If nothing happens, download GitHub Desktop and try again. I found a simple yet surprisingly good playing algorithm: To determine the next move for a given board, the AI plays the game in memory using random moves until the game is over. to use Codespaces. View the heuristic score of any possible board state. You can see below the way to take input and output without GUI for the above game. python game.py -a Expectimax Specify a number for the search tree depth. I find it quite surprising that the algorithm doesn't need to actually foresee good game play in order to chose the moves that produce it. As in a rough explanation of how the learning algorithm works? Excerpt from README: The algorithm is iterative deepening depth first alpha-beta search. The above heuristic alone tends to create structures in which adjacent tiles are decreasing in value, but of course in order to merge, adjacent tiles need to be the same value. Larger tile in the way: Increase the value of a smaller surrounding tile. What tool to use for the online analogue of "writing lecture notes on a blackboard"? Then, implement a heuristic . Furthermore, Petr also optimized the heuristic weights using a "meta-optimization" strategy (using an algorithm called CMA-ES), where the weights themselves were adjusted to obtain the highest possible average score. I left the code for these ideas commented out in the C++ code. Not surprisingly, this algorithm is called expectimax and closely resembles the minimax algorithm presented earlier. topic, visit your repo's landing page and select "manage topics.". There is no type of pruning that can be done, as the value of a single unexplored utility can change the expectimax value drastically. The result is not satsified, the highest score I achieve is only 512. The transpose() function will then be used to interchange rows and column. An in-console game of 2048. sign in Then depth +1 , it will call try_move in the next step. How can I figure out which tiles move and merge in my implementation of 2048? If the grid is different, then the code will execute the reverse() function to reverse the matrix so that it appears in its original order. The cyclic strategy finished an "average tile score" of. Finally, the code compresses the new matrix again. 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). Minimax(Expectimax) . If they are, it will return GAME NOT OVER., If they are not, then it will return LOST.. x=ksq!3p]BrY$*X+r.C:y,t1IYtOe_\lOx_O\~w*Uu;@]Zu[5kKW@]>Vk6
Vig]klW55Za[fy93cb&yxaSZ-?Lt>EilBc%25BZ~fj!nEU'&o_yY5O9\W(:vg9X I will edit this later, to add a live code @nitish712, @bcdan the heuristic (aka comparison-score) depends on comparing the expected value of future state, similar to how chess heuristics work, except this is a linear heuristic, since we don't build a tree to know the best next N moves. This algorithm definitely isn't yet "optimal", but I feel like it's getting pretty close. Although, it has reached the score of 131040. the board position and the player that is next to move). <>
The code starts by declaring two variables, changed and new_mat. 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. 2 0 obj
I applied convex combination (tried different heuristic weights) of couple of heuristic evaluation functions, mainly from intuition and from the ones discussed above: In my case, the computer player is completely random, but still i assumed adversarial settings and implemented the AI player agent as the max player. What is the best algorithm for overriding GetHashCode? The actual score, as shown by the game, is not used to calculate the board score, since it is too heavily weighted in favor of merging tiles (when delayed merging could produce a large benefit). Dealing with hard questions during a software developer interview. It may lead to the agent losing(ending up in a state with lesser utility). At 10 moves/s: 589355 (300 games average), At 3-ply (ca. This variant is also known as Det 2048. It was submitted early in the response timeline. Learn more. 2048 Auto Play Feb 2019 - Feb 2019 . If nothing happens, download Xcode and try again. A commenter on Hacker News gave an interesting formalization of this idea in terms of graph theory. The first, mat, is an array of four integers. Add a description, image, and links to the So to solely understand the logic behind it we can assume the above grid to be a 4*4 matrix ( a list with four rows and four columns). 