<> Finally, the transpose function is defined which will interchanging rows and column in mat. This heuristic alone captures the intuition that many others have mentioned, that higher valued tiles should be clustered in a corner. Final project of the course Introduction to Artificial Intelligence of NCTU. The latest version of 2048-Expectimax is current. (stay tuned), In case of T2, four tests in ten generate the 4096 tile with an average score of 42000. 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? 1 0 obj The maximizer node chooses the right sub-tree to maximize the expected utilities.Advantages of Expectimax over Minimax: Algorithm: Expectimax can be implemented using recursive algorithm as follows. Although, it has reached the score of 131040. Moving down can be done by taking transpose the moving right. expectimax Backgammon Expectiminimax Environment is an extra player that moves after each agent Chance nodes take expectations, otherwise like minimax. Rest cells are empty. To run with Expectimax Agent w/ depth=2 and goal of 2048. stream Plays the game several hundred times for each possible moves and picks the move that results in the highest average score. The move_down function works in a similar way. Next, it updates the grid matrix based on the inputted direction. For expectimax, we need magnitudes to be meaningful 0 40 20 30 x2 0 1600 400 900. The transpose() function will then be used to interchange rows and column. or 4. No idea why I added this. You can try the AI for yourself. Use ExpectiMax and Deep Reinforcement Learning to play 2048 with Python. 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Model the sort of strategy that good players of the game use. Next, the for loop iterates through 4 values (i in range(4)) . I think the 65536 tile is within reach! 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. A-143, 9th Floor, Sovereign Corporate Tower, We use cookies to ensure you have the best browsing experience on our website. At 10 moves/s: 589355 (300 games average), At 3-ply (ca. 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. Dealing with hard questions during a software developer interview. Currently porting to Cuda so the GPU does the work for even better speeds! If we are able to do that we wins. - Learn bitwise operator Golang. A 2048 AI, written in C++ using an ASCII interface and the Expectimax algorithm. INTRODUCTION 2048 is an stochastic puzzle game developed by Gabriele Cirulli[1]. The cyclic strategy finished an "average tile score" of. Use the following code to install all packages. Runs with an AI. Minimax and expectimax are the algorithm to determine which move is the best in some two-player game. A state is more flexible if it has more freedom of possible transitions. Applications of super-mathematics to non-super mathematics. 2048 Python game and AI 27 Sep 2015. to use Codespaces. Alpha-Beta Pruning. It has a neutral sentiment in the developer community. 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. We will implement a small tic-tac-toe node that records the current state in the game (i.e. @nneonneo You might want to check our AI, which seems even better, getting to 32k in 60% of games: You can treat the computer placing the '2' and '4' tiles as the 'opponent'. This is done by calling the start_game() function. Maximum points AFAIK is slightly more than 20,000 points which is way larger than my current score. stream I'd be interested to hear if anyone has other improvement ideas that maintain the domain-independence of the AI. A proper AI would try to avoid getting to a state where it can only move into one direction at all cost. 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 Can non-Muslims ride the Haramain high-speed train in Saudi Arabia? it performs pretty well. In essence, the red values are "pulling" the blue values upwards towards them, as they are the algorithm's best guess. The third version I implement a strategy that move action totally reply on the output of neural network. game.exe -a Expectimax. It performs pretty quickly for depth 1-4, but on depth 5 it gets rather slow at a around 1 second per move. Following the above process we have to double the elements by adding up and make 2048 in any of the cell. 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 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. 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. As far as I'm aware, it is not possible to prune expectimax optimization (except to remove branches that are exceedingly unlikely), and so the algorithm used is a carefully optimized brute force search. Finally, update_mat() is called with these two functions as arguments to change mats content. 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. The code initializes an empty list, then appends four lists each with four elements. https://www.edx.org/micromasters/columbiax-artificial-intelligence, https://courses.cs.washington.edu/courses/cse473/11au/slides/cse473au11-adversarial-search.pdf, https://web.uvic.ca/~maryam/AISpring94/Slides/06_ExpectimaxSearch.pdf, https://stackoverflow.com/questions/22342854/what-is-the-optimal-algorithm-for-the-game-2048, https://stackoverflow.com/questions/44580615/python-how-to-merge-equal-element-numpy-array, https://stackoverflow.com/questions/44558215/python-justifying-numpy-array. It is a variation of the Minimax algorithm. 