27:
707:
175:(boards smaller than 6×6 are automatic draws), and extremely large or infinite boards are of little practical use. 19×19 Go boards might be the most convenient. For a longer and more challenging game, another suggested size is 59×59, or nine Go boards tiled in a larger square (using the join lines between the boards as additional grid lines).
437:
1999 first on the
Chinese popular BBS site bbs.tsinghua.edu.cn and subsequently on the popular overseas Chinese BBS site bbs.mit.edu (now www.mitbbs.com). However, no Connect6 game records existed or were discussed before Prof. Wu introduced the game Connect6. The history from Prof. Wu is as follows.
440:
One day in the summer of 2003, Prof. Wu came up with this game when playing with his daughter. He started considering the potential of the game to be popular, and began to investigate it. To be popular, he reasoned, his game must be fair and complex, so his first plan was to have a computer program
174:
Game board: Connect6 is played on a square board made up of orthogonal lines, with each intersection capable of holding one stone. In theory, the game board can be any finite size from 1×1 up (integers only), or it could be of infinite size. However, boards that are too small may lack strategy
436:
The main stream of the current
Connect6 development started from the presentation by Professor I-Chen Wu. Since the game rules are simple, it is believed that several have thought of the rules earlier. For example, one claims: the idea of the game (Chinese name "六子棋") emerged on the internet around
214:
are generally too complicated to analyze fully.) Herik, Uiterwijk, and
Rijswijck give an informal definition of fairness (Herik, Uiterwijk, and Rijswijck, 2002) as follows: A game is considered a fair game if it is a draw and both players have roughly equal opportunities for making mistakes. From
276:
complexity of
Connect(19,19,6,2,1) is 10, the same as that in Go or Gomoku. If a larger board is used, the complexity is much higher, since the number of moves increases exponentially with board size; it should still be the same as the other two games on the same size board.
378:≈ 10, much higher than that for Gomoku. Alternatively, if one assumes that the total number of stones placed (instead of the number of moves) is the same as that for Gomoku, that leaves us with an average game length of roughly 15. Then the game-tree complexity is roughly
226:
program written by his team play against itself, and the result seemed to show that the game does not favor either one for these templates. Note that the AI program can beat most casual players, but this does not necessarily imply that its strategy is strictly
230:
The initial breakaway (where White plays far away from the initial black stone) is a guaranteed loss for White, according to
Professor Wu. The principle is that Black can essentially ignore White's move, giving Black a three-stone lead that is
271:
is the number of unoccupied spaces before a move. However, the state-space complexity is largely unchanged, since any legal position in one game will also be legal in the other. Based on the standard in Herik, Huntjens, and
Rijswijck, the
209:
In principle, even some complex games are not fair: either the first or second player has an advantage. (Games such as Gomoku have been mathematically proven to give an advantage to one player or another; complex games such as
284:
complexity. Assume that the averaged game length is still 30, the same as the estimation for Gomoku (Allis 1994). Then, the number of grids chosen to put one stone is about 300, and the number of choices of one move is about
426:
376:
147:-like board, except that Black (the first player) places one stone only for the first move. The one who gets six or more stones in a row (horizontally, vertically or diagonally) first wins the game.
326:
178:
Game moves: Black plays first, putting one black stone on one intersection. Subsequently, White and Black take turns, placing two stones on two different unoccupied spaces each turn.
193:
According to
Professor Wu, the handicap of black's only being able to play one stone on the first turn means that the game is comparatively fair; unlike similar games such as
452:. In the first quarter of 2005, they completed the first Connect6 AI program, which already can beat most players. Then Wu's team allowed his AI program to play itself.
181:
Winner: The player who is the first to get six or more stones in a row (horizontally, vertically, or diagonally) wins. (This is a departure from
428:≈ 10, the same order of magnitude as that for Gomoku given in Allis 1994. Again, if a larger board is used, this complexity becomes much higher.
163:
Players and stones: There are two players. Black plays first, and White second. Each player plays with an appropriate color of stones, as in
201:, which have been proven to give the first player a large advantage, possibly no additional compensation is necessary to make the game fair.
504:
143:
Two players, Black and White, alternately place two stones of their own colour, black and white respectively, on empty intersections of a
251:
are infinite as well. Instead, assume that a Go board is used. The game-tree complexities for it are still much higher than those in
381:
331:
614:
288:
750:
889:
869:
874:
499:
455:
In 2005, Wu's team wrote a paper, presented in the 11th
Advances in Computer Games Conference (ACG11), held in
125:
879:
686:
760:
607:
553:
755:
884:
223:
548:
477:
244:
133:
72:
813:
770:
539:
Kung, H.T.; Robinson, John T. (June 1981). "On optimistic methods for concurrency control".
