Connect Four Thesis

The third tier of the tree represents all the possible moves that can be made by the second player.A small subset of the tree (for a small game board) might look like this: Imagine expanding the tree all the way down to the bottom, where the leaf nodes are "terminal" states -- states where one player has won the game, or there is a draw.

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So, while the the perfect tree formula would tell us that there are boards, some smart mathematicians have figured out that there are "only" around 4 trillion different boards. Thankfully, we can use a technique called alpha-beta pruning.

The idea is pretty simple: do not bother searching branches that would either: Now, this is a hand wavey oversimplification of how the process actually works.

PILON: We start seeing laws that allow for children to go to school.

And before you get too excited about some board-game renaissance, consider the sales numbers on board games versus video games. Whatever the case, the instinct to play some kind of game, with some kind of opponent, is extraordinarily common, and long-lived.

It also looks like writing this type of AI is homework for AI classes at Cornell, Northeastern, and Purdue.

I could only find one other Javascript Connect Four AI, which moves substantially faster than mine, but is easily defeated (which is exactly the behavior one would expect).

It'll make it slow down, but it'll get exponentially more difficult. A lot of the boards that you encounter when going down the tree are duplicates (there is more than one way to get to a state).

To avoid recomputing the desirability of these boards, we store them in a hash table.

In order to make moves, the AI applies a minimax strategy.

In other words, the AI assumes that its opponent will always play optimally, and thus tries to minimize the maximum gain of its opponent. The branching factor is approximately seven, and the depth of the tree could be as high as 42.


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