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heuristic_analysis.md

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Heuristic Analysis

Heuristic functions

1rst

The first function in the one given in the lectures. It measures the number of the legal moves for the player in his current position

player_moves

2nd

This function calculates the difference between the number of legal moves for the player and his oponent. It doens't use the absolute value because if it's negative, it means that the oponent has more moves than the player and that is something to take into account

player_moves - opponent_moves

3rd

As the second one, it calculates the difference but squaring the oponent moves giving a penalty to the oponent moves.

player_moves - opponent_moves ** 2

4th

As the third one, it calculates the difference but squaring the player moves

(player_moves ** 2) - opponent_moves

Results

1st

2nd

3rd

4th

Conclussion

The best performance is given by the 3rd option player_moves - opponent_moves ** 2. Looks like givin penalty to the opponent moves is working. But we cannot conclude that that is the best option because all the results are really close to each other. The minimum is 74.52% and the maximum is 77.38%.

I choosed tho because:

  1. It has the best score
  2. It wins 2/3 of the times agains MM_Improved
  3. It performs really well against Alpha Beta

We would need to run much more games in order to be more confident about the results, but the improvement looks minimum though. I wanted to try another heuristic but given the constrain of the Board it wouldn't have a lot of difference with the player moves. I wanted to try the liberty degrees of the player. I mean, the directions where a player can move. If the player is in the center, it can move up, down, right, left, and in 4 diagonals. That's a total of 8 degrees of liberty. If it is in a corner it would have only 3. It sound like a really good feature to introduce in the heuristic, but our game is constrained to only L moves, so it doesn't have a lot of sense with this constrain given that it will be a multiple of the available moves (In the center, a player would have 8 Ls moves and 4 liberty degrees).