From: flee@cs.psu.edu (Felix Lee)
Subject: Re: Go-moku and variants.
Date: Thu, 19 Nov 1992 06:44:10 GMT

Douglas T Ridgway:
> Does anyone know a precise statement of those restrictions?

[Excerpted from _New Rules for Classic Games_]

*Renju*

Played professionally in Japan, and popular in Europe and Russia,
Renju is an outstanding game.  It is similar to Five-in-a-Row, but
with these differences:

1. A board of 15 lines by 15 lines is used.  The reason is that a
larger board tends to favor the first player (Black) too much, while a
smaller board results in too many draws.

2. One player is randomly chosen to be the "tentative Black" player,
who puts a black stone on the board's center point.

3. The other player, known as "tentative White," places a white stone
on the eight intersections adjacent to the black stone.

4. The tentative Black player then adds the next stone, and in so
doing must form one of the 24 patterns shown in [diagram
	. . . 3		. 3 3 3
	. . 2 3		. 2 3 3
	. 1 3 3		. 1 3 3
	3 3 3 3		. 3 3 3
	3 3 3 3		. 3 3 .
] (or a rotation or mirror image of one of them).

5. The tentative White player now has the option of switching sides
and becoming Black or of remaining White.

6. Whichever player is now White places a white stone anywhere on the
board.

7. For the next move (the fifth move in the game), Black suggests two
different choices---which must not be equivalent to each other by
virtue of symmetry---by placing two black stones on the board.  White
chooses one of these two black stones and removes it.

8. White now makes a move anywhere on the board.

9. For the rest of the game, the players take turns placing one stone
of their color on the board.  White may place stones anywhere, without
restriction.  Black's choices, however, are subject to certain
restrictions, known as "prohibited moves":

a. Black may not make an "overline", which is six or more stones of
his color in an unbroken line.  (White may make an overline---and if
he does, he wins, since he has then made five in a row.)

b. Black may not make a "double four", which is a move that
simultaneously makes two "fours".  A "four" is a set of four stones of
one color in a row---not necessarily an unbroken row---that can become
a five-in-a-row with the addition of a single stone.

c. Black may not make a "double three", which is a move that
simultaneously makes two "threes".  A "three" is defined as three
stones in a line that, with the addition of one stone, can become a
"free four".  A "free four" is defined as a "four" that can become a
five in two different ways---that is, an unbroken row of four that has
a vacant point at each end.

Note that Black may make a move that simultaneously creates a three
and a four, which is in fact the usual way for Black to win.
[diagram] shows some examples of threes and fours.

10. Black wins if he makes five in a row.  White wins if he makes five
or more in a row.  White also wins if Black makes a prohibited
move---unless the prohibited move gives Black five in a row, in which
case Black wins.

Renju's rules are an excellent example of how far serious players are
willing to go to fine-tune the rules of a game to balance both sides'
chances.  The rules given are those of the Sweden-based Renju
International Federation, and they have been used in international
competition.  Older, but slightly less complicated rules may be found
in the excellent book on Renju strategy, _Five-in-a-Row (Renju)_ by
two Japanese professional players, Goro Sakata and Wataru Ikawa (Ishi
Press, 1981).
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