2048 expectimax python

The objective of the game is to slide numbered tiles on a grid to combine them to create a tile with the number 2048; however, one can continue to play the game after reaching the goal, creating tiles with larger . (more precisely a expectimax). 542), How Intuit democratizes AI development across teams through reusability, We've added a "Necessary cookies only" option to the cookie consent popup. Bots for the board game quoridor implemented using four algorithms: minimax, minimax with alpha beta pruning, expectimax and monte carlo tree search. Maximum points AFAIK is slightly more than 20,000 points which is way larger than my current score. @ashu I'm working on it, unexpected circumstances have left me without time to finish it. Since there is already a lot of info on that algorithm out there, I'll just talk about the two main heuristics that I use in the static evaluation function and which formalize many of the intuitions that other people have expressed here. 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. This version can run 100's of runs in decent time. I was trying to solve the same problem for a 4x4 grid as a project assignment for the edX course ColumbiaX: CSMM.101x Artificial Intelligence (AI). Try to extend it with the actual rules. Around 80% wins (it seems it is always possible to win with more "professional" AI techniques, I am not sure about this, though.). 2048 Auto Play Feb 2019 - Feb 2019 . Is there a better algorithm than the above? Even though the AI is randomly placing the tiles, the goal is not to lose. A few weeks ago, I wrote a Python implementation of 2048. Next, the start_game() function is declared. Not sure why this doesn't have more upvotes. mat is the matrix object and flag is either W for moving up or S for moving down. Therefore it can be slow. The code starts by creating an empty list, and then it loops through all of the cells in the matrix. 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 initializes an empty list, then appends four lists each with four elements. Dealing with hard questions during a software developer interview. What is the best algorithm for overriding GetHashCode? 10. - Learn bitwise operator Golang. If we are able to do that we wins. Currently porting to Cuda so the GPU does the work for even better speeds! But, when I actually use this algorithm, I only get around 4000 points before the game terminates. The evaluation function tries to keep the rows and columns monotonic (either all decreasing or increasing) while minimizing the number of tiles on the grid. A-143, 9th Floor, Sovereign Corporate Tower, We use cookies to ensure you have the best browsing experience on our website. 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). You signed in with another tab or window. The AI should "know" only the game rules, and "figure out" the game play. I think it will be better to use Expectimax instead of minimax, but still I want to solve this problem with minimax only and obtain high scores such as 2048 or 4096. How can I recognize one? In here we still need to check for stacked values, but in a lesser way that doesn't interrupt the flexibility parameters, so we have the sum of { x in [4,44] }. Finally, an Expectimax strategy with pruned trees outperformed others and get a winning tile two times as high as the original winning target. Surprisingly, increasing the number of runs does not drastically improve the game play. I have refined the algorithm and beaten the game! 2048 can be viewed as a two player game, a human versus computer game. 2048 bot using AI. This is the first article from a 3-part sequence. Such moves need not to be evaluated further. <>/XObject<>/ProcSet[/PDF/Text/ImageB/ImageC/ImageI] >>/Annots[ 23 0 R 31 0 R] /MediaBox[ 0 0 595.2 841.8] /Contents 4 0 R/Group<>/Tabs/S/StructParents 0>> A simplified version of Go game in Python, with AI agents built-in and GUI to play. The code starts by declaring two variables, r and c. These will hold the row and column numbers at which the new 2 will be inserted into the grid. 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. You can view the AI in action or read the source. Plays the game several hundred times for each possible moves and picks the move that results in the highest average score. Sort a list of two-sided items based on the similarity of consecutive items. 2. we have to press any one of four keys to move up, down, left, or right. 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. techno96/2048-expectimax, 2048-expectimax Simulating an AI playing 2048 using the Expectimax algorithm The base game engine uses code from here. I have recently stumbled upon the game 2048. The code can be found on GiHub at the following link: https://github.com/Nicola17/term2048-AI A-143, 9th Floor, Sovereign Corporate Tower, We use cookies to ensure you have the best browsing experience on our website. This offered a time improvement. Excerpt from README: The algorithm is iterative deepening depth first alpha-beta search. The code will check each cell in the matrix (mat) and see if it contains a value of 2048. The median score is 387222. Just for fun, I've also implemented the AI as a bookmarklet, hooking into the game's controls. Can be tried out here: +1. A rust implementation of the famous 2048 game. In this article we will look python code and logic to design a 2048 game you have played very often in your smartphone. Are you sure you want to create this branch? Browse other questions tagged, Where developers & technologists share private knowledge with coworkers, Reach developers & technologists worldwide, @nitish712 by the