Hexployt -- A strategy game for two players
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Instructions
Hexployt is like Connect Four
played
in the zero gravity environment
of outer space. The game is played on a (theoretically) infinite plane,
using a large supply of circular tokens of two different colors. Each player
plays using his color of tokens.
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The simplest starting position is
one token of each color touching each other as in figure 1.
Players alternate turns, adding a token of his color to the plane figure
so that the new token touches at least two other tokens. Each token must
be slid into position rather than being dropped in.
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For example, in figure 2, a token cannot be placed at the position marked by an
asterisk. However, a token can be placed at the location marked by the
small circle, forming an "air bubble". A token can also be positioned at the
small dot, touching four neighbors. Can you find the nine other possible
moves in this figure?
As in Connect Four, each player tries
to get four of his tokens in a row
consecutively in one of the three possible directions.
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In spite of its
simplicity, Hexployt is difficult to analyze. Unlike
Connect Four, there
is never a point when the board is filled up and the game is a draw. Rather,
the game continues, with the playing field ever expanding until one player
finally gains the upper hand. The game is loaded with traps and pitfalls, and
many times the best move is hard to determine.
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There is one more rule designed to prevent one player from forcing a draw.
Although this rule is rarely used, it needs a little explanation.
As one plays the game, one quickly finds that there are some formations
that require immediate defense. One such formation is the snake formation,
shown in figure 3. The red token with a plus sign has just been placed, and
the positions marked with either a circle or an asterisk must be vacant. There
will, of course, be more tokens to the right of this figure which
are not displayed here.
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Unless the blue player has a considerable threat elsewhere on the board, he
will have no choice but place his token at the asterisk on his next move.
Otherwise, the red player could occupy the asterisk, giving him three in a
row. Even though the red player cannot win in the next move, he does
threaten to make the following sequence of moves shown in figure 4.
In this sequence, the red player places his token on the plus sign, forcing
the blue player to respond at the asterisk. Finally, the red player would
win by moving at the pound sign. It looks as though the blue player could
block red at the beginning of this sequence, but alas, any attempt to block
red once the sequence in figure 4 has started yields the same fate.
Hence, to avoid losing, blue must prevent red from occupying the
asterisk in figure 3 by getting there first.
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But this does not eliminate the problem, since the red player could then
respond as in figure 5, placing
his token on the plus sign, and forming yet another snake formation.
Blue would be in exactly the same position as in figure 3, and once again
he would have only one way to prevent red from winning. But red could
form yet another snake position, and so on.
Since the blue player's moves are all forced, the red player could extend
the snake indefinitely and force a draw. In fact, careful analysis of the
game shows that the first player would always be able to force a draw in
this manner.
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To prevent either player from using a snake formation to force a draw, the
following additional rule was added:
A player cannot use 3 consecutive moves to
extend one or more of his snake patterns.
That is, if his last two moves
were to extend the snake pattern as above, he must make some other move before
he can continue to extend his snake. This, of course, would give the other
player a chance to "kill" the snake by moving to the plus sign in figure 5
first.
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Even with this additional rule, the first player seems to have initial control
of the game. As a result the game seems to favor the first player, although a
winning strategy is elusive. One way to make the game more fair is to use the
starting position in figure 6. This position starts with an "air bubble" that
neither player can fill. Because several moves are required before the first
threat is realized, there is more of a "cat and mouse" aspect to this game.
This starting position is referred to by this program as the "long game",
while the starting position in figure 1 is called the "short game".
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That's all there is to Hexployt. Enjoy the game!