Is one better than none
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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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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

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.


What is foresight

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


Related work

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


A tetris comparison without foresight with foresight

A Tetris Comparison Without ForesightWith Foresight


Our goals

Our Goals

  • Discover whether foresight makes the program survive longer.

  • See if certain sequences require no foresight


Zero step look ahead a i

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


Zero step look ahead a i1

Zero-step Look-Ahead A.I.

  • Holes = -1

  • Roughness = -22

  • Piece Average Height = -1.5

  • Remove Line Score = +0

  • Total Score = -24.5


Zero step look ahead a i2

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!


One step look ahead a i

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


How a i 1 makes a move vs a i 0

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


Hypothesis

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


Experiments analysis

Experiments & Analysis

  • Coded a Tetris program with the heuristic algorithm

  • Had Tetris program run repeatable sequences

  • Looked for bad and unexpected moves


Sequences used for analysis

Sequences Used for Analysis

  • SOL Sequence: holes analysis

  • I+? Sequence: I-piece improve survivability?

  • ZTL Sequence: roughness analysis

  • Random Sequence: normal play


Sol sequence a i 0 a i 1

SOL SequenceA.I. 0A.I. 1


I sequences

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


Ztl sequence a i 0 a i 1

ZTL SequenceA.I. 0A.I. 1


Random a i 0 a i 1

Mean: 354

Max: 601

Min: 129

Mean: 556,045

Max: 1,108,432

Min: 72,257

RandomA.I. 0A.I. 1


A i 0 vs a i 1

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


How a i 0 fails

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


How a i 1 fails

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


Conclusions

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


Still in the plans

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


Future work

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 none1

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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