Programming is wonderful! Literally full of wonders. As you write code, it becomes complex, unpredictable, and surprising and you, the author, are never quite sure what it will do. Last weekend, I wrote parts of an AI for a Tetris-like game. It is based on an algorithm called Monte Carlo Tree Search. The approach is deceptively simple, but fascinating…
See for yourself in this screencast:
This program was my team’s entry to the International Contest in Functional Programming, a weekend-long programming competition. The contest challenges participants to save the world by playing a Tetris-like game on a hexagonal grid. Participants write a program that receives a specification of the grid, the blocks and their order, and a time limit within which it needs to produce a sequence of moves. Programs receive points for every block played and for lines cleared. There were additional challenges in the competition, but this blog post focuses on our Tetris AI.
How do computers play Tetris? Our program does it very differently than a human being would. Human players use various heuristics, like keeping the stacks low or avoiding holes. In contrast, the AI is based almost entirely on simulation and on a clever strategy called Monte Carlo Tree Search. Here is how it works:
For every move, the AI evaluates hundreds of alternatives, and chooses the most interesting one based on random playouts. A random playout simply means: “make random moves until the game ends, and report the final score.” Moves with a high average playout score are probably better than moves with a low average playout score.
In our program, this looks as follows (actual, just slightly simplified code. Would you guess this plays Tetris?):
One problem is that there are billions of move combinations, many more than the AI could ever evaluate. This is where Monte Carlo Tree Search has a really clever solution: a playout is always added to the most interesting move, where interestingness takes both exploration and exploitation into account.
Exploration means that the AI tries to explore moves that it knows little about. It wants to explore the move with the fewest number of playouts. Exploitation means that the AI should not waste time on bad moves. It want to explore the move with the highest average score.
Here’s an example for a particular game situation:
. . . . . . . . . . o . . ● ● ● . . . . move | avg score playouts o o o . . . . . . . -----|---------------------- o o o . . o o o . . E | 666 233 o o . . . o o o o . W | 651 205 . o . . o o o . . o SE | 641 189 . . o o o o o . o o SW | 645 195 . . o . o . o o o o CW | 662 225 . o o o o o o o o o CCW | 671 247 . . o . o o o o o .
Here, the AI has most deeply explored moves starting with rotating counter-clockwise. It has spent 247 of its playouts on that option (mostly on the combination “rotate counter-clockwise, then move south-west, then …”) If it were to perform more explorations, it would explore “go south-east, then rotate clockwise, then” because that move is relatively unexplored.
After all these evaluations, the AI chooses to rotate counter-clockwise. It does not necessarily choose the options with the highest score (although in this case CCW does have the highest score). Instead, it chooses the option with most playouts, because that move has consistently been interesting.
Completely random playouts are a rather stupid way of evaluating how promising a move is. In the situation above, most sequences of random moves immediately lose the game. I believe that adding a few heuristics to the playout would be the single most effective way of improving our AI.
I learned a lot about hexagonal grids during this weekend. The Hexagonal Grids page from Red Blob Games has been a treasure trove of information about rotations, cube coordinates, and much more.
One last story I want to tell is about a really interesting bug that we’ve produced during the contest. We found it while watching the AI play, and thinking “hey, this is curious…?” The game rules specify that a block needs to be centered at the top of the grid when it enters play. To center it, our code first computes the width of the block. It turns out that on a hexagonal grid, this is not so easy, because the width depends on the vertical position of the block.
This was very counter-intuitive to me, but here is an example:
columns used width . . . ● . . . 4 . ● ● . . . 2, 3 2 to 4 = 3 . . . ● . . . 4 . . . . ● . 5 . . . ● ● . . 4, 5 4 to 5 = 2 . . . . ● . 5
This issue caused us to spawn the block in the wrong position. Because of this, our solution received zero points whenever the game contained blocks of that particular shape… until we found and fixed the bug.
Our code is now open-source. If you like it or have comments, let me know!