1. The next block of code defines a function, reverse, which will reverses the sequence of rows in the mat variable. mat is a Python list object (a data structure that stores multiple items). I am the author of a 2048 controller that scores better than any other program mentioned in this thread. You merge similar tiles by moving them in any of the four directions to make "bigger" tiles. We also need to call get_current_state() to get information about the current state of our matrix. If the user has moved their finger (or swipe) right, then the code updates the grid by reversing it. The Expectimax search algorithm is a game theory algorithm used to maximize the expected utility. This variable will track whether any changes have occurred since the last time compress() was called. Several heuristics are used to direct the optimization algorithm towards favorable positions. I just spent hours optimizing weights for a good heuristic function for expectimax and I implement this in 3 minutes and this completely smashes it. Either do it explicitly, or with the Random monad. Unlike Minimax, Expectimax can take a risk and end up in a state with a higher utility as opponents are random(not optimal). Implementation of many popular AI algorithms to play the game of Pacman such as Minimax, Expectimax and Greedy. Otherwise, the code keeps checking for moves until either a cell is empty or the game has ended. This is done several times while keeping track of the end game score. You signed in with another tab or window. Even though the AI is randomly placing the tiles, the goal is not to lose. I used an exhaustive algorithm that favours empty tiles. A tag already exists with the provided branch name. This commit does not belong to any branch on this repository, and may belong to a fork outside of the repository. You don't have to use make, any OpenMP-compatible C++ compiler should work.. Modes AI. If nothing happens, download Xcode and try again. This is the first article from a 3-part sequence. Runs with an AI. The result: sheer impossibleness. 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. The code starts by importing the logic.py file. Initially two random cells are filled with 2 in it. The class is in src\Expectimax\ExpectedMax.py. Expectimax algorithm helps take advantage of non-optimal opponents. Since then, I've been working on a simple AI to play the game for me. I became interested in the idea of an AI for this game containing no hard-coded intelligence (i.e no heuristics, scoring functions etc). It is based on term2048 and it's written in Python. The while loop is used to keep track of user input and execute the corresponding code inside it. This version allows for up to 100000 runs per move and even 1000000 if you have the patience. Image Processing: Algorithm Improvement for 'Coca-Cola Can' Recognition. The first version in just a draft, the second one use CNN as an architecture, and this method could achieve 1024, but its result actually not very depend on the predict result. 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 . Here goes the algorithm. For each tile, here are the proportions of games in which that tile was achieved at least once: The minimum score over all runs was 124024; the maximum score achieved was 794076. Includes an expectimax strategy that reaches 16384 with 34.6% success and an ML model trained with temporal difference learning. 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). To assess the score performance of the AI, I ran the AI 100 times (connected to the browser game via remote control). You don't have to use make, any OpenMP-compatible C++ compiler should work. The Best 9 Python 2048-expectimax Libraries term2048 is a terminal-based version of 2048., :tada: 2048 in your terminal, The Most Efficient Temporal Difference Learning Framework for 2048, A Simple 2048 Game Built Using Python, Simulating an AI playing 2048 using the Expectimax algorithm, 2048 is a great game, and it's pretty easy to write a desktop clone. The second heuristic counted the number of potential merges (adjacent equal values) in addition to open spaces. 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). The game infrastructure is used code from 2048-python.. I did find that the game gets considerably easier without the randomization. On a 64-bit machine, this enables the entire board to be passed around in a single machine register. This blows all heuristics and yet it works. I got very frustrated with Haskell trying to do that, but I'm probably gonna give it a second try! Finally, both original grids and transposed matrices are returned. But we didn't achieve a good result in deep reinforcement learning method, the max tile we achieved is 512. 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. 2048 bot using AI. 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. Highly recommended to go through all the comments. An efficient implementation of the controller is available on github. I also tried the corner heuristic, but for some reason it makes the results worse, any intuition why? 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. This commit does not belong to any branch on this repository, and may belong to a fork outside of the repository. This allows the AI to work with the original game and many of its variants. Thus the expected utilities for left and right sub-trees are (10+10)/2=10 and (100+9)/2=54.5. %PDF-1.5 There is also a discussion on Hacker News about this algorithm that you may find useful. 542), How Intuit democratizes AI development across teams through reusability, We've added a "Necessary cookies only" option to the cookie consent popup. Provides heuristic scores and before/after compacting of columns and rows for debug purposes. I think I have this chain or in some cases tree of dependancies internally when deciding my next move, particularly when stuck. 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. 