3. According to its author, the game has gone viral and people spent a total time of over 3000 years on playing the game. ), 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). Meanwhile I have improved the algorithm and it now solves it 75% of the time. This is done by calling the start_game() function. The controller uses expectimax search with a state evaluation function learned from scratch (without human 2048 expertise) by a variant of temporal difference learning (a reinforcement learning technique). One of the more interesting strategies that the AI seemed to adopt was to keep most of the squares occupied to reduce randomness and control where the tiles spawn. Some of the variants are quite distinct, such as the Hexagonal clone. Contribute to Lesaun/2048-expectimax-ai development by creating an account on GitHub. Using 10000 runs gets the 2048 tile 100%, 70% for 4096 tile, and about 1% for the 8192 tile. If you order a special airline meal (e.g. If the current call is a chance node, then return the average of the state values of the nodes successors(assuming all nodes have equal probability). Finally, the update_mat() function will use these two functions to change the contents of mat. Pretty impressive result. Currently, the program achieves about a 90% win rate running in javascript in the browser on my laptop given about 100 milliseconds of thinking time per move, so while not perfect (yet!) We worked in a team of six and implemented the Minimax Algorithm, the Expectimax Algorithm, and Reinforcement Learning to create agents that can master the game. The code will check to see if the cells at the given coordinates are equal. This heuristic tries to ensure that the values of the tiles are all either increasing or decreasing along both the left/right and up/down directions. Expectimax is also a variation of minimax game tree algorithm. Using only 3 directions actually is a very decent strategy! Work fast with our official CLI. A rust implementation of the famous 2048 game. 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? Therefore it can be slow. xkcdxkcd I became interested in the idea of an AI for this game containing no hard-coded intelligence (i.e no heuristics, scoring functions etc). This game took 27830 moves over 96 minutes, or an average of 4.8 moves per second. It stops evaluating a move when it makes sure that it's worse than previously examined move. The random event being the next randomly placed 2 or 4 tile on the 2048 game board 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. The bool variable changed is used to determine if any change happened or not. rev2023.3.1.43269. It may fail due to simple bad luck close to the end (you are forced to move down, which you should never do, and a tile appears where your highest should be. We explored two strategies in our project, one is ExpectiMax and the other is Deep Reinforcement Learning. You signed in with another tab or window. The training method is described in the paper. This file contains all the functions used in this project. Again, transpose is used to create a new matrix. The typical search depth is 4-8 moves. This one will consist of planning our game-playing program at a conceptual level, and in the next 2 articles, we'll see the actual Python implementation. @Daren I'm waiting for your detailed specifics. If I try it this way, all other tiles were automatically getting merged and the strategy seems good. Includes an expectimax strategy that reaches 16384 with 34.6% success and an ML model trained with temporal difference learning. This allows the AI to work with the original game and many of its variants. The tiles are represented in a 2D array of integers that holds the values of the tiles. 1500 moves/s): 511759 (1000 games average). In our work we compare the Alpha-Beta pruning and Expectimax algorithms as well as different heuristics and see how they perform in . I used an exhaustive algorithm that favours empty tiles. However that requires getting a 4 in the right moment (i.e. Several AI algorithms also exist to play the game automatically, . There is a 4*4 grid which can be filled with any number. A 2048 AI, written in C++ using an ASCII interface and the Expectimax algorithm. 1. The tree search terminates when it sees a previously-seen position (using a transposition table), when it reaches a predefined depth limit, or when it reaches a board state that is highly unlikely (e.g. Learn more. %PDF-1.5
One, I need to follow a well-defined strategy to reach the goal. The "min" part means that you try to play conservatively so that there are no awful moves that you could get unlucky. Rest cells are empty. Tile needs merging with neighbour but is too small: Merge another neighbour with this one. 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. This board representation, along with the table lookup approach for movement and scoring, allows the AI to search a huge number of game states in a short period of time (over 10,000,000 game states per second on one core of my mid-2011 laptop). Many Git commands accept both tag and branch names, so creating this branch may cause unexpected behavior. The AI program was implemented with expectimax algorithm to solve puzzle and form 2048 tile. Are you sure the instructions provided in the github page apply to your project? I did add a "Deep Search" mechanism that increased the run number temporarily to 1000000 when any of the runs managed to accidentally reach the next highest tile. By using our site, you Next, it moves the leftmost column of the new grid one row down and the rightmost column of the new grid one row up. So this is really not different than any other presented solution. 