Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

Gomoku is actually a finite two-person game of perfect information. Moreover, if we consider draw as victory of White, then by Zermelo's theorem, exactly one of the two has a winning strategy, either Black or White. In other words, either Black is destined to win, if he does not make any error, or White can at least make a draw.

So my question is which one? the Black or the White?

I have asked a similar question for Go, however, the terminal answer for board 19$\times$19 is still unknown despite of Black having more or less some advantages.

However, for Gomoku there is another story. A programmer asserted that Black has a winning strategy in Gomoku(freestyle). Moreover, (s)he announced (s)he had found this winning strategy and written a program named Gomoku Terminator which "completely terminated the gomoku game". Furthermore, (s)he claimed that the one who first beat the program can earn a bonus $¥920000$ (about $€92000$). But no one has taken this bonus since 2006. So there seems to be sufficient reasons to believe (s)he is right. But I still have a doubt: Do PCs nowadays have enough capability to calculate the whole game tree? Note that the game-tree complexity of Gomoku is PSPACE-complete.

So another question arose: Does Gomoku Terminator(v1.22) really have the winning algorithm for Black?

share|improve this question
add comment

1 Answer

up vote 2 down vote accepted

The Wikipedia article you linked to states that L. Victor Allis showed in $1994$ that black wins on a $15\times15$ board. The "Gomoku Terminator" site you link to has an image of the upper portion of a board with $15$ columns. Thus it seems that this program merely does what was known to be possible in $1994$, and this has no bearing on the open question of the $19\times19$ board. Allis' thesis states that Gomoku used to be played on $19\times19$ boards because that's the size of Go boards, but that the $15\times15$ board has now become the standard.

share|improve this answer
add comment

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.