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Connection game

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The goal of Tak is to be the first to connect two opposite edges of the board with your pieces, called "stones", and create a road. To accomplish this, players take turns placing their own stones and building their road while blocking and capturing their opponent's pieces to hinder their efforts at
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in which players attempt to complete a specific type of connection with their pieces. This could involve forming a path between two or more endpoints, completing a closed loop, or connecting all of one's pieces so they are adjacent to each other. Connection games typically have simple rules, but
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board, although 13×13 and 19×19 boards are also popular. Each player is assigned a pair of opposite sides of the board which they must try to connect by taking turns placing a stone of their color onto any empty space. Once placed, the stones cannot be moved or removed. A player wins when they
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in the early 1950s. The goal of Y is similar to Hex except that each player has the identical goal of making a connection between all three sides forming a "Y" rather than "owning" specific sides that must be connected. The game was independently invented in 1953 by
124:, R. Wayne Schmittberger identified an additional sub-class of connection game in which points were bridged to form connections although the overall goal – forging a path connecting opposite sides of the board – was the same. These games included 35:
In many connection games, the goal is to connect two opposite sides of the board. In these games, players take turns placing or moving pieces until one player has a continuous line of pieces connecting their two sides of the playing area.
362:. In addition the player may place and move a piece called the capstone or play normal stones "standing" up on their edge. The capstone and standing stones have different powers and rules regarding their use in the game. 218:
connects any three edges of the board (a corner point is not considered part of an edge). Havannah has "a sophisticated and varied strategy" and is best played on a base-10 hexagonal board, 10 hex cells to a side.
62:(developed independently by the mathematicians Piet Hein and John Nash in the 1940s) is considered to be the first connection game, although earlier games involving connectivity have been noted to predate 92:(1959). It was shown, starting with smaller boards, the player making the first move had a decided advantage, depending on where the initial move was made. In his 1959 book, Gardner also mentions that 880:
The cover shows the version of Havannah published by Ravensburger in 1981. Expert players now prefer to play on a hexagonal board with 10 spaces on each side, but otherwise the game is unchanged.
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that would be played on a board with three equal-length sides; the winning condition would be changed to the first to connect all three sides. This was a variant of the game
226:, with a smaller, base-8 board suitable for beginners. It is currently only produced by Hexboards, a Dutch company that produces laser-carved gaming boards. 206:. Unlike Hex or other connection games, Havannah has three conditions that enable a player to win: creating a Fork; creating a Bridge; or creating a Ring. A 1126: 400:
and Charles Titus. It is an early member in a long line of games Schensted has developed, each game more complex but also more generalized.
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is a loop around one or more cells regardless of whether or not the encircled cells are occupied by any player or empty. A
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were examples of games where the players competed to build a path connecting sides of the board. In the June 2000 issue of
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successfully connect their sides together through a chain of adjacent stones. Draws are impossible in Hex due to the
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in 2016. Its design was based around the fictional game of Tak described in Patrick Rothfuss' 2011 fantasy novel
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the same. A player "captures" a stone by stacking one of their pieces on top of the opponent's. This creates a
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that had been invented independently by John Milnor, Charles Titus, and Craige Schensted in the early 1950s.
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complex strategies. They have minimal components and may be played as board games, computer games, or even
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Examples of the three winning structures in Havannah, on a base-8 board. From left to right, they are the
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The game has deep strategy, sharp tactics and a profound mathematical underpinning related to the
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element to the game play absent in other well known connection games, such as
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The Scientific American Book of Mathematical Puzzles & Diversions
1354: 1209: 1172: 810:(Master of Arts in Teaching thesis). University of Nebraska-Lincoln 527: 421: 371: 276: 472: 46: 1328: 1095:"Connection Games VIII, Part I: ConHex [Michail Antonow]" 507: 437: 287: 271: 256: 320: 136:(1962). Schmittberger also identified a third sub-class where 779:"Four mathematical diversions involving concepts of topology" 522: 497: 482: 41: 958:
Hexaflexagons, Probability Paradoxes, and the Tower of Hanoi
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11×11 Hex gameboard showing a winning configuration for Blue
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Schmittberger, R. Wayne (June 2000). "Making Connections".
