[Some spelling corrected -- djr]
============================================================================
From: "Daniel Baechli" <dlb@brugg-online.ch>
To: "Dave Rusin" <rusin@math.niu.edu>
Subject: Four in a row, more precise information
Date: Fri, 27 Mar 1998 04:06:52 +0100

[deletia]

Oren Patashnik showed in the article "Qubic :4x4x4 Tic-Tac-Toe",
with help of computer calculations, that there is a win for the first player
in the so-called game 'Qubic'. (As mentioned in his answer cited on your page,
http://www.math.niu.edu/~rusin/papers/uses-math/games/other/n-row )

For clarification one should also mention that there are two slightly but
essentially different versions of three dimensional 'Four in a row'
played on a 4x4x4-board. The proof in the article of Oren Patashnik
considers only one of this two versions.

kind regards

DBaechli
- - - - - - - -


Here are the messages for the more precise information. 

-----------------------------------------------------------------------------

Date: Sat, 24 Jan 1998 13:43:16 +0100
From: Daniel Baechli
To: Oren Patashnik
Subject: Re: Four in a row, is it solved?

Dear Mr. Patashnik

You kindly answered my question in sci.math about
the existence of winning strategies in three-dimensional
four in a row.

Numbers of pages refer to "Qubic :4x4x4 Tic-Tac-Toe":

page 211, fig.10 : Here it is obvious that a 'stone' can be placed
at every free coordinate of the 'board'  ( "..., forcing player X to
block at C, ..." ).
The game I had in mind is played slightly but essentially different:
A 'stone' can be placed at (x,y,z) only iff z=0 or if z>=1 and (x,y,z-1)
is not free (x and y for the coordinates in the plane (simular to chess),
z for the level).

page 203: "From game theory ... for positional games the second
player can't force a win ...". The _argumentation_ (although the
conclusion may be true) doesn't hold for the above proposed rules.

I'm very interested in classifying the game in regardance to winning
strategies, so I appreciate any comment.

DBaechli


-----------------------------------------------------------------------------


Date: Sun, 25 Jan 1998 16:50:33 +0100
From: Oren Patashnik
To: Daniel Baechli
Subject: Re: Four in a row, is it solved?

> [edited]

I believe that the game you refer to is (or at least was) marketed as
Score Four; you may be able search the web for that name to learn
something about it.  I don't recall having seen any analysis of it,
but if you learn anything interesting, please let me know.  You're
right that Score Four is not a positional game; in that sense it is
much closer in nature to Connect Four, a game that was solved by
Victor Allis.  He may be able to tell you something about Score Four,
although he didn't mention anything about it in his PhD thesis, which
was about Artificial Intelligence and similar games.  I myself played
Score Four only a few times, about 25 years ago, and I have no strong
feeling about the strategy problem---that is, whether it is a win for
the first player, for the second player, or a tie, under optimal play.
(Score Four, unlike Qubic, has the additional possibility of a
second-player win.)

-- Oren Patashnik

----------------------------------------------------------------------------