Q: 誰最早證明五子棋一般規則及日本連珠規則必勝?

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A: 據了解,這兩種規則日本連珠專家即早已聲稱證明為黑先必勝。在學界,Allis 等人(Allis 1994; Allis, Herik and Huntjens, 1995) 是第一個證明出一般規則黑必勝。至於日本連珠棋規是Wagner and Virag(Wágner and Virág, 2001)第一個解出來的。

這點也常常會造成學界與棋界之間的誤解!這個差異,在五子棋界(甚至圍棋界、象棋界)而言,許多樹狀變化,對棋士而言即已算是證明了,無須贅述。但對學術界而言,證明必須是十分嚴謹的,若有一小部份樹狀變化分支不夠清楚,就不算證明。例如,擋法有兩百多種,如何證明其他一定是無效的。因此,在學術界,普遍的認知是五子棋界所提供的,尚無法說是證明。下述這段英文引述自Allis 1994論文中(第一個證明出一般規則黑必勝的作者),5.1節之第二段:

In Japan professional renju players (renju being a complicated variant of go-moku) have studied go-moku in detail and have stated that the player to move first (black) has an assured win (Sakata and Ikawa, 1981). These statements are sometimes accompanied by a list of main variations, such as the 32-page analysis in Sakata and Ikawa (1981). Close examination of these analyses reveals that in each position only a small number of white moves are analyzed.  For example, after black's first move at the center of a 15x15 board, white has 35 distinct moves, of which 2 are adjacent to black's first move, ignoring symmetrically equivalent moves. In Sakata and Ikawa (1981) only the variations after 2 moves adjacent to black's first move are discussed. As far as we know, prior to this work no complete proof of black's win in go-moku has been published.

最後兩句話是說:Sakata and Ikawa只有考慮到黑第一手後白的兩種棋(鄰近黑第一手棋)之後的變化。因此Allis無法認定有完整的證明。原則上,除非有人能提供其他相關資料或證據,來顯示更早即已有證明,我們將採用學術界的說法。


Allis, L. V. (1994). Searching for solutions in games and artificial intelligence, Ph.D. Thesis, University of Limburg, Maastricht.

L.V. Allis, H.J. van den Herik, M.P.H. Huntjens, Go-Moku solved by new search techniques, Comput. Intelligence: An Internat. J. 12 (1) (1995) 7–24.

Sakata, G. and Ikawa, W. (1981). Five-In-A-Row. Renju. The Ishi Press, Inc., Tokyo, Japan.

Wágner, J., Virág, I. (2001) Solving Renju, ICGA Journal, Vol. 24 (1) 30–34.