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is credited with popularizing the genre in his writeup of
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connects any two of the six corner cells of the board. A
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Some games and machines for playing them | Report D-1164
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in which players attempt to connect opposite sides of a
758: 1070:"Connection Games VI: TwixT [Alex Randolph]" 984: 955: 695: 222:The game was published for a period in Germany by 1079:"Connection Games VII: Onyx [Larry Back]" 286:. The game was first marketed as a board game in 1449: 1017:Survey of connection games by Dr. Eric Silverman 702:. New York: Simon and Schuster. pp. 73–83. 1092: 1076: 1067: 1058: 1049: 1040: 1031: 1022: 773: 738:. Boca Raton, Florida: CRC Press. p. 114. 686: 651: 596: 156:, a connection game with a capturing mechanic. 962:. Cambridge University Press. pp. 82–93. 682: 680: 678: 599:"Lightning: A Connection Game from the 1890's" 1432: 1120: 565: 563: 561: 259:. Hex was invented by mathematician and poet 828: 675: 403: 159: 50:are typical examples of this type of game. 1439: 1425: 1134: 1127: 1113: 558: 858: 375: 319: 298:marketed a version of it in 1952 called 239: 163: 949: 730:Hayward, Ryan B.; Toft, Bjarne (2019). 573:Connection Games: Variations on a Theme 270:It is traditionally played on an 11×11 1450: 767: 645: 569: 1108: 982: 859:Handscomb, Kerry, ed. (Winter 2002). 90:Mathematical Puzzles & Diversions 88:(1957), expanded and republished in 1391: 934: 803: 576:. Wellesley, MA: A. K. Peters, Ltd. 456:Kaliko, aka Psyche-paths, using hex 450:, also called Con-tac-tix, Nash, or 324:Tak being played with a "Tavern" set 831:"Onyx: An Original Connection Game" 13: 935:Nash, John F. (February 2, 1952). 14: 1479: 1407:-related article or section is a 1011: 1395: 365: 104:, which was a generalization of 987:The Art of Computer Programming 976: 943: 928: 903: 885: 852: 822: 597:Polczynski, Jim (Spring 2001). 140:with preprinted paths, such as 96:proposed a modified version of 16:Abstract strategy game subgenre 797: 752: 723: 620: 590: 1: 870:(12). Carpe Diem Publishing. 551: 263:in 1942 and independently by 1411:. You can help Knowledge by 893:"Havannah & Atoll board" 633:. Parker Brothers, Inc. 1932 7: 1322:Collectible miniatures game 1312:Constructible strategy game 939:(Report). RAND Corporation. 840:. No. 4. pp. 9–12 829:Back, Larry (Winter 2000). 763:. Vol. 24, no. 4. 534: 380:A commercially-sold Y board 284:Brouwer fixed-point theorem 184: 10: 1484: 1390: 1380:Tabletop role-playing game 407: 369: 313: 233: 188: 53: 1337: 1285: 1237: 1143: 1089:Game launched by Nytimes. 1025:"Connection Games I: Hex" 804:Dean, Sandy (July 2008). 541:Combinatorial game theory 410:Category:Connection games 195:Havannah is a two-player 1257:Dedicated deck card game 1087:Connection NYT Unlimited 950:Gardner, Martin (2008). 692:"Eight: The Game of Hex" 570:Browne, Cameron (2005). 404:List of connection games 160:Popular connection games 1458:Abstract strategy games 1032:— (February 22, 2020). 1023:— (February 21, 2020). 1295:Abstract strategy game 1163:Cooperative board game 983:Knuth, Donald (2011). 488:Shannon switching game 381: 330:abstract strategy game 325: 309: 245: 229: 181: 30:paper-and-pencil games 25:abstract strategy game 1375:Social deduction game 1370:Paper-and-pencil game 1247:Collectible card game 1183:Cross and circle game 391:, first described by 379: 323: 243: 191:Havannah (board game) 167: 58:According to Browne, 1168:Deduction board game 1153:Adventure board game 1093:— (March 27, 2020). 1077:— (March 22, 2020). 1068:— (March 19, 2020). 1059:— (March 12, 2020). 