Is One Better than None? Does foresight allow an artificial intelligence to survive longer in Tetris? William Granger and Liqun Tracy Yang
Jan 14, 2016
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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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.
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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
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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
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A Tetris Comparison Without Foresight With Foresight
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Our Goals
Discover whether foresight makes the program survive longer.
See if certain sequences require no foresight
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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
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Zero-step Look-Ahead A.I. Holes = -1 Roughness = -22 Piece Average Height
= -1.5 Remove Line Score =
+0 Total Score = -24.5
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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!
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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
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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
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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
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Experiments & Analysis
Coded a Tetris program with the heuristic algorithm
Had Tetris program run repeatable sequences
Looked for bad and unexpected moves
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Sequences Used for Analysis
SOL Sequence: holes analysis
I+? Sequence: I-piece improve survivability?
ZTL Sequence: roughness analysis
Random Sequence: normal play
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SOL SequenceA.I. 0 A.I. 1
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I + ? Sequences
All two piece sequences with an
I-piece SZI sequence
SOLI sequence
Infinite Loop for AI0 and AI1
Infinite Loop for AI0 and AI1
AI0 clears the board, AI1 goes to infinite loop
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ZTL SequenceA.I. 0 A.I. 1
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RandomA.I. 0 A.I. 1
Mean: 354 Max: 601 Min: 129
Mean: 556,045 Max: 1,108,432 Min: 72,257
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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
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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
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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
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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
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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
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Future Work
See how a two-step look-ahead performs
N-step look-ahead Super Tetris? (five or
more piece blocks)
Is One Better than None?
Does foresight allow an artificial intelligence to survive longer in Tetris?
William Granger and Liqun Tracy Yang