Saturday, September 20, 2008

Clockwise-Counterclockwise Game

Here is another game I came up with (which, as is usually
the case, may or may not be original).
For 2 players.
A circle is drawn on paper and the outside of the circle
is marked into 26 equally sized spaces (like a clock
with 26 hours).
Each space is labeled with a different letter, A to Z.
The game starts at position A.
On each move, a player starts at the position last visited
by his opponent, player 1 moves clockwise around the circle,
player 2 moves counter-clockwise.
When a player finishes moving, he/she places a mark at the
space she/he lands upon.
Players move 1 space on their own first move, 2 spaces on
their own second move, 3 spaces on their own third move, etc,
until on their last and tenth moves they move 10 spaces each.
Players on their kth move can do one of two things:
*Move k spaces (in their direction), counting already landed
on spaces. The player should not land on an already moved onto space.
*Move k EMPTY spaces (spaces with no marks) in their direction.
If part of the circle looks like this (after being flatted out):
.A . B . C . D . E . F . G
and the last player moved to A, and it is the 4th move,
the player whose turn it is (if moving to the right)
can either move to E (4 spaces, whether marked or not)
or to G (4 unmarked spaces).
During an entire kth move, a player either always counts the moved
on spaces or always does not count the moved on spaces as part of
the kth move. In other words, there is no mixing during a move of
counting methods. But player can use different counting methods on
different moves.
Now, at the game's beginning, each player secretly picks a space
they believe the final move of the game (the 2nd player's 10th move)
will land upon or near, and they secretly write the letter of this
space down.
The player whose guess is closest to the actual last position of the
game wins the game.
What would be a good strategy for this game?
(It might seem at first that the last player to move has a lot of
power over where the game ends up. But the last player will be
forced probably to count only empty spaces, since they otherwise
would likely land on an already landed on space, which is forbidden.)
Leroy Quet

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