way, your algorithm is greedy since you have. This is necessary in order to move right or up. Since the game is a discrete state space, perfect information, turn-based game like chess and checkers, I used the same methods that have been proven to work on those games, namely minimax search with alpha-beta pruning. Specify a number for the search tree depth. The red line shows the algorithm's best random-run end game score from that position. According to its author, the game has gone viral and people spent a total time of over 3000 years on playing the game. What are examples of software that may be seriously affected by a time jump? @nneonneo I ported your code with emscripten to javascript, and it works quite well. This allows the AI to work with the original game and many of its variants. If nothing happens, download GitHub Desktop and try again. Pretty impressive result. A 2048 AI, written in C++ using an ASCII interface and the Expectimax algorithm. Is there a proper earth ground point in this switch box? For a machine that has g++ installed, getting this running is as easy as. Two possible ways of organizing the board are shown in the following images: To enforce the ordination of the tiles in a monotonic decreasing order, the score si computed as the sum of the linearized values on the board multiplied by the values of a geometric sequence with common ratio r<1 . Several AI algorithms also exist to play the game automatically, . However, none of these ideas showed any real advantage over the simple first idea. Refining the algorithm so that it always reaches 16k/32k for a non-random game might be another interesting challenge You are right, it's harder than I thought. Expectimax requires the full search tree to be explored. However that requires getting a 4 in the right moment (i.e. Here: The model has changed due to the luck of being closer to the expected model. 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). If different nodes have different probabilities the expected utility from there is given by. The precise choice of heuristic has a huge effect on the performance of the algorithm. Finally, the update_mat() function will use these two functions to change the contents of mat. The starting move with the highest average end score is chosen as the next move. A proper AI would try to avoid getting to a state where it can only move into one direction at all cost. There seems to be a limit to this strategy at around 80000 points with the 4096 tile and all the smaller ones, very close to the achieving the 8192 tile. I think I have this chain or in some cases tree of dependancies internally when deciding my next move, particularly when stuck. The various heuristics are weighted and combined into a positional score, which determines how "good" a given board position is. It is very easy but hard to achieve its goal. This is a simplified check of the possibility of having merges within that state, without making a look-ahead. After each move, a new tile appears at random empty position with a value of either 2 or 4. The add_new_2() function begins by choosing two random numbers, r and c. It then uses these numbers to specify the row and column number at which the new 2 should be inserted into the grid. 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. The code starts by importing the random package. =) That means it achieved the elusive 2048 tile three times on the same board. Then it moves down using the move_down function. 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A fun distraction when you don't have time to aim for a high score: Try to get the lowest score possible. The transpose() function will then be used to interchange rows and column. Next, it compresses the new grid again and compares the two results. It is a variation of the Minimax algorithm. Here we evaluate faces that have the possibility to getting to merge, by evaluating them backwardly, tile 2 become of value 2048, while tile 2048 is evaluated 2. My approach encodes the entire board (16 entries) as a single 64-bit integer (where tiles are the nybbles, i.e. In theory it's alternating 2s and 4s. If the search depth is limited to 6 moves, the AI can easily execute 20+ moves per second, which makes for some interesting watching. It is based on term2048 and it's written in Python. There is no type of pruning that can be done, as the value of a single unexplored utility can change the expectimax value drastically. This project was and implementation and a solver for the famous 2048 game. But we didn't achieve a good result in deep reinforcement learning method, the max tile we achieved is 512. def cover_left (matrix): new= [ [0,0,0,0], [0,0,0,0], [0,0,0,0], [0,0,0,0]] for i . In testing, the AI achieves an average move rate of 5-10 moves per second over the course of an entire game. If you were to run this code on a 33 matrix, it would move the top-left corner of the matrix one row down and the bottom-right corner of the matrix one row up. 10 2048 . Time complexity: O(bm)Space complexity: O(b*m), where b is branching factor and m is the maximum depth of the tree.Applications: Expectimax can be used in environments where the actions of one of the agents are random. There are 2 watchers for this library. 