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I have successfully figured out how the minimax algorithm works for a game like chess, where a game tree is used, and you assign a value to the terminal nodes and propagate that value up the tree.

Is there a way to represent this algorithm mathematically? If so, how would I go about showing it?

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A simple google search gives plenty of results.

If you have a look at the entry in wikipedia for Minimax it has mathematical representations as well as some basic pseudocode and tree representations to help grasp the concept.

Proving it would be a matter of going through the regular methods of a mathematical proof and would probably be a bit complicated. It is far easier to discuss this by way of graphs.

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