Date: Sat, 10 Jan 1998 11:21:32 -0800 (PST)
From: Oren Patashnik
To: rusin@vesuvius.math.niu.edu
Subject: Re: Four in a row, is it solved?

> In article <68lvg0$bj2$1@ubnnews.unisource.ch>,
> Daniel Baechli <dlb@brugg-online.ch> wrote:
> >My question is concerning Four in a row played
> >on a 8x8 board in two dimensions or with a 4x4x4
> >board in three dimensions.
> >The obligate question - is the optimal
> >strategy determined for any of the two?

Here's a response I sent him via email:

I'm assuming your question concerns four-in-a-row in tic-tac-toe-like
games.  A good reference is Berlekamp, Conway, and Guy's book "Winning
Ways", Academic Press, 1982.  It's in two volumes, and chapter 22 (in
volume 2) discusses games like these.  They don't report on the status
of the 8x8 game, but they report that four-in-a-row on a 5x5 board is
a tie.  I've never played four-in-a-row on an NxN board, but my
slightly educated guess is that it's a first-player win if N >= 7 and
a tie if N <= 6, so my guess is that 8x8 is a first-player win.  If
you learn anything about any of these four-in-a-row NxN games for any
N bigger than 5, I'd very much appreciate hearing about it.

As for four-in-a-row on a 4x4x4 board: I proved in 1977, via a
computer program, that it's a first-player win.  My paper describing
the proof is "Qubic: 4x4x4 Tic-Tac-Toe", Mathematics Magazine,
53(4):202--216, September 1980.  If you'd like a reprint let me know.

        -- Oren Patashnik