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A finite game (sometimes called a founded game [1] or a well-founded game [2]) is a two-player game which is assured to end after a finite number of moves. Finite games may have an infinite number of possibilities or even an unbounded number of moves, so long as they are guaranteed to end in a finite number of turns.
An infinite universe (unbounded metric space) means that there are points arbitrarily far apart: for any distance d, there are points that are of a distance at least d apart. A finite universe is a bounded metric space, where there is some distance d such that all points are within distance d of each other.
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On Numbers and Games was also a fruit of the collaboration between Berlekamp, Conway, and Guy. Combinatorial games are generally, by convention, put into a form where one player wins when the other has no moves remaining. It is easy to convert any finite game with only two possible results into an equivalent one where this convention applies.
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Free-to-play (F2P) refers to video games which give players access to a significant portion of their content without paying. There are several kinds of free-to-play games, but the most common is based on the freemium software model.
A finite game is played for the purpose of winning, an infinite game for the purpose of continuing the play. Finite games are those instrumental activities - from sports to politics to wars - in which the participants obey rules, recognize boundaries and announce winners and losers. The infinite game - there is only one - includes any authentic ...