786:
691:
631:
600:
248:
8:
807:
745:
676:
476:
The program NCTU6, rewritten by
Professor Wu, won gold in the Connect6 tournament at the
566:
445:
469:
On
September 20–September 21, 2005, the game was covered by many news media in
460:
105:
570:
259:, since many more moves are possible placing two stones than one—specifically
838:
696:
558:
97:
85:
666:
661:
494:
113:
706:
639:
466:
In September 2005, ThinkNewIdea Limited built the first Connect6 game server.
26:
863:
449:
155:
The rules of Connect6 are very simple and similar to the traditional game of
219:
Each player always has one more stone than the other after making each move.
828:
198:
562:
843:
823:
765:
654:
623:
273:
818:
791:
721:
281:
164:
144:
121:
215:
this, it is argued that Connect6 is fair in the following senses:
848:
801:
737:
649:
644:
470:
456:
448:
student of Prof. Wu, Dei-Yen Huang, joined Wu's project as his
252:
222:
For about one thousand opening templates, Professor Wu let the
194:
182:
168:
156:
137:
129:
124:
at Department of Computer Science and Information Engineering,
93:
592:
681:
671:
519:
514:
509:
489:
256:
211:
421:{\displaystyle \left({\frac {300\times 300}{2}}\right)^{15}}
371:{\displaystyle \left({\frac {300\times 300}{2}}\right)^{30}}
587:
321:{\displaystyle \left({\frac {300\times 300}{2}}\right)}
384:
334:
291:
328:
or 45,000. Thus, the game-tree complexity is about
420:
370:
320:
441:play the game to see how fair and complex it is.
861:
608:
538:
505:List of Taiwanese inventions and discoveries
615:
601:
235:However, this evidence is not conclusive.
25:
552:
243:If Connect6 uses an infinite board, both
862:
267:−1)/2 moves are possible, where
596:
541:ACM Transactions on Database Systems
13:
120:) introduced in 2003 by Professor
14:
901:
581:
751:Harary's generalized tic-tac-toe
705:
622:
532:
500:Games played with Go equipment
126:National Chiao Tung University
1:
588:The organization for Connect6
525:
238:
280:Now, let us investigate the
16:Abstract strategy board game
7:
483:
204:
10:
906:
761:Strategy-stealing argument
431:
890:Games played on Go boards
779:
714:
703:
630:
117:
109:
101:
89:
68:
60:
52:
44:
36:
24:
150:
870:Abstract strategy games
875:Paper-and-pencil games
478:11th Computer Olympiad
422:
372:
322:
249:game-tree complexities
771:Paper-and-pencil game
563:10.1145/319566.319567
423:
373:
323:
880:Taiwanese inventions
756:Hales–Jewett theorem
692:Ultimate tic-tac-toe
382:
332:
289:
677:Quantum tic-tac-toe
185:, where it must be
21:
814:Three men's morris
444:In spring 2004, a
418:
368:
318:
132:, is a two-player
31:A game of Connect6
19:
857:
856:
787:Nine men's morris
406:
356:
312:
79:
78:
897:
746:Kaplansky's game
715:Related concepts
709:
697:Wild tic-tac-toe
617:
610:
603:
594:
593:
575:
574:
556:
536:
427:
425:
424:
419:
417:
416:
411:
407:
402:
391:
377:
375:
374:
369:
367:
366:
361:
357:
352:
341:
327:
325:
324:
319:
317:
313:
308:
297:
119:
111:
103:
91:
29:
22:
18:
905:
904:
900:
899:
898:
896:
895:
894:
860:
859:
858:
853:
775:
710:
701:
667:Order and Chaos
662:Number Scrabble
626:
621:
584:
579:
578:
554:10.1.1.101.8988
537:
533:
528:
495:Game complexity
486:
434:
412:
392:
390:
386:
385:
383:
380:
379:
362:
342:
340:
336:
335:
333:
330:
329:
298:
296:
292:
290:
287:
286:
241:
231:insurmountable.
207:
189:five in a row.)