2048-expectimax-ai has no bugs, it has no vulnerabilities, it has a Permissive License and it has low support. Learn more. I had an idea to create a fork of 2048, where the computer instead of placing the 2s and 4s randomly uses your AI to determine where to put the values. The reading for this option consists of four parts: (a) some optional background on the game and its recent resurgence in popularity, (b) Search in The Elements of Artificial Intelligence with Python, which includes material on minimax search and alpha-beta pruning, (c) the lecture slides on Expectimax search linked from our course calendar . You signed in with another tab or window. Actually, if you are completely new to the game, it really helps to only use 3 keys, basically what this algorithm does. My attempt uses expectimax like other solutions above, but without bitboards. I became interested in the idea of an AI for this game containing no hard-coded intelligence (i.e no heuristics, scoring functions etc). There was a problem preparing your codespace, please try again. Python Programming Foundation -Self Paced Course, Conway's Game Of Life (Python Implementation), Python implementation of automatic Tic Tac Toe game using random number, Rock, Paper, Scissor game - Python Project, Python | Program to implement Jumbled word game, Python | Program to implement simple FLAMES game. Increasing the number of runs from 100 to 100000 increases the odds of getting to this score limit (from 5% to 40%) but not breaking through it. << /Length 5 0 R /Filter /FlateDecode >> Without randomization I'm pretty sure you could find a way to always get 16k or 32k. There is a 4*4 grid which can be filled with any number. 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). 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. The code uses expectimax search to evaluate each move, and chooses the move that maximizes the search as the next move to execute. The optimization search will then aim to maximize the average score of all possible board positions. This is amazing! If it isnt over yet, we add a new row to our matrix using add_new_2(). An efficient implementation of the controller is available on github. I ran 100,000 games testing this versus the trivial cyclic strategy "up, right, up, left, " (and down if it must). 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. 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. A set of AIs for the 2048 tile-merging game. Moving down can be done by taking transpose the moving right. Implementation of reinforcement learning algorithms to solve pacman game. Connect and share knowledge within a single location that is structured and easy to search. Then it calls the reverse() function to reverse the matrix. Unlike Minimax, Expectimax can take a risk and end up in a state with a higher utility as opponents are random(not optimal). This process is repeated for every row in the matrix. While Minimax assumes that the adversary(the minimizer) plays optimally, the Expectimax doesnt. The while loop runs until the user presses any of the keyboard keys (W, S, A, D). Several benchmarks of the algorithm performances are presented. The changed variable will be set to True once the matrix has been merged and therefore represents the new grid. I played with many possible weight assignments to the heuristic functions and take a convex combination, but very rarely the AI player is able to score 2048. A tag already exists with the provided branch name. Not surprisingly, this algorithm is called expectimax and closely resembles the minimax algorithm presented earlier. %PDF-1.3 Alpha-Beta Pruning. This is done by appending an empty list to each row and then referencing the individual list items within that row. If any cells have been modified, then their values will be updated within this function before it returns them back to the caller. The most iconic AI for 2048 is probably the one developed by Matt Overlan, which is really well designed and very interesting when you look at the nuts and bolts of how it works; however, if you're just watching it play through, this stategy appears distinctly inhuman. The following animation shows the last few steps of the game played where the AI player agent could get 2048 scores, this time adding the absolute value heuristic too: The following figures show the game tree explored by the player AI agent assuming the computer as adversary for just a single step: I wrote a 2048 solver in Haskell, mainly because I'm learning this language right now. The solution I propose is very simple and easy to implement. Theoretical limit in a 4x4 grid actually IS 131072 not 65536. How can I figure out which tiles move and merge in my implementation of 2048? This variant is also known as Det 2048. 2048 is a single-player sliding tile puzzle video game written by Italian web developer Gabriele Cirulli and published on GitHub. | Learn more about Ashes Mondal's work experience, education, connections & more by visiting their profile on LinkedIn I think the 65536 tile is within reach! Watching this playing is calling for an enlightenment. Similar to what others have suggested, the evaluation function examines monotonicity . Are you sure the instructions provided in the github page apply to your project? stream The code firstly reverses the grid matrix. How did Dominion legally obtain text messages from Fox News hosts? Running 10000 runs with a temporary increase to 1000000 near critical positions managed to break this barrier less than 1% of the times achieving a max score of 129892 and the 8192 tile. The class is in src\Expectimax\ExpectedMax.py. In my case, this depth takes too long to explore, I adjust the depth of expectimax search according to the number of free tiles left: The scores of the boards are computed with the weighted sum of the square of the number of free tiles and the dot product of the 2D grid with this: which forces to organize tiles descendingly in a sort of snake from the top left tile. 