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According to Cameron, the hypergame paradox proceeds as follows: A game is considered as well founded if ANY play of the game ends in a finite number of moves. A hypergame is where the first player chooses well founded a game, and then the second player begins that game (the game is played with the roles reversed). Is the hypergame wf? It should be, because the first player has to choose a wf game, and so it must end in a finite number of moves. But then, as it is well founded, the second player can choose the hypergame, and then the players can choose the hypergame ad infinitum, contradicting the hypergames wf-ness. I do not see how this contradicts the hypergames wf-ness. The definition of a hypergame clearly sttaes that ANY play of the game ends in a finite number of moves. Well, the hypergame begins on the first go, and then if the second player chose tic-tac-toe (or any wf game except the hypergame), the game would be over in a finite number of moves in this case, making it well founded. Surely one case of the hypergame not ending in a finite number of moves does not contradict its wf-ness. I feel like I am being incredibly stupid but I just can't see how this is a paradox.

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    When saying "according to ..." it is common to give an accurate citation and reference.2012-12-17

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