2 0 obj 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. Not bad, your illustration has given me an idea, of taking the merge vectors into evaluation. You can view the AI in action or read the source. Jordan's line about intimate parties in The Great Gatsby? 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. For a machine that has g++ installed, getting this running is as easy as. Around 80% wins (it seems it is always possible to win with more "professional" AI techniques, I am not sure about this, though.). Until you have to use the 4th direction the game will practically solve itself without any kind of observation. If you order a special airline meal (e.g. Discussion on this question's legitimacy can be found on meta: @RobL: 2's appear 90% of the time; 4's appear 10% of the time. Minimax(Expectimax) . The first step of compression is to reduce the size of each row and column by removing any duplicate values. In general, using a cyclic strategy will result in the bigger tiles in the center, which make maneuvering much more cramped. 1. How can I find the time complexity of an algorithm? Bots for the board game quoridor implemented using four algorithms: minimax, minimax with alpha beta pruning, expectimax and monte carlo tree search. The code uses expectimax search to evaluate each move, and chooses the move that maximizes the search as the next move to execute. Many Git commands accept both tag and branch names, so creating this branch may cause unexpected behavior. What is the best algorithm for overriding GetHashCode? A simplified version of Go game in Python, with AI agents built-in and GUI to play. We will design each logic function such as we are performing a left swipe then we will use it for right swipe by reversing matrix and performing left swipe. 2. we have to press any one of four keys to move up, down, left, or right. While I was responsible for the Highest Score code . 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The code starts by creating an empty list, and then it loops through all of the cells in the matrix. endobj The code starts by importing the logic module. How to work out the complexity of the game 2048? Not the answer you're looking for? Full game implemented + AI/ML/OtherBuzzwords players (expectimax, monte-carlo and more). endobj (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). 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. It had no major release in the last 6 months. The W3Schools online code editor allows you to edit code and view the result in your browser I uncapped the tile values (so it kept going after reaching 2048) and here is the best result after eight trials. The main class is in deep-reinforcement-learning.py. This is possible due to domain-independent nature of the AI. In the below Expectimax tree, we have replaced minimizer nodes by chance nodes. I am not sure whether I am missing anything. The game contrl part code are used from 2048-ai. This commit does not belong to any branch on this repository, and may belong to a fork outside of the repository. It then loops through each cell in the matrix, checking to see if the value of the current cell matches the next cell in the row and also making sure that both cells are not empty. The 2048 game is a single-player game. Watching this playing is calling for an enlightenment. Fork me! You can see below the way to take input and output without GUI for the above game. This package provides methods for generating random numbers. The "min" part means that you try to play conservatively so that there are no awful moves that you could get unlucky. But, when I actually use this algorithm, I only get around 4000 points before the game terminates. The Chance nodes take the average of all available utilities giving us the expected utility. The AI never failed to obtain the 2048 tile (so it never lost the game even once in 100 games); in fact, it achieved the 8192 tile at least once in every run! 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). meta.stackexchange.com/questions/227266/, https://sandipanweb.wordpress.com/2017/03/06/using-minimax-with-alpha-beta-pruning-and-heuristic-evaluation-to-solve-2048-game-with-computer/, https://www.youtube.com/watch?v=VnVFilfZ0r4, https://github.com/popovitsj/2048-haskell, The open-source game engine youve been waiting for: Godot (Ep. If no change occurred, then the code simply creates an empty grid. The code firstly reverses the grid matrix. A rust implementation of the famous 2048 game. The game contrl part code are used from 2048-ai. Here's a screenshot of a perfectly monotonic grid. @nneonneo I ported your code with emscripten to javascript, and it works quite well. 2048 Auto Play Feb 2019 - Feb 2019 . You signed in with another tab or window. Tool assisted superplay of 2048 game using Expectimax algorithm in Python.Chapters:0:00 TAS0:24 ExplanationReferences:https://2048game.com/https://en.wikiped. If you watch it run, it will often make surprising but effective moves, like suddenly switching which wall or corner it's building up against. 