CROSS AND CIRCLE GAME VS HEX

Cross and circle is a board game design used for race games played throughout the world. The basic design comprises a circle divided into four equal portions by a cross inscribed inside it like four spokes in a wheel; the classic example of this design is Yut. However, the term "cross and circle game" is also applied to boards that replace the circle with a square, and cruciform boards that collapse the circle onto the cross; all three types are topologically equivalent. Ludo and Parcheesi (both descendants of Pachisi) are examples of frequently played cruciform games. The category may also be expanded to include circular or square boards without a cross which are nevertheless quartered (Zohn Ahl), and boards that have more than four spokes (Aggravation, Trivial Pursuit). The game board for the Aztec game Patolli consists of a collapsed circle without an interior cross and thus has the distinction of being a cross that is a circle (topologically), without being a cross plus circle. Tokens are moved around spaces drawn on the circle and on the cross, with the goal of being the first player to move all tokens all the way around the board. Generally the circle of the cross and circle forms the primary circuit followed by the players' pieces. The function of the cross is more variable; for example, in Yut the cross forms shortcuts to the finish, whereas in Pachisi the four spokes are used as player-specific exits and entrances to the pieces' home. In non-race games (like Coppit and Trivial Pursuit) all paths may be undifferentiated in function.

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Hex is a two player abstract strategy board game in which players attempt to connect opposite sides of a hexagonal board. Hex was invented by mathematician and poet Piet Hein in 1942 and independently by John Nash in 1948. It is traditionally played on an 11×11 rhombus board, although 13×13 and 19×19 boards are also popular. Each player is assigned a pair of opposite sides of the board which they must try to connect by taking turns placing a stone of their color onto any empty space. Once placed, the stones are unable to be moved or removed. A player wins when they successfully connect their sides together through a chain of adjacent stones. Draws are impossible in Hex due to the topology of the game board. The game has deep strategy, sharp tactics and a profound mathematical underpinning related to the Brouwer fixed-point theorem. The game was first marketed as a board game in Denmark under the name Con-tac-tix, and Parker Brothers marketed a version of it in 1952 called Hex; they are no longer in production. Hex can also be played with paper and pencil on hexagonally ruled graph paper. Hex-related research is current in the areas of topology, graph and matroid theory, combinatorics, game theory and artificial intelligence.

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