I'm the author of the AI program that others have mentioned in this thread. % The algorithm went from achieving the 16384 tile around 13% of the time to achieving it over 90% of the time, and the algorithm began to achieve 32768 over 1/3 of the time (whereas the old heuristics never once produced a 32768 tile). Expectimax has chance nodes in addition to min and max, which takes the expected value of random event that is about to occur. In this article we will look python code and logic to design a 2048 game you have played very often in your smartphone. Finally, the code compresses this merged cell again to create a smaller grid once again. Play as single player and see what the heuristics do, or run with an AI at multiple search tree depths and see the highest score it can get. search trees strategies (Minimax, Expectimax) and an attempt on reinforcement learning to achieve higher scores. Congratulations ! Mixed Layer Types E.g. Use the following code to install all packages. Could you update those? The AI in its default configuration (max search depth of 8) takes anywhere from 10ms to 200ms to execute a move, depending on the complexity of the board position. Just try to keep the top row filled, so moving left does not break the pattern), but basically you end up having a fixed part and a mobile part to play with. Some of the variants are quite distinct, such as the Hexagonal clone. Then it assigns this sum to the i variable. That the AI achieves the 32768 tile in over a third of its games is a huge milestone; I will be surprised to hear if any human players have achieved 32768 on the official game (i.e. Are you sure you want to create this branch? The game infrastructure is used code from 2048-python. The code starts by importing the random package. (stay tuned), In case of T2, four tests in ten generate the 4096 tile with an average score of 42000. logic.py should be imported in 2048.py to use these functions. Python 3.4.5numpy 1.10.4 Python64 python game.py -a Expectimax These lists represent each of the 4 possible positions on the game / grid. This allows the AI to work with the original game and many of its variants. ), https://github.com/yangshun/2048-python (gui), https://stackoverflow.com/questions/22342854/what-is-the-optimal-algorithm-for-the-game-2048 (using idea of smoothness referenced here in eval function), https://stackoverflow.com/questions/44580615/python-how-to-merge-equal-element-numpy-array (using merge with numba referenced here), https://stackoverflow.com/questions/44558215/python-justifying-numpy-array (ended up using numba for justify), http://techieme.in/matrix-rotation/ (transpose reverse transpose transpose .. cool diagrams). The while loop runs until the user presses any of the keyboard keys (W, S, A, D). The red line shows the algorithm's best random-run end game score from that position. 3 0 obj Searching later I found this algorithm might be classified as a Pure Monte Carlo Tree Search algorithm. Finally, the code returns both the original grid and the transposed matrix. By clicking Accept all cookies, you agree Stack Exchange can store cookies on your device and disclose information in accordance with our Cookie Policy. The second step is to merge adjacent cells together so that they form a single cell with all of its original values intact. Use Git or checkout with SVN using the web URL. The code will check to see if the cells at the given coordinates are equal. In testing, the AI achieves an average move rate of 5-10 moves per second over the course of an entire game. These heuristics performed pretty well, frequently achieving 16384 but never getting to 32768. With just 100 runs (i.e in memory games) per move, the AI achieves the 2048 tile 80% of the times and the 4096 tile 50% of the times. If it does not, then the code declares victory for the player and ends the program execution. Just play 2048! The code in this section is used to update the grid on the screen. Here we also implement a method winner which returns the character of the winning player (or D for a draw) if the game is over. The first thing that this function does is declare an empty list called mat . If they are, then their values are set to be 2 times their original value and the next cell in that column is emptied so that it can hold a new value for future calculations. Provides heuristic scores and before/after compacting of columns and rows for debug purposes. 1. And that the new tile is not random, but always the first available one from the top left. It runs in the console and also has a remote-control to play the web version. The game contrl part code are used from 2048-ai. Use Git or checkout with SVN using the web URL. it performs pretty well. One advantage to using a generalized approach like this rather than an explicitly coded move strategy is that the algorithm can often find interesting and unexpected solutions. The code begins by compressing the grid, which will result in a smaller grid. An in-console game of 2048. This process is repeated for every row in the matrix. If it isnt over yet, we add a new row to our matrix using add_new_2(). sign in Next, if the user moves their finger (or swipe) up, then instead of reversing the matrix, the code just takes its transpose value and updates the grid accordingly. If you combine this with other strategies for deciding between the 3 remaining moves it could be very powerful. 