THE IMPORTANCE OF A PIECE DIFFERENCE FEATURE TO BLONDIE24

Belal Al-Khateeb Graham Kendall bxk@cs.nott.ac.uk gxk@cs.nott.ac.uk

School of Computer Science (ASAP Group)

University of Nottingham

Outline

- Introduction - Checkers - Samuel’s Checkers Program- Blondie24- Brunette24- Experimental Setup - Results and Discussion- Conclusions

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Checkers3

Opening Board of Checkers (Black moves first)

Checkers4

Black Forced to make Jump move

Checkers5

Black Gets King

Samuel’s Checkers Program

- 1959, Arthur Samuel started to look at Checkers

- The determination of weights through self-play

- 39 Features

- Included look-ahead via mini-max (Alpha-Beta)

- Defeated Robert Nealy

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Blondie24

- Produced by Fogel in 1999-2000

- Neural network as an evaluation function.

- Values for input nodesRed (Black) – positiveWhite – negativeEmpty – zero

- Piece differential

- Subsections (sub-boards)

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Blondie248

Blondie24’s EANN Architecture

Blondie24

- Initial population of 30 neural networks (players).

- Each neural network plays 5 games (as red) against 5 randomly chosen players:-+1 for a win0 for a draw-2 for a loss

-Best 15 players retained, the other 15 players eliminated.

-Copy the best 15 players (replacing the worst 15) and mutate the weights.

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Blondie24

-Repeat the process for 840 generations and the best player after these generations is retained.

- Played 165 games at zone.com.

- Rating: 2045.85 at that time

- In top 500 of over 120,000 players on zone.com at that time.

-Better than 99.61% of registered players on zone.com

- End Product

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Blondie24

-Fogel received many comments about Blondie24 design. One of them is concerned with the piece difference feature and how it affects the learning process of Blondie24.

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Piece-count

Win Draw Lose

Blondie24 12 0 2

Table1: Results of Playing 14 Games between Blondie24 and Piece-count Using Material Advantage to Break Tie.

Blondie24

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Piece-count

Win Draw Lose

Blondie24 10 3 1

- It is clear that Blondie24 is significantly better than a piece-count player, and by using a standard rating formula, the results suggest that Blondie24 is about 311 to 400 points better than the piece-count player.

Table2: Results of Playing 14 Games between Blondie24 and Piece-count Using Blitz98 to Break Tie.

Brunette24

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- Designed by Evan Hughes as a re-implementation of Blondie24.

- Hughes used the same structure that is used for Blondie24.

- Hughes used the same experiment as Fogel to show the importance of a piece difference.

Brunette24

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Piece-countWin Draw Lose

Evolved Piece Count

680 300 20

- By using a standard rating formula, the results suggest that the evolved piece difference player is about 528 points better than piece difference player.

Table3: Results of Playing 1000 Games between the Evolved Piece Count player and Piece-count player.

Brunette24

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- By using a standard rating formula, the results suggest that the evolved piece difference player is about 80 points better than xcheckers.

Xcheckers

Win Draw Lose

Evolved Piece Count

220 660 120

Table4: Results of Playing 1000 Games between the Evolved Piece Count player and xcheckers.

Experimental Setup

- Two implementations of Blondie24 were done, one with a piece difference feature, which is called Blondie24-RPD, while the other is without a piece difference feature and is called Blondie24-R.

- Our previous efforts to enhance Blondie24 introduced a round robin tournament. The resultant player (Blondie24-RR) is used to show the importance of the piece difference feature. This is done by implementing a player which is the same as Blondie24-RR, but, without a piece difference feature. This player is called Blondie24-RRNPD.

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Experimental Setup

-To measure the effect of a piece difference feature in Blondie24, Blondie24-RPD was played against Blondie24-R by using the idea of a two-move ballot.

- The games were played until either one side wins or a draw is declared after 100 moves for each player.

-The same procedure was also used to play Blondie24-RR against Blondie24-RRNPD

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Results and Discussion18

Opponent:Blondie24-R

Win Draw Lose

Blondie24-RPD

59 14 13

-By using a standard rating formula, the results suggest that Blondie24-RPD is about 428 points better than Blondie24-R.

Table 5: Results when Playing Blondie24-RPD against Blondie24-R using the Two-Move Ballot

Results and Discussion19

Opponent: Blondie24-RNPD

Win Draw Lose

Blondie24-RR 61 16 9

- By using a standard rating formula, the results suggest that Blondie24-RR is about 489 points better than Blondie24-RRNPD.

Table 6: Results when Playing Blondie24-RR against Blondie24-RRNPD using the Two-Move Ballot

Conclusions

-Piece difference feature is important to the design of Blondie24.

-Neural network is also an important element of the whole design but the results presented here demonstrate a simple feature is able to significantly improve the overall playing strength.

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References21

1- Samuel, A. L., Some studies in machine learning using the game of checkers 1959,1967.

2- Fogel D. B., Blondie24 Playing at the Edge of AI, United States of America Academic Press, 2002.

3- Chellapilla K. and Fogel, D. B., Anaconda defeats hoyle 6-0: A case study competing an evolved checkers program against commercially available software 2000.

4- Fogel D. B. and Chellapilla K., Verifying anaconda's expert rating by competing against Chinook: experiments in co-evolving a neural checkers player.

5- Chellapilla K. and Fogel D.B., Evolution, Neural Networks, Games, and Intelligence,” 1999..

6- Chellapilla K. and Fogel D. B., Evolving an expert checkers playing program without using human expertise.

7- Chellapilla K. and Fogel D. B., Evolving neural networks to play checkers without relying on expert knowledge.1999.

Questions/Discussions

Thank You

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