HEX VS LOST CITIES

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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Lost Cities is a 60-card card game, designed in 1999 by game designer Reiner Knizia and published by several publishers. The objective of the game is to mount profitable expeditions to one or more of the five lost cities (the Himalayas, the Brazilian Rain Forest, the Desert Sands, the Ancient Volcanos and Neptune's Realm). The game was originally intended as a 2-player game, but rule variants have been contributed by fans to allow 1 or 2 further players, causing Reiner Knizia himself to later provide semi-official 4-player rules. Lost Cities is a fast-moving game, with players playing or discarding, and then replacing, a single card each turn. Cards represent progress on one of the five color-coded expeditions. Players must decide, during the course of the game, how many of these expeditions to actually embark upon. Card-play rules are quite straightforward, but because players can only move forward on an expedition (by playing cards which are higher-numbered than those already played), making the right choice in a given game situation can be quite difficult. An expedition that has been started will earn points according to how much progress has been made when the game ends, and after three rounds, the player with the highest total score wins the game. Each expedition that is started but not thoroughly charted incurs a negative point penalty (investment costs). Interaction between players is indirect, in that one cannot directly impact another player's expeditions. However, since players can draw from the common discard piles, they are free to make use of opposing discards. Additionally, since the available cards for a given expedition are finite, progress made by an opponent in a given color can lead to difficulty making progress in that same color. The game's board, while designed to supplement the theme, is optional and consists only of simple marked areas where players place discards. If Lost Cities had four expeditions instead of five, it could be played with a standard deck of playing cards. When doing so, the face cards would represent investment cards, with numbered cards two through ten serving as the expedition progress cards.

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