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Path: utzoo!watmath!clyde!cbosgd!ihnp4!bentley!kwh
From: kwh@bentley.UUCP (KW Heuer)
Newsgroups: net.puzzle
Subject: Re: Inverse Tic-Tac-Toe
Message-ID: <602@bentley.UUCP>
Date: Fri, 28-Feb-86 10:20:09 EST
Article-I.D.: bentley.602
Posted: Fri Feb 28 10:20:09 1986
Date-Received: Sat, 1-Mar-86 16:27:38 EST
References: <873@spp2.UUCP>
Organization: AT&T Bell Laboratories, Liberty Corner
Lines: 27

In article <873@spp2.UUCP> spp2!stassen (Chris Stassen) writes:
>Suppose we keep the same rules of playing (3x3 board, alternating
>turns, etc.), but change the requirements for winning.  The winner of
>the game is the player who forces his OPPONENT to occupy three squares
>in a row.

It is a draw under rational play.  The first player can start in the
center and then mirror his opponent.  I don't have a quick proof for
the second player, but clearly he has the advantage of having one
less mark to place.

The interesting thing about this game is that the optimal first move
is the center, which at first glance might seem like a good point to
avoid.  In fact, I believe the first player loses if he doesn't play
there, or if he doesn't mirror his opponent's next move.  This game
was analyzed in _Mathematics Magazine_ ca. 1975-1980 (sorry I can't
pinpoint it; it's also possible it was in _The American Mathematical
Monthly_ instead).

Now, a related question.  A friend (since deceased) once told me that
on a 4x4 board, with the winner being the first to achieve a line of
three of his own marks *and one of his opponents*, the game is a
second-player win.  Does anybody have further knowledge of this?
(I realize the game is slightly ill-defined -- the game x22 o11 x23
o31 x44 o41 x43 o24 x21 seems to win for both players)

Karl W. Z. Heuer (ihnp4!bentley!kwh), The Walking Lint