153:
48:No setup needed
32:
17:
12:
11:
5:
903:
893:
892:
887:
885:In-a-row games
882:
877:
872:
855:
854:
852:
851:
846:
841:
836:
831:
826:
821:
816:
811:
804:
799:
798:
797:
789:
783:
781:
777:
776:
774:
773:
768:
763:
758:
753:
748:
743:
735:
718:
716:
712:
711:
704:
702:
700:
699:
694:
689:
684:
679:
674:
669:
664:
659:
658:
657:
647:
642:
640:3D tic-tac-toe
636:
634:
628:
627:
620:
619:
612:
605:
597:
591:
590:
583:
582:External links
580:
577:
576:
530:
529:
527:
524:
523:
522:
517:
512:
507:
502:
497:
492:
485:
482:
433:
430:
415:
410:
405:
401:
398:
395:
389:
365:
360:
355:
351:
348:
345:
339:
316:
311:
307:
304:
301:
295:
240:
237:
233:
232:
228:
220:
206:
203:
191:
190:
179:
176:
172:
152:
149:
77:
76:
70:
66:
65:
62:
58:
57:
54:
50:
49:
46:
42:
41:
38:
34:
33:
30:
15:
9:
6:
4:
3:
2:
902:
891:
888:
886:
883:
881:
878:
876:
873:
871:
868:
867:
865:
850:
847:
845:
842:
840:
837:
835:
832:
830:
827:
825:
822:
820:
817:
815:
812:
810:
809:
805:
803:
800:
795:
794:
793:
790:
788:
785:
784:
782:
780:Similar games
778:
772:
769:
767:
764:
762:
759:
757:
754:
752:
749:
747:
744:
742:
740:
736:
734:
732:
728:
724:
720:
719:
717:
713:
708:
698:
695:
693:
690:
688:
685:
683:
680:
678:
675:
673:
670:
668:
665:
663:
660:
656:
653:
652:
651:
648:
646:
643:
641:
638:
637:
635:
633:
629:
625:
618:
613:
611:
606:
604:
599:
598:
595:
589:
586:
585:
572:
568:
564:
560:
555:
550:
546:
542:
535:
531:
521:
518:
516:
513:
511:
508:
506:
503:
501:
498:
496:
493:
491:
488:
487:
481:
479:
474:
472:
467:
464:
462:
458:
453:
451:
450:master thesis
447:
442:
438:
429:
413:
408:
403:
399:
396:
393:
387:
363:
358:
353:
349:
346:
343:
337:
314:
309:
305:
302:
299:
293:
283:
278:
275:
270:
266:
262:
258:
254:
250:
246:
236:
229:
225:
221:
218:
217:
216:
213:
202:
200:
196:
188:
184:
180:
177:
173:
170:
166:
162:
161:
160:
158:
148:
146:
141:
139:
135:
134:strategy game
131:
127:
123:
115:
107:
99:
95:
87:
83:
75:, Observation
74:
71:
67:
63:
59:
55:
51:
47:
43:
39:
35:
28:
23:
833:
829:Connect Four
806:
796:Tic-Stac-Toe
738:
730:
726:
722:
544:
540:
534:
475:
468:
465:
454:
443:
439:
435:
279:
268:
264:
260:
242:
234:
208:
199:Connect Four
192:
186:
154:
142:
81:
80:
53:Playing time
844:Toss Across
766:Futile game
655:Treblecross
624:Tic-tac-toe
274:state space
245:state-space
136:similar to
96:: liùzǐqí;
864:Categories
819:Nine Holes
792:Score Four
547:(2): 213.
526:References
239:Complexity
56:10–60 min.
45:Setup time
549:CiteSeerX
397:×
347:×
303:×
282:game tree
122:I-Chen Wu
834:Connect6
632:Variants
571:61600099
484:See also
463:, 2005.
227:optimal.
205:Fairness
106:Japanese
82:Connect6
73:Strategy
20:Connect6
849:Pentago
802:Gobblet
650:Notakto
432:History
187:exactly
98:Chinese
86:Chinese
37:Players
808:Quarto
645:Gomoku
569:
551:
471:Taiwan
461:Taiwan
457:Taipei
446:master
253:Gomoku
195:Gomoku
183:Gomoku
169:Gomoku
157:Gomoku
138:Gomoku
130:Taiwan
114:Korean
100::
94:Pinyin
88::
69:Skills
61:Chance
733:-game
682:Renju
672:Pente
567:S2CID
520:Teeko
515:Renju
510:Pente
490:Chess
257:Renju
212:chess
151:Rules
824:Achi
741:game
255:and
247:and
197:and
167:and
110:六目並べ
64:None
839:OXO
687:SOS
559:doi
400:300
394:300
350:300
344:300
306:300
300:300
128:in
102:連六棋
90:六子棋
866::
565:.
557:.
543:.
480:.
473:.
459:,
414:15
364:30
224:AI
165:Go
159::
145:Go
140:.
118:육목
116::
112:;
108::
92:;
739:n
731:k
729:,
727:n
725:,
723:m
616:e
609:t
602:v
573:.
561::
545:6
409:)
404:2
388:(
359:)
354:2
338:(
315:)
310:2
294:(
269:n
265:n
263:(
261:n
171:.
104:;
84:(
40:2
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.