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. You signed in with another tab or window. % The decision rule implemented is not quite smart, the code in Python is presented here: An implementation of the minmax or the Expectiminimax will surely improve the algorithm. 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. Moving up can be done by taking transpose then moving left. Several linear path could be evaluated at once, the final score will be the maximum score of any path. Expectimax Algorithm. Since then, I've been working on a simple AI to play the game for me. We also need to call get_current_state() to get information about the current state of our matrix. 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. The expectimax search itself is coded as a recursive search which alternates between "expectation" steps (testing all possible tile spawn locations and values, and weighting their optimized scores by the probability of each possibility), and "maximization" steps (testing all possible moves and selecting the one with the best score). The code in this section is used to update the grid on the screen. Congratulations ! So, I thought of writing a program for it. 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 code compresses the grid by copying each cells value to a new list. Many Git commands accept both tag and branch names, so creating this branch may cause unexpected behavior. rev2023.3.1.43269. Therefore we decided to develop an AI agent to solve the game. In ExpectiMax strategy, we tried 4 different heuristic functions and combined them to improve the performance of this method. I managed to find this sequence: [UP, LEFT, LEFT, UP, LEFT, DOWN, LEFT] which always wins the game, but it doesn't go above 2048. 4. or This is in contrast to most AIs (like the ones in this thread) where the game play is essentially brute force steered by a scoring function representing human understanding of the game. (This is the link of my blog post for the article: https://sandipanweb.wordpress.com/2017/03/06/using-minimax-with-alpha-beta-pruning-and-heuristic-evaluation-to-solve-2048-game-with-computer/ and the youtube video: https://www.youtube.com/watch?v=VnVFilfZ0r4). Only get around 4000 points before the game an empty list to each row then. Does n't have time to finish it AI would try to get the lowest score.! How did Dominion legally obtain text messages from Fox News hosts after each move, a human versus computer.. Of 5-10 moves per second over the simple first idea 16 entries ) as a two player game, new. Cookies to ensure you have played very often in your smartphone out '' the game it! And a solver for the 2048 tile-merging game a software developer interview of either 2 or.. Get information about the current state of our matrix more upvotes ) and see if it a... Into a positional score, which determines how `` good '' a given board is. The entire board ( 16 entries ) as a single location that is structured and easy to.. To interchange rows and column achieved the elusive 2048 tile three times on the performance the! C++ using an ASCII interface and the Expectimax doesnt algorithm, I thought of writing a program it. Your code with emscripten to javascript, and it works quite well modified, then their will. Can view the AI should `` know '' only the game for me @ nneonneo I ported code. To True once the matrix AI Agent to solve pacman game initializes an empty list, appends... The number of runs in decent time the next move to execute a tag already exists with the branch. Sure you want to create this branch may cause unexpected behavior, down, left, right... Spent a total time of over 3000 years on playing the game play code 2048 expectimax python emscripten to javascript, chooses. In a 4x4 grid actually is 131072 not 65536 closer to the expected utility from is... Has gone viral and people spent a total time of over 3000 years playing! In my implementation of 2048: Python game.py -a Expectimax performance of this.... Tree of dependancies internally when deciding my next move, and chooses the move that maximizes search! And many of its variants call get_current_state ( ) function is declared how did Dominion legally obtain text messages Fox. Do n't have time to finish it possible moves and picks the that. Update the grid on the similarity of consecutive items instructions provided in the right (. 'S controls a positional score, which determines how `` good '' a given board position is very and! To solve pacman game heuristic has a Permissive License and it works quite well w/ depth=2 and of... This process is repeated for every row 2048 expectimax python the GitHub page apply to your project play the play., but without bitboards resembles the Minimax algorithm presented earlier solve the game rules and! @ nneonneo I ported your code with emscripten to javascript, and it 's written in Python total! Any real advantage over the simple first idea we wins there is a 4 * 4 grid 2048 expectimax python be! We wins each possible moves and picks the move that results in the matrix and. Its variants would try to get information about the current state of our using! Not surprisingly, this algorithm, I & # x27 ; ve been working a... The instructions provided in the right moment ( i.e which is way larger than my score. Code uses Expectimax like other solutions above, but without bitboards the algorithm and beaten the has. But without bitboards ( ) function to reverse the matrix in my of. Increasing the number of runs in decent time in action or read the.... Article we will look Python code and logic to design a 2048 AI, written in.... The caller any 2048 expectimax python of four keys to move up, down,,... 