Simple new strategy game
Gary Wong
play, simple to explain, understandable by a child, and played with just pen
and paper. Like noughts and crosses (tic-tac-toe to Americans), but with
some scope for skill. Of course many such games exist, but ones I know
already don't count :-)
I came up with this: choose an integer n greater than 2, and draw an
n by n grid. The players (X and O) alternate n-1 turns each to mark an
empty cell X or O as appropriate. After n-1 turns, they continue to
alternate marking empty cells, except that no cell may be marked unless
2 of its neighbours (orthogonally or diagonally, i.e. the 4 corner cells
have 3 neighbours; edge cells have 5 and others have 8) have already been
marked by the player. A player loses if unable to move.
(The two phase "place then move" structure is similar to Nine Mens'
Morris. The rule for new cells is somewhat like Conway's Game of
Life. Some of the territorial nature is vaguely reminiscent of Go.
Alternation of placing 2 types of pieces without capture has been
done practically everywhere: hex, go-moku, connect four...)
The 3x3 game is a trivial win for the first player; the second player
can win on even size boards by playing moves symmetrical to the first
(though this is easily avoided by declaring the result where neither
player can move as either a draw or first player win).
Offhand, I can't determine who wins on other size boards. Any comments,
strategies, or solutions?
Cheers,
Gary.
--
Gary Wong, Department of Computer Science, University of Arizona
ga...@cs.arizona.edu http://www.cs.arizona.edu/~gary/
Jonathan R. Ferro
In the 3x3 case, say, does the "free move" part of the game last until
each player has moved once (two player turns) or each player has moved
twice (two game turns)? I guess from your discussion that it must be
the latter.
In the "restricted move" part of the game, must an play in an empty cell
be adjacent to exactly two same-player neighbors or can there be more?
I think that if you are going to say "A player loses if unable to move",
then there should not also be extra rules for what happens when the
board fills--the next player to move should just lose immediately. This
may just mean that you have to disregard even-size boards.
--
Jon Ferro, ECE Systems Administrator
Gary Wong
> In the 3x3 case, say, does the "free move" part of the game last until
> each player has moved once (two player turns) or each player has moved
> twice (two game turns)? I guess from your discussion that it must be
> the latter.
Sorry for the terse description. You're right; in a 3x3 game there will
be 4 free moves (2 each). In the 5x5 case there would be 4 moves each,
for 8 in total. There's no deep reason why there are that many moves,
it just seemed roughly appropriate.
> In the "restricted move" part of the game, must an play in an empty cell
> be adjacent to exactly two same-player neighbors or can there be more?
Oops! There must be at two or more, sorry for the ambiguity.
> I think that if you are going to say "A player loses if unable to move",
> then there should not also be extra rules for what happens when the
> board fills--the next player to move should just lose immediately. This
> may just mean that you have to disregard even-size boards.
Fair enough. An alternative (and almost equivalent) means of scoring is
to continue (passing if necessary) until neither player can move, and
then counting cells. But I agree that the immediate loss rule is simplest
and appears fair on odd-size boards.
Dan
> Last night I was trying to think of a 2 player game that would be quick to
> play, simple to explain, understandable by a child, and played with just pen
> and paper. Like noughts and crosses (tic-tac-toe to Americans), but with
> some scope for skill. Of course many such games exist, but ones I know
> already don't count :-)
>
> I came up with this: choose an integer n greater than 2, and draw an
> n by n grid. The players (X and O) alternate n-1 turns each to mark an
> empty cell X or O as appropriate. After n-1 turns, they continue to
> alternate marking empty cells, except that no cell may be marked unless
> 2 of its neighbours (orthogonally or diagonally, i.e. the 4 corner cells
> have 3 neighbours; edge cells have 5 and others have 8) have already been
> marked by the player. A player loses if unable to move.
>
> (The two phase "place then move" structure is similar to Nine Mens'
> Morris. The rule for new cells is somewhat like Conway's Game of
> Life. Some of the territorial nature is vaguely reminiscent of Go.
> Alternation of placing 2 types of pieces without capture has been
> done practically everywhere: hex, go-moku, connect four...)
>
> The 3x3 game is a trivial win for the first player; the second player
> can win on even size boards by playing moves symmetrical to the first
> (though this is easily avoided by declaring the result where neither
> player can move as either a draw or first player win).
>
> Offhand, I can't determine who wins on other size boards.
The first player. He makes the first move at the center and proceeds to
move symmetrically to his opponent.
Dan
Jonathan R. Ferro
> The first player. He makes the first move at the center and proceeds to
> move symmetrically to his opponent.
This only shows that the first player cannot lose during the "free
placement" phase of the game. What happens when the second player makes
his last free move and the first player cannot imitate it because it is
not legal as a restricted move?