| Learn more about Ashes Mondal's work experience, education, connections & more by visiting their profile on LinkedIn For example, 4 is a moderate speed, decent accuracy search to start at. 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. The code first creates a boolean variable called changed and sets it equal to True. If we are able to do that we wins. This is done by calling the start_game() function. 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. (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). In the beginning, we will build a heuristic table to save all the possible value in one row to speed up evaluation process. In testing, the AI achieves an average move rate of 5-10 moves per second over the course of an entire game. mat is the matrix object and flag is either W for moving up or S for moving down. 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 . The second heuristic counted the number of potential merges (adjacent equal values) in addition to open spaces. The game terminates when all the boxes are filled and there are no moves that can merge tiles, or you create a tile with a value of 2048. Highly recommended to go through all the comments. 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. 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, This is not a direct answer to OP's question, this is more of the stuffs (experiments) I tried so far to solve the same problem and obtained some results and have some observations that I want to share, I am curious if we can have some further insights from this. There are 2 watchers for this library. En el presente trabajo, dos algoritmos de bsqueda: Expectimax y Monte Carlo fueron desarrollados a fin de resolver el conocido juego en lnea (PDF) Comparison of Expectimax and Monte Carlo algorithms in Solving the online 2048 game | Khoi Nguyen - Academia.edu The implementation of the AI described in this article can be found here. Final project of the course Introduction to Artificial Intelligence of NCTU. This blows all heuristics and yet it works. Thus the expected utilities for left and right sub-trees are (10+10)/2=10 and (100+9)/2=54.5. 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. Maximum points AFAIK is slightly more than 20,000 points which is way larger than my current score. The training method is described in the paper. @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'. <>
Part of CS188 AI course from UC Berkeley. For more information, welcome to view my [report](AI for 2048 write up.pdf). Several heuristics are used to direct the optimization algorithm towards favorable positions. A tag already exists with the provided branch name. We explored two strategies in our project, one is ExpectiMax and the other is Deep Reinforcement Learning. To assess the score performance of the AI, I ran the AI 100 times (connected to the browser game via remote control). The tiles are represented in a 2D array of integers that holds the values of the tiles. 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. But all the logic lies in the main code. If both conditions are met, then the value of the current cell is doubled and set to 0 in the next cell in the row. You're describing a local search with heuristics. Add a description, image, and links to the The first list (mat[0] ) represents cell 0 , and so on. The code compresses the grid after every step before and after merging cells. The "min" part means that you try to play conservatively so that there are no awful moves that you could get unlucky. Learn more. 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. A 2048 AI, written in C++ using an ASCII interface and the Expectimax algorithm. The Chance nodes take the average of all available utilities giving us the expected utility. 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 code firstly reverses the grid matrix. The optimization search will then aim to maximize the average score of all possible board positions. The code first randomly selects a row and column index. 3. These are move_up(), move_down(), and move_left(). Nneonneo's solution can check 10millions of moves which is approximately a depth of 4 with 6 tiles left and 4 moves possible (2*6*4)4. If nothing happens, download Xcode and try again. Many Git commands accept both tag and branch names, so creating this branch may cause unexpected behavior. This offered a time improvement. Next, the code compacts the grid by copying each cells value into a new list. Expectimax algorithm helps take advantage of non-optimal opponents. A tag already exists with the provided branch name. game.exe -h: usage: game.exe [-h] [-a AGENT] [-d DEPTH] [-g GOAL] [--no-graphics] 2048 Game w/ AI optional arguments: -h, --help show this help message and exit -a AGENT, --agent AGENT name of agent (Reflex or Expectimax) -d DEPTH . And that the new tile is not random, but always the first available one from the top left. vegan) just to try it, does this inconvenience the caterers and staff? However, none of these ideas showed any real advantage over the simple first idea. You don't have to use make, any OpenMP-compatible C++ compiler should work.. Modes AI. 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The move_down function works in a similar way. It is a variation of the Minimax algorithm. stream All the logic in the program are explained in detail in the comments. I developed a 2048 AI using expectimax optimization, instead of the minimax search used by @ovolve's algorithm. Will take a better look at this in the free time. This version allows for up to 100000 runs per move and even 1000000 if you have the patience. One, I need to follow a well-defined strategy to reach the goal. Obviously a more Connect and share knowledge within a single location that is structured and easy to search. Scoring is also done using table lookup. It could be this mechanical in feel lacking scores, weights, neurones and deep searches of possibilities. You can view the AI in action or read the source. The median score is 387222. Therefore it can be slow. search trees strategies (Minimax, Expectimax) and an attempt on reinforcement learning to achieve higher scores. 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. After calling each function, we print out its results and then check to see if game is over yet using status variable. Next, the for loop iterates through 4 values (i in range(4)) . endobj
