03/02/2006 Archived Entry: "Go Moku"

In elementary school, I solved Tic Tac Toe. That is to say, that I sat down and thought out the best possible strategies and realized that the player who makes the first move has the advantage. Anyone who’s played even two games of 3T knows that the center is the most valuable position, I had formalized it a little bit and worked out the sequence in which first player should make his moves to win. At the same time, I strategized for second player and realized that under perfect play the best second player can expect is a draw. 3T became deeply flawed and much too simplistic; I never played it again.

Fast forward to last weekend. Etienne showed me Go Moku, it’s like Tic Tac toe except you have to make sequences of 5 instead of 3 and you play on a board that is 19x19 using a Go board and accompanying pieces. Because the board is so much bigger (I’ve yet to have a game where I’ve reached the edges) and you have to make sequences of 5, the complexity is vastly increased.

Doing a bit of research though, I found that Go Moku is even more flawed than TTT! It turns out that it’s been proven first player can always force a win if he plays perfectly! Even a perfect game from second player will lose. In TTT, player 2 can at least hope for a draw. This is just unacceptable! Go Moku has lost a lot of its luster this day.

In a more pragmatic view though, perfect play for a human is probably impossible. The game’s much too complex for that. Even after playing a few dozen rounds, I didn’t really see the benefit of the first played piece. It’s probably not until very high level play that one can recognize the importance of the middle position.

In Go, there is a similar situation. A large difference in skill levels will often be offset by a few (very few) pieces put on the board for the weaker player before the stronger player can make a move. It is very difficult to grasp that in a 19x19 board with games going for more than 200 moves how 5 extra pieces can be considered a handicap. Heck, Tic Tac Toe requires at most 5 moves at most from each player.

Replies: 9 comments

Screw all these other games, you only need one:

KARATE!

Posted by Dave @ 03/02/2006 04:08 PM EST

Karate! Or is it Katana.

"I'm fooling you!"

Posted by djkimothy @ 03/03/2006 02:17 PM EST

http://www.bibmath.net/jeux/gomoku.php3
Test your might!

Posted by Étienne @ 03/04/2006 02:56 AM EST

No kim!

"Are you tricking me?!?"

Posted by Anonymous @ 03/05/2006 04:37 AM EST

I've seen a variant of what you're describing as the final puzzle in the 11th Hour computer game.
You could win either by forming a line of 5, or capturing 5 pairs of your opponent's pieces (you capture a pair by placing your pieces on either end of two of the opponent's pieces: X00X).

Speaking of games where the first player always wins, have you ever been presented with 15 matches (one row of three, one row of five, one row of seven) and told to pick any number of matches from any single row (each person taking turns)?

Posted by Arshwana @ 03/09/2006 01:13 PM EST

what's the matches object...to own the last match?

Posted by rayne @ 03/09/2006 02:30 PM EST

Yeah.

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