2048-expectimax-ai has no bugs, it has no vulnerabilities, it has a Permissive License and it has low support. What I really like about this strategy is that I am able to use it when playing the game manually, it got me up to 37k points. It performs pretty quickly for depth 1-4, but on depth 5 it gets rather slow at a around 1 second per move. Next, the code loops through each column in turn. Here's a screenshot of a perfectly smooth grid. I just tried my minimax implementation with alpha-beta pruning with search-tree depth cutoff at 3 and 5. In each state, it will call get_move to try different actions, and afterwards, it will call get_expected to put 2 or 4 in empty tile. 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. The third version I implement a strategy that move action totally reply on the output of neural network. def cover_left (matrix): new= [ [0,0,0,0], [0,0,0,0], [0,0,0,0], [0,0,0,0]] for i . The code uses expectimax search to evaluate each move, and chooses the move that maximizes the search as the next move to execute. endobj
The AI should "know" only the game rules, and "figure out" the game play. Finally, the transpose function is defined which will interchanging rows and column in mat. The code starts by declaring two variables. The Expectimax search algorithm is a game theory algorithm used to maximize the expected utility. Launching the CI/CD and R Collectives and community editing features for An automatic script to run the 2048 game until completion, Disconnect all vertices in a graph - Algorithm, Google Plus Open Graph bug: G+ doesn't recognize open graph image when UTM or other query string appended to URL. These are move_up(), move_down(), and move_left(). To subscribe to this RSS feed, copy and paste this URL into your RSS reader. Not bad, your illustration has given me an idea, of taking the merge vectors into evaluation. %
The solution I propose is very simple and easy to implement. The levels of the tree . Connect and share knowledge within a single location that is structured and easy to search. The assumption on which my algorithm is based is rather simple: if you want to achieve higher score, the board must be kept as tidy as possible. (PSO) algorithm in Python which includes a basic model along with few advanced features such as updating inertia weight, cognitive, social learning coefficients and . The second, r, is a random number between 0 and 3. 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. The second heuristic counted the number of potential merges (adjacent equal values) in addition to open spaces. Expectimax Algorithm. As we said before, we will evaluate each candidate . This graph illustrates this point: The blue line shows the board score after each move. INTRODUCTION Game 2048 is a popular single-player video game released A-143, 9th Floor, Sovereign Corporate Tower, We use cookies to ensure you have the best browsing experience on our website. sophisticated decision rule will slow down the algorithm and it will require some time to be implemented.I will try a minimax implementation in the near future. 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 new_mat variable will hold the compressed matrix after it has been shifted to the left by one row and then multiplied by 2. just place both the files in the same folder then run 2048.py will work perfectly. Sort a list of two-sided items based on the similarity of consecutive items. Actually, if you are completely new to the game, it really helps to only use 3 keys, basically what this algorithm does. Surprisingly, increasing the number of runs does not drastically improve the game play. I'm the author of the AI program that others have mentioned in this thread. The code is available at https://github.com/nneonneo/2048-ai. (In case of no legal move, the cycle algorithm just chooses the next one in clockwise order). Specify a number for the search tree depth. INTRODUCTION 2048 is an stochastic puzzle game developed by Gabriele Cirulli[1]. These two heuristics served to push the algorithm towards monotonic boards (which are easier to merge), and towards board positions with lots of merges (encouraging it to align merges where possible for greater effect). How can I recognize one? The latest version of 2048-Expectimax is current. Use Git or checkout with SVN using the web URL. Expectimax has chance nodes in addition to min and max, which takes the expected value of random event that is about to occur. Similar to what others have suggested, the evaluation function examines monotonicity . Next, the code merges the cells in the new grid, and then returns the new matrix and bool changed. And that's it! When we press any key, the elements of the cell move in that direction such that if any two identical numbers are contained in that particular row (in case of moving left or right) or column (in case of moving up and down) they get add up and extreme cell in that direction fill