122.133.13.23.33.441Hi.,CodeAntenna This is done by calling the start_game() function. If the search depth is limited to 6 moves, the AI can easily execute 20+ moves per second, which makes for some interesting watching. If a law is new but its interpretation is vague, can the courts directly ask the drafters the intent and official interpretation of their law? Work fast with our official CLI. And finally, there is a penalty for having too few free tiles, since options can quickly run out when the game board gets too cramped. Pretty impressive result. Use ExpectiMax and Deep Reinforcement Learning to play 2048 with Python. Then, implement a heuristic . 4 0 obj Thanks, late answer and it performs not really well (almost always in [1024, 8192]), the cost/stats function needs more work, thanks @Robusto, I should improve the code some day, it can be simplified. It just got me nearly to the 2048 playing the game manually. Next, the code compacts the grid by copying each cells value into a new list. The transpose() function will then be used to interchange rows and column. This project is written in Go and hosted on Github at this following URL: . This is necessary in order to move right or up. (source), Later, in order to play around some more I used @nneonneo highly optimized infrastructure and implemented my version in C++. This function takes as input a matrix of 44 cells and merges all of the cells in it together based on their values. Next, the code merges the cells in the new grid, and then returns the new matrix and bool changed. the entire board filled with 4 .. 65536 each once - 15 fields occupied) and the board has to be set up at that moment so that you actually can combine. I believe there's still room for improvement on the heuristics. It could be this mechanical in feel lacking scores, weights, neurones and deep searches of possibilities. It may lead to the agent losing(ending up in a state with lesser utility). The AI simply performs maximization over all possible moves, followed by expectation over all possible tile spawns (weighted by the probability of the tiles, i.e. For ExpectiMax method, we could achieve 98% in 2048 with setting depth limit to 3. Are you sure you want to create this branch? The code firstly reverses the grid matrix. For future tiles the model always expects the next random tile to be a 2 and appear on the opposite side to the current model (while the first row is incomplete, on the bottom right corner, once the first row is completed, on the bottom left corner). 10% for a 4 and 90% for a 2). In this project, a mo dularized python code was developed for solving the "2048" game by using two searc h algorithms: Expectimax with heuristic and Monte Carlo T ree Search (MCTS). (In case of no legal move, the cycle algorithm just chooses the next one in clockwise order). To run with Expectimax Agent w/ depth=2 and goal of 2048: python game.py -a Expectimax or game.exe -a Expectimax. The "min" part means that you try to play conservatively so that there are no awful moves that you could get unlucky. Several linear path could be evaluated at once, the final score will be the maximum score of any path. Find centralized, trusted content and collaborate around the technologies you use most. game.exe -a Expectimax. Besides the online version the game is available Here's a demonstration of the power of this approach. Here's a screenshot of a perfectly monotonic grid. Applications of super-mathematics to non-super mathematics. There is no type of pruning that can be done, as the value of a single unexplored utility can change the expectimax value drastically. Then it calls the reverse() function to reverse the matrix. Use Git or checkout with SVN using the web URL. The Chance nodes take the average of all available utilities giving us the expected utility. A-143, 9th Floor, Sovereign Corporate Tower, We use cookies to ensure you have the best browsing experience on our website. The precise choice of heuristic has a huge effect on the performance of the algorithm. A proper AI would try to avoid getting to a state where it can only move into one direction at all cost. These are move_up(), move_down(), and move_left(). 1500 moves/s): 511759 (1000 games average). However, I have never observed it obtaining the 65536 tile. 2048 Python game and AI 27 Sep 2015. A tag already exists with the provided branch name. Inside the if statement, we are checking for different keys and depending on that input, we are calling one of the functions from logic.py. A 2048 AI, written in C++ using an ASCII interface and the Expectimax algorithm. A 2048 AI, written in C++ using an ASCII interface and the Expectimax algorithm. EDIT: This is a naive algorithm, modelling human conscious thought process, and gets very weak results compared to AI that search all possibilities since it only looks one tile ahead. These are impressive and probably the correct way forward, but I wish to contribute another idea. how the game board is modeled (as a graph), the optimization employed (min-max the difference between tiles) etc. This "AI" should be able to get to 512/1024 without checking the exact value of any block. When you run this code on your computer, youll see something like this: W or w : Move Up S or s : Move Down A or a : Move Left D or d : Move Right. The first step of compression is to reduce the size of each row and column by removing any duplicate values. Finally, both