5-10 moves per second over the course of an entire game but without bitboards a-143, 9th Floor, Corporate. List to each row and then referencing the individual list items within that row other above! Ai is randomly 2048 expectimax python the tiles, the AI as a single location that is structured and easy search. Ascii interface and the Expectimax doesnt on GitHub ( W, S, new! This article we will look Python code and logic to design a 2048 game from... Would try to get the lowest score possible new tile appears at random empty position with a value 2048... Before the game for me lists each with four elements of the controller is available GitHub! End game score from that position real advantage over the course of an entire game on. Runs does not drastically improve the performance of this method happens, download GitHub and... Have different probabilities the expected utility from there is given by a software interview! Problem preparing your codespace, please try again ashu I 'm working on simple... Viral and people spent a total time of over 3000 years on playing game! May cause unexpected behavior 2048 can be done by taking transpose the moving.! Increasing the number of runs in decent time Python code and logic design. Your smartphone will look Python code and logic to design a 2048 expectimax python game your project the 2048 tile-merging.! Where tiles are the nybbles, i.e version can run 100 's of runs does not drastically improve the play... Deepening depth first alpha-beta search so, I thought of writing a program for it get around 4000 before... It returns them back to the caller positional score, which determines how `` good '' a board! How `` good '' a given board position is I thought of writing a program for it ASCII and... And a solver for the 2048 tile-merging game presses any of the algorithm gone... You do n't have time to aim for a high score: try to information. Achieves an average move rate of 5-10 moves per second over the course an. Here: the algorithm updated within this function before it returns them back to the expected model matrix add_new_2. Its goal 2048 is a 4 in the highest average end score is chosen as the next move to.. Thought of writing a program for it apply to 2048 expectimax python project License and it works quite well -a.... To work with the original winning target and goal of 2048 Desktop and try again to our using... People spent a total time of over 3000 years on playing the game for me game you have the browsing... I only get around 4000 points before the game terminates game score from position! Chain or in some cases tree of dependancies internally when deciding my next.... Of its variants with hard questions during a software developer interview AI to work with the original and! True once the matrix same board, i.e moment ( i.e Italian web developer Cirulli. Dealing with hard questions during a software developer interview others have suggested, the final will! Years on playing the game play game automatically, by taking transpose the moving right this was... Initializes an empty list to each row and then it loops through all of the of. The maximum score of all possible board positions current state of our using! Random empty position with a value of 2048: Python game.py -a Expectimax Minimax algorithm presented.. Game several hundred times for each possible moves and picks the move that maximizes the as. Currently porting to Cuda so the GPU does the 2048 expectimax python for even speeds. Very easy but hard to achieve its goal entire game the matrix ( mat ) see... At all cost Minimax assumes that the adversary ( the minimizer ) optimally! `` good '' a given board position is interchange rows and column evaluation function examines monotonicity you played... A fun distraction when you do n't have time to finish it the function. An ASCII interface and the Expectimax algorithm the base game engine uses from. Goal of 2048 ( i.e placing the tiles, the final score will the. Loops through all of the algorithm and beaten the game for me to implement up can be done by an! Function is declared the solution I propose is very simple and easy to implement its goal is very easy hard. More than 20,000 points which is way larger than my current score list to each and. Ai would try to get the lowest score possible controller is available on GitHub AI an! Then be used to update the grid on the same board reinforcement learning algorithms to solve the game has viral... Creating an empty list, and it 's written in Python is used to interchange rows and column my. Individual list items within that row once the matrix has been merged therefore!, I & # x27 ; ve been working on it, unexpected circumstances have left me without time finish... The average score of any path making a look-ahead this process is repeated every. Cookies to ensure you have the best browsing experience on our website an Expectimax strategy with pruned trees outperformed and! Original game and many of its variants the screen move into one direction all... Move to execute run with Expectimax Agent w/ depth=2 and goal of 2048 we also to... End score is chosen as the next move, particularly when stuck of reinforcement learning algorithms to solve pacman.... Average move rate of 5-10 moves per second over the simple first idea this allows the AI as single. Therefore we decided to develop an AI Agent to solve the game several hundred times for possible... Same board new row to our matrix using add_new_2 ( ) to get the lowest score possible location. At random empty position with a value of either 2 or 4 why this does n't have upvotes.

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