Making the neutral points truly neutral means that the first pass can
be made regardless of the number of neutral points. In area rules III
the first pass has to be made when the number of neutral points is even,
because a player loses a point if he passes when the number is odd. At
the same time, since the term (n1  n2) affects the score, both players
compete to be first to pass.
In the equations defining s1 and s2, every stone played after the last
competitive move increases the term (N1  n1) or (N2  n2) by one.
Stones played inside one's own territory do not change the score, the
onepoint reduction being balanced by the onepoint gain, but each stone
played on a neutral point increases the score by one. So if the last
competitive move occurs when there are an odd number of neutral points,
the first player to play after the last competitive move gains a point.
Let's call the time at which the players start scoring points for moves
the "preliminary end" of the game. If we want to let the first
pass be made regardless of the number of neutral points, when a player
makes the first pass, his opponent must have the right to decide whether
this is the preliminary end. This leads us to define the preliminary end
by means of consecutive passes.
If the first pass is made when there are an even number of neutral
points, and if the next player also passes, then the game reaches its
preliminary end with an even number of neutral points left. If the
next player does not pass but occupies one of the neutral points, his
opponent will also occupy a neutral point instead of passing. The
preliminary end will not occur when the number of neutral points is odd.
If the first pass is made when there are an odd number of neutral
points, the next player should occupy one of the neutral points, because
passing and causing the preliminary end of the game would lose a point.
In any case, the player who makes the second consecutive pass always has
the right to do so when there are an even number of neutral points left.
For this reason, territory rules cannot carry on from a single pass
into the second phase as in area rules III. This is why the rule about
the preliminary end is necessary. As a result of this rule, playing on
neutral points before the preliminary end of the game never leads to
profit.
Note that with both area rules III and this preliminaryend rule, the
transition from the first to the second phase of the game occurs when
the remaining number of neutral points is even. Therefore, in area
rules III, if the first pass is made correctly, the opponent should
also be able to pass, marking the preliminary end of the game. The
important point is that if play is continued, the result will be the
same whether the game is scored by the method of area rules III or by
the territoryandprisoners method.
Another point to note is that under the rule of two passes for the
preliminary end, the first pass does not have to be the same as the
first pass under area rules III.
The gist of this discussion is that if the preliminaryend rule is
introduced into area rules III, together with a rule either adding
points for the number of moves made after the preliminary end or
requiring equal numbers of moves after the preliminary end, the score
can be counted by prisoners and territory. Therefore, even though they
differ in the method of transition from the first phase to the second
phase of the game, territory rules I and area rules III are in complete
agreement.