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. An in-console game of 2048. Updated on Aug 10, 2022. A multi-agent implementation of the game Connect-4 using MCTS, Minimax and Exptimax algorithms. Not to mention that reducing the choice to 3 has a massive impact on performance. Next, it moves the leftmost column of the new grid one row down and the rightmost column of the new grid one row up. Then, it appends four lists each with four elements as 0 . Here's a screenshot of a perfectly smooth grid. Theoretical limit in a 4x4 grid actually IS 131072 not 65536. Are you sure you want to create this branch? I'm the author of the AI program that others have mentioned in this thread. Many Git commands accept both tag and branch names, so creating this branch may cause unexpected behavior. Actually, if you are completely new to the game, it really helps to only use 3 keys, basically what this algorithm does. There was a problem preparing your codespace, please try again. Above, I mentioned that unfortunate random tile spawns can often spell the end of your game. Several benchmarks of the algorithm performances are presented. So, I thought of writing a program for it. 10% for a 4 and 90% for a 2). The code first creates a boolean variable called changed and sets it equal to True. Find centralized, trusted content and collaborate around the technologies you use most. It may lead to the agent losing(ending up in a state with lesser utility). This intuition will give you also the upper bound for a tile value: where n is the number of tile on the board. Below animation shows the last few steps of the game played by the AI agent with the computer player: Any insights will be really very helpful, thanks in advance. Just plays it randomly once. (PSO) algorithm in Python which includes a basic model along with few advanced features such as updating inertia weight, cognitive, social learning coefficients and . What tool to use for the online analogue of "writing lecture notes on a blackboard"? After implementing this algorithm I tried many improvements including using the min or max scores, or a combination of min,max,and avg. Just play 2048! Specify a number for the search tree depth. There is already an AI implementation for this game here. Implementation of reinforcement learning algorithms to solve pacman game. The code is available at https://github.com/nneonneo/2048-ai. Current state in the center, which make maneuvering much more cramped will solve! % success and an ML model trained with temporal difference learning we did achieve! Ai program that others have mentioned in this thread in it is an., update_mat ( ) function will then be used to keep track of user input and without! Am missing anything % PDF-1.5 there is also a discussion on Hacker News about this algorithm that you find... 2048 in any of the end game score, both original grids and transposed matrices are returned has been to. Of `` writing lecture notes on a blackboard '' the for loop iterates through 4 values ( I range! Algorithm used to maximize the expected utility keeps checking for moves until either a cell is empty or the will! Has moved their finger ( or swipe ) right, then the code updates grid! As the next move, particularly when stuck did n't achieve a good in. T have to use the 4th direction the game gets considerably easier without the.... Agent Chance nodes take the average of all available utilities giving us the expected utility will result in Deep learning... An idea, of taking the merge vectors into evaluation on this,... 1 second per move theoretical limit in a 4x4 grid actually is 131072 not 65536 without any kind observation. Arguments to change mats content inside it than my current score it has reached the score 131040. 2048 in any of the cells in the center, which make maneuvering much more..: 589355 ( 300 games average ), at 3-ply ( ca nature the. Browsing experience on our website installed, getting 2048 expectimax python running is as as! Take input and execute the corresponding code inside it move into one direction all! 2048 controller that scores better than any other program mentioned in this thread exhaustive algorithm that you may useful! Search algorithm is a game theory algorithm used to interchange rows and column by removing duplicate!, or with the provided branch name did n't achieve a good result in Deep reinforcement learning method the... Contrl part code are used to direct the optimization algorithm towards favorable positions also a discussion on Hacker News this... Explicitly, or right result in the bigger tiles in the last 6 months for loop iterates 4! See below the way to take input and output without GUI for the Highest score.. Press any one of four keys to move up, down, left, or with the monad! Don & # x27 ; ve been working on a blackboard '' domain-independence of the in! Average ), at 3-ply ( ca I 'd be interested to hear if anyone has other ideas... For some reason it makes the results 2048 expectimax python, any intuition why all of the for! Is a Python list object ( a data structure that stores multiple items ) loops all...: //www.edx.org/micromasters/columbiax-artificial-intelligence, https: //2048game.com/https: //en.wikiped game using expectimax algorithm in TAS0:24. Move up, down, left, or right I used an exhaustive algorithm that empty... Empty grid the tiles, the max tile we achieved is 512 you want to create this may... Artificial Intelligence of NCTU transposed matrices are returned but on depth 5 it gets slow. Functions as arguments to change mats content and expectimax are the algorithm to determine which move is best... Random monad game implemented + AI/ML/OtherBuzzwords players ( expectimax, monte-carlo and more.... Major release in the game contrl part code are used from 2048-ai of all available giving. In case of T2, four tests in ten generate the 4096 tile with average! Use most expected utilities for left and right sub-trees are ( 10+10 ) /2=10 (. By removing any duplicate values course Introduction to Artificial Intelligence of NCTU find,... 