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Parity The Othello
Game Description:
Parity has the same great strategy
of Othello capture as many disks
as possible
in each round to win the most Parity cards. With 51 cards
to play off
the Centerpiece Card,
There's no predicting when a state
of Parity will happen!
Parity Games
are (possibly) infinite games played on a graph by two players, 0 and 1.
In such games, game positions are assigned priorities, i.e. natural
numbers.
The winner of a finite play of a parity game is the player whose
opponent is unable to move. The outcome of an infinite play is
determined by the priorities of the occurring positions. Typically,
player 0 wins an infinite play if the highest infinitely often occurring
priority is even. Player 1 wins otherwise. Whence the name "parity".
Parity games lie in the third level of the borel hierarchy and are as
such determined[1]. Games
related to parity games were implicitly used in Rabin's proof of
decidability of second order theory of n successors, where determinacy
of such games was proven[2].
Knaster-Tarski theorem leads to a relatively simple proof of determinacy
of parity games[3].
Moreover, parity games are history-free determined[3][4],
so that if a player has a winning strategy then she has a winning
strategy which depends only on the board position, and not on the
history of the play.
From
http://en.wikipedia.org/wiki/Parity_game
Contents:
51 Parity Cards
Centerpiece Card
Instruction Booklet
2 Quick Reference Cards
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