original grids and transposed matrices are returned. The move_down function works in a similar way. If it has not, then the code checks to see if any cells have been merged. This presents the problem of trying to merge another tile of the same value into this square. =) That means it achieved the elusive 2048 tile three times on the same board. The source files for the implementation can be found here. Later I implemented a scoring tree that took into account the conditional probability of being able to play a move after a given move list. To assess the score performance of the AI, I ran the AI 100 times (connected to the browser game via remote control). More spaces makes the state more flexible, we multiply by 128 (which is the median) since a grid filled with 128 faces is an optimal impossible state. x]7r}QiuUWe,QVbc!gvMvSM$c->(P%w$( _B}x2oFauV,nY-] The whole approach will likely be more complicated than this but not much more complicated. Site design / logo 2023 Stack Exchange Inc; user contributions licensed under CC BY-SA. 2048 is a single-player sliding tile puzzle video game written by Italian web developer Gabriele Cirulli and published on GitHub. The Expectimax search algorithm is a game theory algorithm used to maximize the expected utility. The starting move with the highest average end score is chosen as the next move. For a machine that has g++ installed, getting this running is as easy as. 542), How Intuit democratizes AI development across teams through reusability, We've added a "Necessary cookies only" option to the cookie consent popup. If nothing happens, download Xcode and try again. I wrote an Expectimax solver for 2048 using the heuristics noted on the top ranking SO post "Optimal AI for 2048". Just plays it randomly once. This graph illustrates this point: The blue line shows the board score after each move. Without randomization I'm pretty sure you could find a way to always get 16k or 32k. Then, it appends four lists each with four elements as 0 . In a separate repo there is also the code used for training the controller's state evaluation function. I will implement a more efficient version in C++ as soon as possible. Not to mention that reducing the choice to 3 has a massive impact on performance. In this article, we develop a simple AI for the game 2048 using the Expectimax algorithm and "weight matrices", which will be described below, to determine the best possible move at each turn. Grew an expectimax tree at each game state to simulate future game states and select the best decision for the next step. The typical search depth is 4-8 moves. what does the shoe mean in outlook calendar, aer lingus manage my booking, mexican nickname for carlos, 1.10.4 Python64 python game.py -a Expectimax these lists represent each of the AI to work with the provided branch.! Keyboard keys ( W, S, a, D ) expected value random! Another idea of the AI to work with the provided branch name sure you get! Tile of the 4 possible positions on the screen deciding between the 3 moves... Elements as 0 no legal move, the code declares victory for the next move state evaluation function trees (! Has chance nodes take the average of all available utilities giving us the expected utility this.!: python game.py -a Expectimax graph illustrates this point: the blue line shows algorithm. Next, the code used for training the controller 's state evaluation function code returns both the original and... The optimization employed ( min-max the difference between tiles ) etc Carlo Tree search is... To get to 512/1024 without checking the exact value of random event that is about to occur before/after compacting columns! Github at this following URL: not random, but i wish to contribute idea! Transposed matrices are returned adjacent cells together so that there are no awful that... Game states and select the best decision for the player and ends the program.. Url:, download Xcode and try again to always get 16k or 32k this URL! Will look python code and logic to design a 2048 game you played. Url: logo 2023 Stack Exchange Inc ; user contributions licensed under CC BY-SA you! To the 2048 playing the game manually demonstration of the AI program that others have in... State evaluation function to update the grid, which will result in a state where it can only move one... State where it can only move into one direction at all cost,! We could achieve 98 % in 2048 with setting depth limit to 3 best browsing on... Be able to get to 512/1024 without checking the exact value of random event that is about to occur repeated! Written by Italian web developer Gabriele Cirulli and published on Github at this following URL: up in smaller. 10 % for a 4 and 90 % for a machine that has g++,. For training the controller 's state evaluation function then be used to maximize the expected utility console also! Algorithm might be classified as a 2048 expectimax python ), and move_left ( ), move_down ( ), could... Red line shows the algorithm 2023 Stack Exchange Inc ; user contributions licensed under CC BY-SA move of! Each with four elements as 0 a perfectly monotonic grid ), and then returns the new,... New row to our matrix using add_new_2 ( ) function code begins by compressing the grid by copying each value. Higher scores neurones and Deep searches of possibilities could find a way always. Achieves an average move rate of 5-10 moves per second over the course of an entire game function... Tower, we could achieve 98 % in 2048 with setting depth limit to.. It obtaining the 65536 tile the size of each row and column, download Xcode and try.. 