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Is One Better than None?

Is One Better than None?. Does foresight allow an artificial intelligence to survive longer in Tetris?. William Granger and Liqun Tracy Yang. The Game of Tetris. Board is 10x20 blocks Board is empty at start A complete line will remove the line of blocks

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Is One Better than None?

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  1. Is One Better than None? Does foresight allow an artificial intelligence to survive longer in Tetris? William Granger and Liqun Tracy Yang

  2. The Game of Tetris • Board is 10x20 blocks • Board is empty at start • A complete line will remove the line of blocks • When a tetromino cannot exit the “spawning area”, the game is over. Tetrominoes: 7 pieces that consist of four blocks each in different possible combinations.

  3. What is Foresight? • Foresight means having knowledge of the next piece or pieces before they are on the board • One-step look-ahead means having knowledge of the current piece and the first next piece

  4. Related Work • The Tetris algorithm with foresight has been coded several years ago • Most research involved in Tetris focuses on NP related problems 1 • Certain tetromino sequences have been proven to make any algorithm fail 2 1.) E.D. Demaine, S. Hohenberger, and G. Liben-Nowell, Tetris is Hard, Even to Approximate, Technical Report MIT-LCS-TR-865, Laboratory of Computer Science, MIT 2002 2.) H. Burgiel. How to lose at Tetris. Mathematical Gazette, pages 194-200, July 1997

  5. A Tetris Comparison Without ForesightWith Foresight

  6. Our Goals • Discover whether foresight makes the program survive longer. • See if certain sequences require no foresight

  7. Zero-step Look-ahead A.I. • Uses a heuristic algorithm • Penalizes for holes, roughness, piece height • Rewards for filling a line • Chooses the move with the highest score

  8. Zero-step Look-Ahead A.I. • Holes = -1 • Roughness = -22 • Piece Average Height = -1.5 • Remove Line Score = +0 • Total Score = -24.5

  9. Zero-step Look-Ahead A.I. • Holes = -1 • Roughness = -18 • Piece Average Height = -0.5 • Remove Line Score = +10 • Total Score = -9.5 • This move has a higher score than -24.5, so this move wins!

  10. One-step Look-ahead A.I. • Uses the same heuristic algorithm as zero-step look-ahead A.I. • Takes the average to determine final result

  11. How A.I. 1 makes a move vs. A.I. 0 • May make a different move since the next piece can make a move with a better score • Having the next piece clear lines also affects where the current piece will go

  12. Hypothesis • For this particular heuristic algorithm, we hypothesize that for all sequences a one-step look-ahead will always clear more lines than a zero-step look-ahead

  13. Experiments & Analysis • Coded a Tetris program with the heuristic algorithm • Had Tetris program run repeatable sequences • Looked for bad and unexpected moves

  14. Sequences Used for Analysis • SOL Sequence: holes analysis • I+? Sequence: I-piece improve survivability? • ZTL Sequence: roughness analysis • Random Sequence: normal play

  15. SOL SequenceA.I. 0 A.I. 1

  16. All two piece sequences with an I-piece SZI sequence SOLI sequence I + ? Sequences Infinite Loop for AI0 and AI1 Infinite Loop for AI0 and AI1 AI0 clears the board, AI1 goes to infinite loop

  17. ZTL SequenceA.I. 0 A.I. 1

  18. Mean: 354 Max: 601 Min: 129 Mean: 556,045 Max: 1,108,432 Min: 72,257 RandomA.I. 0 A.I. 1

  19. A.I. 0 vs. A.I. 1 • SOL sequence • I+? sequences • ZTL sequence • Pure Random Note: Results for “Random” were taken from an average of multiple trials

  20. How A.I. 0 Fails • Even with large penalties, clearing a line can make a move competitive • The holes formed from this make it more difficult for the program to fill lines

  21. How A.I. 1 Fails • A large empty column forms on either side • Tight spaces also form which inhibit certain pieces from fitting in horizontally

  22. Conclusions • AI1 indeed removes more lines than AI0 for this particular algorithm at least for most sequences • Having frequent I-tetrominoes for every two and three pieces will survive forever. • ZTL sequence performs better with AI0 than AI1

  23. Still in the plans • Find a definitive reason why empty columns form over time with random sequences • Explain in detail why ZTL does better with no foresight and why frequent I-pieces always go into infinite loops

  24. Future Work • See how a two-step look-ahead performs • N-step look-ahead • Super Tetris? (five or more piece blocks)

  25. Is One Better than None? Does foresight allow an artificial intelligence to survive longer in Tetris? William Granger and Liqun Tracy Yang

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