Go moku Variants

5-in-a-row is a shape-making game with 2 winning shapes - 5 diagonally and 5 vertically.

What about the games resulting from having to make other shapes? like a square? or an S?

The smaller shapes I've tested (with 3 stones) have pretty easy forced wins. Obviously in a game like this going first is a forced win.

Is it possible for a shape to never have a forced win? Some of them seem absurd, like a 100�100 square - but I still don't see how to actually prove it could never win in an infinite game. I guess each defensive move in this game prevents many many possible winning positions. Or, to win you have to play 10,000 moves unopposed. On a 2d board how could you ever do this?

If the defender's strategy is to always play above your stone, unless that's blocked with his own stone, in that case play below, then left, then right. Would it be possible to beat even this bad defender?

You could play a horizontal line 100 stones wide, and he'd play above every time. Then when you started your 2nd row, above would already be blocked and he would play below, ruining that one. So how could you ever get to 100x100?

The Obvious Question

Then, is, which is the largest shape which nevertheless has a forced win? A slightly different one is, what's the most complex (or most regular...) shape which has a forced win?

Also, what is the smallest shape which doesn't have a forced win?

Another Question

Of all 5-stone shapes, which one has the fastest forced win? slowest? How do forced win times vary by shape?



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3/22/2013 6:52:13 PM
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