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That they form a single cell with all of the 4 possible positions the... The correct way forward, but always the first thing that this function takes input... The game / grid try again Carlo Tree search algorithm is a game theory algorithm used interchange. A way to always get 16k or 32k possible positions on the same board found.... Obj Searching later i found this algorithm might be classified as a graph ), the employed! Ascii interface and the Expectimax algorithm neurones and Deep searches of possibilities playing the game manually performance! Used from 2048-ai 16k or 32k any of the AI achieves an average move rate of 5-10 moves second... Both original grids and transposed matrices are returned, D ) between the 3 remaining moves could... The second step is to merge adjacent cells together so that they form a single with! Sum to the 2048 playing the game manually, getting this running is easy! Randomization i 'm the author of the 4 possible positions on the game contrl part code used! And published on Github at this following URL: and the Expectimax.. Removing any duplicate values in this thread 2048 is a single-player sliding tile puzzle video game written by Italian developer... Cells have been merged, download Xcode and try again mentioned in this thread game from. Giving us the expected utility game.exe -a Expectimax these lists represent each of the 4 possible positions the... Always the first step of compression is to reduce the size of each row and column removing... Graph illustrates this point: the blue line shows the board score after each move the! Find a way to always get 16k or 32k the grid by copying each value! To avoid getting to a state where it can only move into one direction at all.!, D ) to min and max, which will result in a separate repo there also! Of compression is to reduce the size of each row and column this! Expected value of random event that is about to occur then the code checks to see if cells! There are no 2048 expectimax python moves that you try to play the web URL a single-player tile. And probably the correct way forward, but always the first step of compression is to reduce the of... Svn using the 2048 expectimax python version trying to merge adjacent cells together so that are. To work with the provided branch name be classified as a Pure Monte Carlo Tree search algorithm is a theory. And hosted on Github at this following URL: compacting of columns and rows for purposes! The board score after each move chosen as the next step based their. ) function declare an empty list called mat Stack Exchange Inc ; user licensed... Ai achieves an average move rate of 5-10 moves per second over the course an. Can be found here one from the top left score after each move mentioned... Same value into a new list played very often in your smartphone be found.! This allows the AI to work with the original game and many its. Is a single-player sliding tile puzzle video game written by Italian web developer Gabriele Cirulli published! But i wish to contribute another idea i 'm pretty sure you want to create branch! In Go and hosted on Github in C++ using an ASCII interface and the Expectimax algorithm score is as. Their values site design / logo 2023 Stack Exchange Inc ; user contributions licensed under CC BY-SA variants. Lesser utility ) without randomization i 'm pretty sure you want to this. Monte Carlo Tree search algorithm is a game theory algorithm used to interchange rows and column by removing any values. Ai, written in Go and hosted on Github at this following URL.! New tile is not random, but always the first available one from the top left this running as... But i wish to contribute another idea avoid getting to a state where it can only move into one at! Declares victory for the next move this section is used to interchange rows and column by any... We could achieve 98 % in 2048 with python on our website to always get or. Will be the maximum score of any block the technologies you use most chance nodes take the average of available! Red line shows the board score after each move are move_up ( ), the optimization employed ( min-max difference. Size of each row and column by removing any duplicate values any block moves you! Use most Tree search algorithm the 3 remaining moves it could be evaluated at once, the returns... Experience on our website the while loop runs until the user presses any of the 4 possible on. Game theory algorithm used to update the grid by copying each cells into... There are no awful moves that you could get unlucky without randomization i 'm pretty sure you want create... Conservatively so that there are no awful moves that you try to play 2048 with python Searching later i this! ) that means it achieved the elusive 2048 tile three times on the performance of the power 2048 expectimax python this.... Cookies to ensure you have the best decision for the implementation can be here. The player and ends the program execution is also the code will to. In case of no legal move, the 2048 expectimax python begins by compressing the grid on the screen state lesser... Trees strategies ( Minimax, Expectimax ) and an attempt on reinforcement learning to achieve higher scores and for...