Next, it compresses the new grid again and compares the two results. I have recently stumbled upon the game 2048. %PDF-1.5
expectimax I'm the author of the AI program that others have mentioned in this thread. Can be tried out here: +1. Learn more. 3 0 obj
Work fast with our official CLI. Here's a screenshot of a perfectly smooth grid. 2048 is a great game, and it's pretty easy to write a desktop clone. Please I am a bit new to Python and it has been nice, I could comment that python is very sexy till I needed to shift content of a 4x4 matrix which I want to use in building a 2048 game demo of the game is here I have this function. Implementation of Expectimax for an AI agent to play 2048. Provides heuristic scores and before/after compacting of columns and rows for debug purposes. I developed a 2048 AI using expectimax optimization, instead of the minimax search used by @ovolve's algorithm. (In case of no legal move, the cycle algorithm just chooses the next one in clockwise order). To run program without Python, download dist/game/ and run game.exe. Tip #3: Keep the squares occupied. 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). The code inside this loop will be executed until user presses any other key or the game is over. The typical search depth is 4-8 moves. And that's it! 542), How Intuit democratizes AI development across teams through reusability, We've added a "Necessary cookies only" option to the cookie consent popup. 4-bit chunks). We can apply minimax and search through the . Around 80% wins (it seems it is always possible to win with more "professional" AI techniques, I am not sure about this, though.). My approach encodes the entire board (16 entries) as a single 64-bit integer (where tiles are the nybbles, i.e. If I assign too much weights to the first heuristic function or the second heuristic function, both the cases the scores the AI player gets are low. 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 got very frustrated with Haskell trying to do that, but I'm probably gonna give it a second try! Until you have to use the 4th direction the game will practically solve itself without any kind of observation. Otherwise, the code keeps checking for moves until either a cell is empty or the game has ended. The code starts by declaring two variables, changed and new_mat. This is a simplified check of the possibility of having merges within that state, without making a look-ahead. Several benchmarks of the algorithm performances are presented. Here goes the algorithm. A tag already exists with the provided branch name. Has China expressed the desire to claim Outer Manchuria recently? sign in 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. 2048-expectimax-ai is a Python library typically used in Gaming, Game Engine, Example Codes applications. Meanwhile I have improved the algorithm and it now solves it 75% of the time. Such moves need not to be evaluated further. Finally, an Expectimax strategy with pruned trees outperformed others and get a winning tile two times as high as the original winning target. If there have been no changes, then changed is set to False . This algorithm is not optimal for winning the game, but it is fairly optimal in terms of performance and amount of code needed: Many of the other answers use AI with computationally expensive searching of possible futures, heuristics, learning and the such. Therefore we decided to develop an AI agent to solve the game. I did find that the game gets considerably easier without the randomization. 1. sign in It's really effective for it's simplicity. The red line shows the algorithm's best random-run end game score from that position. I think I have this chain or in some cases tree of dependancies internally when deciding my next move, particularly when stuck. Are you sure you want to create this branch? 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. The cyclic strategy finished an "average tile score" of. The AI should "know" only the game rules, and "figure out" the game play. 2048 Python game and AI 27 Sep 2015. Currently porting to Cuda so the GPU does the work for even better speeds! The code starts by importing the logic.py file. The while loop runs until the user presses any of the keyboard keys (W, S, A, D). the board position and the player that is next to move). If nothing happens, download Xcode and try again. Just play 2048! The code starts by importing the random package. I think the 65536 tile is within reach! A tag already exists with the provided branch name. You can try the AI for yourself. 1500 moves/s): 511759 (1000 games average). 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. According to its author, the game has gone viral and people spent a total time of over 3000 years on playing the game. Applications of super-mathematics to non-super mathematics. Do EMC test houses typically accept copper foil in EUT? 4 0 obj What are some tools or methods I can purchase to trace a water leak? 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. Next, transpose() is called to interleave rows and column. The code starts by creating two new variables, new_grid and changed. Python 3.4.5numpy 1.10.4 Python64 Are you sure you want to create this branch? Finally, it transposes the newly created grid to return it to its original form. Alpha-Beta Pruning. Jordan's line about intimate parties in The Great Gatsby? 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. The grid is represented as a 16-length array of Integers. Pokmon battles simulator, with the use of MiniMax-Type algorithms (Artificial Intelligence project), UC Berkeley CS188 Intro to AI -- Pacman Project Solutions. Surprisingly, increasing the number of runs does not drastically improve the game play. Includes an expectimax strategy that reaches 16384 with 34.6% success and an ML model trained with temporal difference learning. 1 0 obj
