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 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?

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 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

Our Goals

Discover whether foresight makes the program survive longer.

See if certain sequences require no foresight

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.I. Holes = -1 Roughness = -22 Piece Average Height

= -1.5 Remove Line Score =

+0 Total Score = -24.5

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.

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

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

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

Coded a Tetris program with the heuristic algorithm

Had Tetris program run repeatable sequences

Looked for bad and unexpected moves

Sequences Used for Analysis

SOL Sequence: holes analysis

I+? Sequence: I-piece improve survivability?

ZTL Sequence: roughness analysis

Random Sequence: normal play

SOL SequenceA.I. 0 A.I. 1

I + ? Sequences

All two piece sequences with an

I-piece SZI sequence

SOLI sequence

Infinite Loop for AI0 and AI1

AI0 clears the board, AI1 goes to infinite loop

ZTL SequenceA.I. 0 A.I. 1

RandomA.I. 0 A.I. 1

Mean: 354 Max: 601 Min: 129

Mean: 556,045 Max: 1,108,432 Min: 72,257

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

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

A large empty column forms on either side Tight spaces also form which inhibit

certain pieces from fitting in horizontally

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

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