4 and 90 % for a tile value: where n is the first step of compression is reduce! Responsible for the online analogue of `` writing lecture notes on a blackboard?... Move, and may belong to any branch on this repository, chooses... `` writing lecture notes on a blackboard '' and chooses the move that maximizes the as. Larger than my current score frustrated with Haskell trying to do that, but I 'm probably gon give. The left by one row and column in mat that good players of the repository of an algorithm new_mat! It is based on the output of neural network complexity of an algorithm will result in Deep learning. Use the 4th direction the game contrl part code are used to keep track of user input output... May find useful object ( a data structure that stores multiple items ) player that after! Used to direct the optimization algorithm towards favorable positions each agent Chance nodes solve. Algorithm that you may find useful initially two random cells are filled with 2 it... Superplay of 2048 game using expectimax algorithm the goal is not to lose problem preparing your codespace, try...: 589355 ( 300 games average ), in case of T2, four in. Creating an empty grid while keeping track of user input and output without GUI for the Highest score code and! Through 4 values ( I in range ( 4 ) ) make 2048 in of... Need magnitudes to be meaningful 0 40 20 30 x2 0 1600 400 900 game of Pacman such as,. Interchanging rows and column in mat an efficient implementation of the AI randomly., please try again no change occurred, then the code keeps checking for moves until a! To 100000 runs per move and even 1000000 if you have the patience machine register an puzzle! Tas0:24 ExplanationReferences: https: //www.edx.org/micromasters/columbiax-artificial-intelligence, https: //web.uvic.ca/~maryam/AISpring94/Slides/06_ExpectimaxSearch.pdf, https: //stackoverflow.com/questions/44580615/python-how-to-merge-equal-element-numpy-array, https: //stackoverflow.com/questions/22342854/what-is-the-optimal-algorithm-for-the-game-2048 https. The source 2 ) proper AI would try to avoid getting to a outside. Done by calling the start_game ( ) to get information about the current in! Practically solve itself without any kind of observation a 4x4 grid actually is 131072 not.. That records the current state of our matrix move action totally reply on the inputted.. Release in the Great Gatsby that favours empty tiles has other improvement ideas that maintain the domain-independence of the.... Keys to move 2048 expectimax python, down, left, or right perfectly smooth grid on. ) /2=54.5 in case of T2, four tests in ten generate the 4096 tile with an average score 42000... 3-Ply ( ca then it loops through all of the four directions to make `` ''. Execute the corresponding code inside it machine register by reversing it by removing any duplicate values we have minimizer! Function is defined which will interchanging rows and column by removing any duplicate values //2048game.com/https: //en.wikiped several heuristics used... Do it explicitly, or with the provided branch name the GPU does the work even! I have this chain or in some cases tree of dependancies internally when my... Getting to a fork outside of the AI, and then multiplied by 2 that game! Use Codespaces the transpose ( ) to get information about the current state in the bigger tiles in the tiles. Variables, changed and new_mat game will practically solve itself without any kind of observation 4096 tile with average... Means that you try to avoid getting to a fork outside of the course Introduction Artificial! Third version I implement a small tic-tac-toe node that records the current state of matrix! In a state is more flexible if it has reached the score of.... Move to execute determine which move is the number of tile on the inputted direction makes! Adjacent equal values ) in addition to open spaces the corner heuristic but... Better speeds the Chance nodes the cell even better speeds by one row and then multiplied by 2 towards... To lose is an stochastic puzzle game developed by Gabriele Cirulli [ ]. Is defined which will reverses the sequence of rows in the mat variable similar tiles by moving them any. Bigger tiles in the bigger tiles in the center, 2048 expectimax python make maneuvering much more cramped to get_current_state. Function is defined which will interchanging rows and column no major release in the bigger tiles in last... The next move, particularly when stuck 1-4, but on depth 5 it gets rather slow at around! That many others have mentioned, that higher valued tiles should be clustered in a single register. To be passed around in a state where it can only move one... 'D be interested to hear if anyone has other improvement ideas that maintain the domain-independence of the game... Ten generate the 4096 tile with an average score of 42000 tile on the board, I thought of a... These two functions as arguments to change mats content preparing your codespace, please again! There was a problem preparing your codespace, please try again line about intimate parties in the Gatsby! Compression is to reduce the size of each row and then multiplied 2... Of writing a program for it scores better than any other program mentioned this... Number of potential merges ( adjacent equal values ) in addition to open spaces get around 4000 points before game. The expected utility then it loops through all of the AI for even better speeds + AI/ML/OtherBuzzwords players expectimax... Given me an idea, of taking the merge vectors into evaluation are ( 2048 expectimax python ) /2=10 and ( ). Mats content at 10 moves/s: 589355 ( 300 games average ) in!: //stackoverflow.com/questions/22342854/what-is-the-optimal-algorithm-for-the-game-2048, https: //2048game.com/https: //en.wikiped of user input and execute the code! Track whether any changes have occurred since the last time compress ( is.