256 ? ? ? ? ?
Progressive Mancala (1x11) 11 879 ? ? ? ? ? ?
Pyramidis (2-p) 5 25 165 8 ? ? ? ?
Ruma (4x6;4) 6 36 216 6 ? ? ? ?
Space Walk (2-p) 18 630 10,716 18 ? ? ? ?
Waurie 10 116 1,005 1,258 ? ≥57 13 50
Kánji-guti 6 36 207 6 ? ? ? ?
Kotu-baendum 2 12 76 7 ? ≥49 ≤19 29
Layli Goobalay (2x12;4) 12 106 1,048 12 ? ? ? ?
Rath (2x13;4) 12 119 ? 12 ? ? ? ?
Sadeqa I 10 84 735 10 ? ? ? ?
Selus [Massawa] 9 71 544 9 ? ≥23 ≤11 17
Takti 3* 9 28 10 ? ? ? ?
Toguz Kumalak 9 73 570 9 5.0 ≥414 11 114
Toguz Poddavki 8 43 146 9 ? ? ? ?

* After the first simultaneous move.

Games With AT LEAST SOME Separate Sowing Area

Name of the Game k(1) k(2) k(3) m (+) m n (+) n (-) n
Bao la Kimasai 8 64 416 16 ? ? ? ?
Bao la Kiswahili 4 14 34 25 4.2 ≥239 5 55
Bawo (kuu=10) 8,610 ? ? ? ? ? ? 47
Katra Fandatsaka 5 41 118 25 ? ? ? 75
Cups (2x10) 10 100 784 20 ? ? ? ?
Hawalis 14 182 ? 14 2.5 ≥117 ≤26 64
Hus (4x24) 16 1,296 ? 48 ? ? ? ?
Katro (6x6) 6 72 720 36 ? ? ? ?
Kiela (4x10; expert) >9x10^6 ? ? ? ? ≥99 3 ?
Kisolo (4x7) 7 49 370 13 ? ? ? ?
Mbelele 36 1,244 ? 36 ? ? ? ?
Mefuvha 1,874 ? ? ? ? ? ? ?
Mwambulula 16 256 2,625 32 ? ? ? ?
Omweso 7.5x10^11 5.6x10^23 ? 7.5x10^11 ? ? ? ?
Sowing (1x24;3) 21 420 ? 23 ? ? ? ?
Tchouba (4x40) 120,160 ? ? 120,160 ? ? ? ?
Trias 12 144 ? ? ? ? ? ?
Tsoro (4x21) 34 1,156 ? ? ? ? ? ?


Abbreviations

k(1) Board positions after the first turn
k(2) Board positions after the second turn
k(3) Board positions after the third turn
m (+) Maximum branching factor (theoretical); in 55Stones: maximum decisions
m Average branching factor (real games)
n (+) Maximum game length (real game)
n (-) Shortest game length (theoretical)
n Average game length (real games)
n/a Not applicable
2-p Two-person game
Partisan Pits are owned by a player
Expert Expert variant (see rules)
2x10;8 2 rows, each one with 10 pits, 8 seeds (usually in each pit)

Some Outstanding Mindsports

General characteristics of outstanding mindsports:

  • Draws and ties ≤ 10%
  • Average game length ≥ 40 plies, but ≤ 300 plies
  • Game play (any stage) is not opaque
Name of the Game k(1) k(2) k(3) m (+) m n (+) n (-) n Notes
Abande (hex-4) 6 18 124 ? ? ≥63 44 53 modern pure capture game with stacking
Akron (9x9) 15 861 23,506 81 ? ≥110 (real play) 17 (theory) 60 modern connection game; three-dimensional
Bao la Kiswahili 4 14 34 25 4.2 ≥239 5 (theory) 55 traditional four-row mancala; tournaments
Bashni 7 49 316 ? ? ≥84 ≤24 60 traditional stacking checkers; tournaments
Bohnenspiel 6 36 206 6 ? ≥94 ≤17 40 traditional two-row mancala; tournaments
Camelot 46 4,922 ? ? ? ≥153 (real play) 8 (theory 52 modern reach-a-cell game; tournaments
Cannon 10 100 3,950 ? ? ≥120 (real play) 13 (theory) 57 modern reach-a-cell game; Internet tournaments
Dvonn 16 495 4,989 48 ? ≥90 (tournament) 49 (theory) 78 modern pure capture game with stacking; tournaments
En Gehé (2x50;4) 50 1,964 ? 50 ? ? ? 200 largest traditional two-row mancala
Entrapment (7x7; 3 roamers) 10 255 11,262 ? ? ≥108 (real play) ≤27 (real play) 59 pure capture game
Epaminondas 57 6,498 ? ? ? ≥111 7 (theory) 54 modern back rank game
Exxit 1 1 1 ? ? ≥167 (real play) ≤50 (real play) 121 modern territorial game; tournaments
Focus (rules for advanced players) 192 27,658 ? ? ? ≥178 (real play) ≤36 (real play) 63 pure capture game; stacking
Go / Weiqi 55 16,435 6,696,000 361 240 411 (tournament) 142 (tournament) 250 traditional territorial game; tournaments
Gorgon (best with forced captures) 7 98 1,834 ? ? ≥103 (real play) ≤46 (theory) 75 modern checkers variant; no draws
Havannah (hex-10) 30 6,231 ? 271 235 ≥144 (tournament) 6 (theory) 66 modern connection game; Internet tournaments
Hawalis 14 182 ? 14 2.5 ≥117 ≤26 64 traditional four-row mancala; tournaments
Hex (14x14) 56 9,702 ? 195 ? 196 (theory) 27 (theory) 70 modern connection game; tournaments
Kalah (2x6;6) 10 60 325 1,258 4.75 ≥62 ≤15 49 modern two-row mancala; tournaments
Kiela (4x10; expert) >9x10^6 ? ? ? ? ≥99 3 ? traditional four-row mancala; tournaments
Omweso 7.5x10^11 5.6x10^23 ? 7.5x10^11 ? ? ? ? traditional four-row mancala; tournaments
Othello 1 3 13 33 10 64 13 (theory) 58 modern territorial game; tournaments
Oust (hex-7) 16 1,197 ? 126 ? ≥59 4 (theory) 48 modern territorial game; the game is also played on larger boards (hex-8, hex-9 or hex-10)
Pikemen (12 points; 2 player) 77 8,352 ? ? ? ≥87 ≤18 44 modern pure capture game; Internet tournaments
Ponte del Diavolo (12x12) 2,397 ? ? 19,740 ? ≥73 ≤63 69.5 modern territorial game; Internet tournaments
Quax (11x11) 21 1,881 ? 121 ? ≥76 21 (theory) 60 modern connection mancala
Ruma (4x6;4 - 2 player) 6 36 216 6 ? ? ? ? modern four-row mancala
Salta 9 81 594 54 ? 240 173 (tournament) 230 modern back rank game; tournaments
Shogi 30 900 25,500 ? 80 ≥400 7 115 traditional chess game; tournaments; the longest endgame problem numbers 1,525 plies
Songo Ewondo 7 49 309 7 ? ≥168 14 (theory) 100 traditional two-row mancala; tournaments
Susan (hex-6) 27 1,488 ? 185 ? >150 (estimated; real play) 4 (theory) 70 (estimated) modern pure capture game
Tchouba (4x40) 120,160 ? ? ? ? ? ? ? largest traditional four-row mancala
Toguz Kumalak 9 73 570 9 5.0 ≥414 11 (theory) 114 traditional two-row mancala; tournaments

Abbreviations as explained above.

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By: Ralf Gering
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