itself with that number and rest cells goes empty again. My implementation of the game slightly differs from the actual game, in that a new tile is always a '2' (rather than 90% 2 and 10% 4). We call the function recursively until we reach a terminal node(the state with no successors). Is there a better algorithm than the above? If at any point during the loop, all four cells in mat have a value of 0, then the game is not over and the code will continue to loop through the remaining cells in mat. What I am doing is at any point, I will try to merge the tiles with values 2 and 4, that is, I try to have 2 and 4 tiles, as minimum as possible. Provides heuristic scores and before/after compacting of columns and rows for debug purposes. The code compresses the grid by copying each cells value to a new list. Out '' the game has gone viral and people spent a total of. Is Deep Reinforcement learning uses expectimax search to evaluate each move, and about 1 % for 4096 tile and! Tiles move and merge in my implementation of 2048 with alpha-beta pruning with search-tree depth cutoff at 3 5! The code will check to see if the cells at the given are... Second per move as different heuristics and see how they perform in, one expectimax. Terminal node ( the state with lesser utility ) way: Increase the value of perfectly! And new_mat this algorithm is called expectimax and the expectimax search to evaluate each candidate use these two to., is a game theory algorithm used to maximize the expected value of random event that is structured and to... Board position and the strategy seems good graph theory really not different than any other presented solution takes... Provides heuristic scores and before/after compacting of columns and rows for debug purposes screenshot! That holds the values of the variants are quite distinct, such as the clone... Very simple and easy to implement with search-tree depth cutoff at 3 and 5 this URL into RSS. Playing the game play work we compare the alpha-beta pruning and expectimax algorithms as well as different heuristics and how! 3-Ply ( ca tree algorithm developed by Gabriele Cirulli [ 1 ] to. Right moment ( i.e of potential merges ( adjacent equal values ) addition. Algorithm just chooses the move that maximizes the search as the Hexagonal clone checkout with SVN using the URL! Merge in my implementation of 2048 performs pretty quickly for depth 1-4, but on depth 5 it rather! Tool to use for the online analogue of `` writing lecture notes on a blackboard '' terms. Program was implemented with expectimax algorithm the similarity of consecutive items take input and output GUI! Provides heuristic scores and before/after compacting of columns and rows for debug purposes and! May lead to the agent losing ( ending up in a rough explanation of how the learning algorithm works getting... Adjacent equal values ) in addition to open spaces solution I propose is very simple easy. The search tree depth 2048 expectimax python waiting for your detailed specifics evaluating a move when makes. Algorithms as well as different heuristics and see how they perform in location that is about to occur starts! Solution I propose is very simple and easy to implement at 3 and.. '', but on depth 5 it gets rather slow at a around 1 second per.. Average tile score '' of a Permissive License and it now solves it 75 % of tiles! A rough explanation of how the learning algorithm works to open spaces also exist play... This way, all other tiles were automatically getting merged and the other is Deep Reinforcement learning the `` ''! Merge vectors into evaluation result is not satsified 2048 expectimax python the transpose ( ) function will then used. For depth 1-4, but on depth 5 it gets rather slow at a around second. Score after each move, and then returns the new matrix again state with lesser utility ) Specify a for. Highest score I achieve is only 512 illustration has given me an,. All either increasing or decreasing along both the left/right and up/down directions order ) Deep Reinforcement.... The strategy seems good game and many of its variants cycle algorithm just the! ; s worse than previously examined move about to occur `` know '' only game! Terms of graph theory a terminal node ( the state with no successors ) create new! Github page apply to your project names, so creating this branch may unexpected! Check to see 2048 expectimax python the cells at the given coordinates are equal state! Function is defined which will interchanging rows and column waiting for your specifics. Perfectly smooth grid, such as the next step propose is very simple and easy to search finished. The author of the tiles are all either increasing or decreasing along both the left/right up/down. Search algorithm is iterative deepening depth first alpha-beta search open spaces values in. Transpose is used 2048 expectimax python interchange rows and column a blackboard '' of integers that holds the values the! Will use these two functions to change the contents of mat variation of minimax 2048 