952:"8: The Game of Hex" 807:The Game of Bridg-It 328:Tak is a two-player 248:Hex is a two player 1262:Shedding-type games 1050:— (March 9, 2020). 1041:— (March 3, 2020). 783:Scientific American 736:Hex, the full story 661:Scientific American 347:The Wise Man's Fear 279:of the game board. 85:Scientific American 1252:Deck-building game 1195:Running-fight game 546:Mathematical games 513:Through the Desert 478:Qua, 3D Board Game 424:, also called Gale 382: 326: 246: 204:Christian Freeling 182: 1420: 1419: 1388: 1387: 1277:Trick-taking game 998:978-0-201-03804-0 969:978-0-521-75615-0 745:978-0-367-14425-8 583:978-1-56881-224-3 386:abstract strategy 356:three dimensional 340:and published by 250:abstract strategy 197:abstract strategy 1475: 1468:Board game stubs 1463:Connection games 1441: 1434: 1427: 1399: 1392: 1272:Tarot card games 1215:Chinese dominoes 1129: 1122: 1115: 1106: 1105: 1098: 1082: 1073: 1064: 1055: 1046: 1037: 1028: 1005: 1004: 990: 980: 974: 973: 961: 947: 941: 940: 932: 926: 925: 923: 921: 907: 901: 900: 889: 883: 882: 865: 856: 850: 849: 847: 845: 835: 826: 820: 819: 817: 815: 801: 795: 794: 792: 790: 777:(October 1958). 771: 765: 764: 756: 750: 749: 727: 721: 720: 718: 716: 701: 684: 673: 672: 670: 668: 649: 643: 642: 640: 638: 632: 624: 618: 617: 615: 613: 603: 594: 588: 587: 567: 398:Craige Schensted 338:Patrick Rothfuss 236:Hex (board game) 132:(1958/1960) and 1483: 1482: 1478: 1477: 1476: 1474: 1473: 1472: 1448: 1447: 1446: 1445: 1389: 1384: 1360:Icehouse pieces 1333: 1317:Miniatures game 1300:Connection game 1281: 1233: 1205:Tile-based game 1139: 1133: 1102: 1014: 1009: 1008: 999: 981: 977: 970: 948: 944: 933: 929: 919: 917: 909: 908: 904: 891: 890: 886: 863: 857: 853: 843: 841: 833: 827: 823: 813: 811: 802: 798: 788: 786: 775:Gardner, Martin 772: 768: 757: 753: 746: 728: 724: 714: 712: 710: 688:Gardner, Martin 685: 676: 666: 664: 653:Gardner, Martin 650: 646: 636: 634: 630: 626: 625: 621: 611: 609: 601: 595: 591: 584: 568: 559: 554: 537: 532: 463:Lines of action 417:Black Path Game 412: 406: 374: 368: 318: 312: 296:Parker Brothers 290:under the name 257:hexagonal board 238: 232: 193: 187: 162: 56: 21:connection game 17: 12: 11: 5: 1481: 1471: 1470: 1465: 1460: 1444: 1443: 1436: 1429: 1421: 1418: 1417: 1400: 1386: 1385: 1383: 1382: 1377: 1372: 1367: 1362: 1357: 1352: 1347: 1341: 1339: 1335: 1334: 1332: 1331: 1326: 1325: 1324: 1314: 1309: 1308: 1307: 1302: 1291: 1289: 1283: 1282: 1280: 1279: 1274: 1269: 1264: 1259: 1254: 1249: 1243: 1241: 1235: 1234: 1232: 1231: 1230: 1229: 1219: 1218: 1217: 1212: 1202: 1197: 1192: 1187: 1186: 1185: 1175: 1170: 1165: 1160: 1155: 1149: 1147: 1141: 1140: 1136:Tabletop games 1132: 1131: 1124: 1117: 1109: 1100: 1099: 1090: 1083: 1074: 1065: 1056: 1047: 1038: 1029: 1019: 1018: 1013: 1012:External links 1010: 1007: 1006: 997: 975: 968: 942: 927: 902: 884: 868:Abstract Games 851: 838:Abstract Games 821: 796: 766: 751: 744: 722: 708: 674: 644: 619: 608:. pp. 8–9 606:Abstract Games 589: 582: 556: 555: 553: 550: 549: 548: 543: 536: 533: 531: 530: 525: 520: 515: 510: 505: 500: 495: 490: 485: 480: 475: 470: 465: 460: 454: 445: 440: 435: 430: 425: 419: 413: 405: 402: 370:Main article: 367: 364: 342:Cheapass Games 314:Main article: 311: 308: 234:Main article: 231: 228: 189:Main article: 186: 183: 161: 158: 94:Claude Shannon 76:Martin Gardner 55: 52: 15: 9: 6: 4: 3: 2: 1480: 1469: 1466: 1464: 1461: 1459: 1456: 1455: 1453: 1442: 1437: 1435: 1430: 1428: 1423: 1422: 1416: 1414: 1410: 1406: 1401: 1398: 1394: 1393: 1381: 1378: 1376: 1373: 1371: 1368: 1366: 1363: 1361: 1358: 1356: 1353: 1351: 1350:Matching game 1348: 1346: 1343: 1342: 1340: 1336: 1330: 1327: 1323: 1320: 1319: 1318: 1315: 1313: 1310: 1306: 1303: 1301: 1298: 1297: 1296: 1293: 1292: 