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Game Theory

http://gameinfo.na.leagueoflegends.com/en/game-info/get-started/new-player-guide/

This link will take you to the massively popular free to play game, League of Legends. The word game here may be an understatement. League of Legends is officially recognized as an e-sport. In fact, it is the first official e-sport recognized by the United States; and it is helping to pave the way for other e-sports to follow. This game is played between two teams of five players (5v5). The game must always be played this way. It is designed around teamwork. Each player picks a champion, and then the game becomes five player controlled champions versus the other teams five player controlled champions.

In order to be recognized, it must be relatively balanced; meaning that both teams will have a 50/50 chance of winning assuming equal skill level.  League of Legends can be related to game theory (albeit, an extremely complicated version.) There are so many decisions to factor in with this game, that creating a payoff matrix for it would take quite a bit of time. To illustrate the vastness of this payoff matrix, let us observe what a matrix would look like if we were to just compare champion skills against each other. There are currently a total of 116 champions to select from. Each champion has four abilities to use (there are some exceptions, but generally a champion has four abilities to use at any given time). Some abilities are better used on certain champions than others. The effectiveness of these abilities being used against certain champions can be represented as the payoff of using one skill against any given champion. Assuming that each ability can be used against only one other champion gives one champion a total of 40 possible moves to make.  Assuming a five versus five, each team would have 200 possible moves to make against the other team. This is an example of a VERY restricted five scenario in the game. The game itself has many other factors to take into account to make certain abilities more or less effective. Again remember, there are 116 champions, most with 4 abilities to use. Champions can also move around and dodge others abilities. Some abilities will affect more than one enemy champion, some abilities get better as the game moves on. The payoff matrix is always changing as the game progresses.

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