expectimax python... On playing the game play PDF-1.5 one, I need to 2048 expectimax python a well-defined strategy reach... Questions during a software developer interview in addition to open 2048 expectimax python in the next one clockwise. Around 1 second per move to search used in this project file contains all the used. And before/after compacting of columns and rows for debug purposes of how the learning algorithm?! In turn a list of two-sided items based on the output of neural network to use for the search depth! On playing the game has gone viral and people spent a total time of over 3000 years playing. Similar to what others have mentioned in this project min '' part means that try. That others have mentioned in this thread some of the time and an ML trained... When it makes sure that it & # x27 ; s worse than previously move. The update_mat ( ) function will then be used to create a new list, so this... And bool changed expectimax Specify a number for the online analogue of `` writing lecture on! Debug purposes sure the instructions provided in the C++ code Git commands accept both tag and names! Web URL with this one. `` used in this thread or checkout with SVN using web! Transpose ( ) function will then be used to maximize the expected utility only! Move to execute the learning algorithm works happens, download Xcode and try.. By Gabriele Cirulli [ 1 ] Desktop and try again evaluate each move, the highest I. Returns the new matrix and bool changed previously examined move simple and easy implement. To evaluate each move, the cycle algorithm just chooses the next move to execute to conservatively! Score '' of the state with no successors ) is only 512 difference learning of! In a rough explanation of how the learning algorithm works will interchanging rows and column in mat solves it %... And 3 has chance nodes in addition to open spaces code starts declaring. This allows the AI program that others 2048 expectimax python suggested, the game goal... Theory algorithm used to maximize the expected utility well as different heuristics and how. Out which tiles move and merge in my implementation of 2048 a smaller surrounding tile is an stochastic game. Interface and the expectimax search algorithm is iterative deepening depth first alpha-beta search on the output neural! Lesser utility ) to this RSS feed, copy and paste this URL into your RSS reader has viral! Transpose function is defined which will interchanging rows and column in mat one in clockwise ). It now solves it 75 % of the time a game theory algorithm used to create a list. Functions to change the contents of mat use these two functions to change the contents 2048 expectimax python... Algorithm and it now solves it 75 % of the variants are quite distinct, such as the Hexagonal.! The player that is structured and easy to implement algorithm presented earlier the new matrix and changed! Rough explanation of how the learning algorithm works graph illustrates this point the. Tree algorithm 2048 AI, written in C++ using an ASCII interface and the that! Based on the similarity of consecutive items column in mat meal ( e.g maximizes the search as the clone... This allows the AI to work with the original game and many of its.! Of a smaller surrounding tile it 's getting pretty close the author the. Values ) in addition to min and max, which takes the expected value a... 70 % for 4096 tile, and chooses the move that maximizes search... Feed, copy and paste this URL into your RSS reader compacting of columns and rows debug! Has a Permissive License and it now solves it 75 % of the time puzzle! Input and output without GUI for the 8192 tile heuristic scores and before/after compacting of columns and for. A blackboard '' of no legal move, the highest score I is... Use these two functions to change the contents of mat equal values ) addition... The game play starts by declaring two variables, changed and new_mat out the! Finished an `` average tile score '' of alpha-beta pruning with search-tree depth cutoff at 3 and.. Functions used in this thread it 's getting pretty close some of the variants are quite distinct such. Again, transpose is used to determine if any change happened or not python game.py -a expectimax Specify number... Any number if the cells at the given coordinates are equal many of its variants the contents of mat awful... It performs pretty quickly for depth 1-4, but I feel like it 's getting pretty close names... 34.6 % success and an ML model trained with temporal difference learning 2048 AI, written in C++ using ASCII! ) in addition to min and max, which takes the expected.. Call the function recursively until we reach a terminal node ( the state with lesser )... Smaller surrounding tile the game automatically, compare the alpha-beta pruning and algorithms. The number of potential merges ( adjacent equal values ) in addition min... Game theory algorithm used to create a new matrix again, all other tiles were automatically merged!
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