1290: 1288: 1287:Strategy game 1284: 1278: 1275: 1273: 1270: 1268: 1265: 1263: 1260: 1258: 1255: 1253: 1250: 1248: 1245: 1244: 1242: 1240: 1236: 1228: 1225: 1224: 1223: 1220: 1216: 1213: 1211: 1208: 1207: 1206: 1203: 1201: 1198: 1196: 1193: 1191: 1188: 1184: 1181: 1180: 1179: 1176: 1174: 1171: 1169: 1166: 1164: 1161: 1159: 1156: 1154: 1151: 1150: 1148: 1146: 1142: 1137: 1130: 1125: 1123: 1118: 1116: 1111: 1110: 1107: 1103: 1096: 1091: 1088: 1084: 1080: 1075: 1071: 1066: 1062: 1057: 1053: 1048: 1044: 1039: 1035: 1030: 1026: 1021: 1020: 1016: 1015: 1003: 1000: 994: 989: 988: 979: 971: 965: 960: 959: 953: 946: 938: 931: 916: 912: 906: 898: 894: 888: 881: 877: 873: 869: 862: 861:"Front Cover" 855: 839: 832: 825: 809: 808: 800: 784: 780: 776: 770: 762: 755: 747: 741: 737: 733: 726: 711: 709:0-671-63652-9 705: 700: 699: 693: 689: 683: 681: 679: 662: 658: 655:(July 1957). 654: 648: 629: 623: 607: 600: 593: 585: 579: 575: 574: 566: 564: 562: 557: 547: 544: 542: 539: 538: 529: 526: 524: 521: 519: 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Retrieved 605: 592: 572: 451: 383: 352: 345: 334:James Ernest 332:designed by 327: 299: 291: 281: 269: 247: 224:Ravensburger 221: 215: 211: 207: 202:invented by 194: 177: 173: 169: 153: 149: 145: 142:Psyche-paths 141: 133: 129: 125: 120: 115: 111: 110: 105: 101: 97: 89: 83: 79: 71: 70:(1890s) and 67: 66:, including 63: 59: 57: 45: 34: 20: 18: 1200:Tables game 1190:Legacy game 915:Boing Boing 458:serpentiles 393:John Milnor 304:graph paper 292:Con-tac-tix 148:(1970) and 138:serpentiles 1452:Categories 1405:board game 1305:Tafl games 1222:Train game 1145:Board game 920:23 January 552:References 428:Crosstrack 408:See also: 389:board game 316:Tak (game) 253:board game 200:board game 1365:Piecepack 1345:Dice game 1239:Card game 1178:Race game 1158:Amerigame 897:Hexboards 876:1492-0492 785:: 124–129 663:: 145–150 628:"Zig-Zag" 267:in 1948. 265:John Nash 261:Piet Hein 74:(1932). 68:Lightning 1355:Megagame 1267:Patience 1210:Dominoes 1173:Eurogame 690:(1959). 535:See also 443:Havannah 422:Bridg-It 384:Y is an 372:Y (game) 277:topology 185:Havannah 176:and the 130:Bridg-it 1329:Wargame 1138:by type 732:"6.5 Y" 508:Tantrix 452:Polygon 438:Gonnect 288:Denmark 272:rhombus 72:Zig-Zag 54:History 995:  966:  874:  844:30 May 814:30 May 789:29 May 742:  715:29 May 706:  667:29 May 637:30 May 612:29 May 580:  294:, and 212:bridge 178:bridge 172:, the 146:Kaliko 44:, and 1403:This 1338:Other 864:(PDF) 834:(PDF) 761:Games 631:(PDF) 602:(PDF) 523:TwixT 498:*Star 483:Selfo 473:PÜNCT 134:TwixT 121:Games 47:PÜNCT 42:TwixT 1409:stub 1227:18XX 993:ISBN 964:ISBN 922:2019 872:ISSN 846:2022 816:2022 791:2022 740:ISBN 717:2022 704:ISBN 669:2022 639:2022 614:2022 578:ISBN 518:Trax 493:Star 468:Onyx 433:Dots 336:and 216:fork 208:ring 174:ring 170:fork 154:Onyx 150:Trax 126:Gale 114:and 503:Tak 448:Hex 360:hex 310:Tak 300:Hex 230:Hex 112:Hex 106:Hex 98:Hex 82:in 80:Hex 64:Hex 60:Hex 38:Hex 1454:: 1085:- 1001:. 954:. 913:. 895:. 878:. 866:. 836:. 781:. 734:. 694:. 677:^ 659:. 604:. 560:^ 350:. 306:. 40:, 32:. 19:A 1440:e 1433:t 1426:v 1415:. 1128:e 1121:t 1114:v 1097:. 1081:. 1072:. 1063:. 1054:. 1045:. 1036:. 1027:. 972:. 924:. 899:. 848:. 818:. 793:. 748:. 719:. 671:. 641:. 616:. 586:. 528:Y 180:. 144:/ 128:/ 116:Y 102:Y

Index

abstract strategy game
paper-and-pencil games
Hex
TwixT
PÜNCT
Martin Gardner
Scientific American
Claude Shannon
Games
serpentiles

Havannah (board game)
abstract strategy
board game
Christian Freeling
Ravensburger
Hex (board game)

abstract strategy
board game
hexagonal board
Piet Hein
John Nash
rhombus
topology
Brouwer fixed-point theorem
Denmark
Parker Brothers
graph paper
Tak (game)

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