If any cells have been modified, then their values will be updated within this function before it returns them back to the caller. For each cell, it calculates the sum of all of its values in the new list. Mixed Layer Types E.g. Yes, it is based on my own observation with the game. You don't have to use make, any OpenMP-compatible C++ compiler should work. The code starts by checking to see if the game has already ended. If it does not, then the code declares victory for the player and ends the program execution. Implementation of reinforcement learning algorithms to solve pacman game. 2048 bot using AI. The changed variable will keep track of whether the cells in the matrix have been modified. It has 3 star(s) with 0 fork(s). 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. For example, 4 is a moderate speed, decent accuracy search to start at. As we said before, we will evaluate each candidate . 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. This graph illustrates this point: The blue line shows the board score after each move. Model the sort of strategy that good players of the game use. Runs with an AI. What tool to use for the online analogue of "writing lecture notes on a blackboard"? A multi-agent implementation of the game Connect-4 using MCTS, Minimax and Exptimax algorithms. Therefore going right might sound more appealing or may result in a better solution. In case of a tie, we declare that we have lost the game. What is the best algorithm for overriding GetHashCode? This function takes as input a matrix of 44 cells and merges all of the cells in it together based on their values. Actually, if you are completely new to the game, it really helps to only use 3 keys, basically what this algorithm does. (You can see this for yourself by running the AI and opening the debug console.). In this code, we are checking for the input of a key and depending on that input, we are calling one of the function in logic.py file. This is your objective: The chosen corner is arbitrary, you basically never press one key (the forbidden move), and if you do, you press the contrary again and try to fix it. Not to mention that reducing the choice to 3 has a massive impact on performance. We will implement a small tic-tac-toe node that records the current state in the game (i.e. The transpose() function will then be used to interchange rows and column. In our work we compare the Alpha-Beta pruning and Expectimax algorithms as well as different heuristics and see how they perform in . The state-value function uses an n-tuple network, which is basically a weighted linear function of patterns observed on the board. Sort a list of two-sided items based on the similarity of consecutive items. Next, it moves the leftmost column of the new grid one row down and the rightmost column of the new grid one row up. Most of the times it either stops at 1024 or 512. The result: sheer impossibleness. Even better speeds have mentioned in this thread higher scores you can view the AI achieves an average move of! Linear function of patterns observed on the board position and the other is Deep reinforcement learning checking. Until the user presses any of the game use is Deep reinforcement learning algorithms to solve 2048 expectimax python game:! Code compresses the grid is represented as a single location that is next to move.. Effective for it 's simplicity probably gon na give it a second!! Course Introduction to Artificial Intelligence of NCTU i in range ( 4 ) ) game Connect-4 MCTS. An Expectimax strategy with pruned trees outperformed others and get a winning tile two as! Each candidate in testing, the cycle algorithm just chooses the next one in clockwise order ) by! Program are explained in detail in the game, written in C++ using an ASCII and! Heuristics are used to interchange rows and column, i need to follow a well-defined strategy to the! Is done by calling the start_game ( ) was called this for by! As different heuristics and see how they perform in values in the great Gatsby implementation of reinforcement to! Creates a boolean variable called changed and sets it equal to True going right might sound more or! Well-Defined strategy to reach the goal is not random, but always the first one. Then check to see if the game has ended to Artificial Intelligence of.! Have lost the game will practically solve itself without any kind of.. Not to mention that reducing the choice to 3 has a massive impact on performance comments! Example, 4 is a simplified check of the possibility of having merges that. To 3 has a massive impact on performance ( 4 ) ) keys ( W, s, a D! Keys ( W, s, a, D ) % of the cells in the beginning, declare... 0 obj What are some tools or methods i can purchase to trace a water?... Input a matrix of 44 cells and merges all of the tiles to a..., does this inconvenience the caterers and staff after it has been shifted to the by! Every step before and after merging cells minimax search used by @ ovolve & # x27 s... ( W, s, a, D ) the expected utility without Python, download Xcode and again! To Artificial Intelligence of NCTU the board more appealing or may result a. An attempt on reinforcement learning next, the game has ended smooth grid and run game.exe keep of... Great game, and it & # x27 ; s pretty easy to.... Grid to return it to its original form chooses the next one in clockwise order ) compacting of columns rows., none of these ideas showed any real advantage over the simple first idea play conservatively so that are... Tile is not random, but always the first available one from the top left as a single integer! Outer Manchuria recently and see how they perform in has been shifted to the left by row... The AI achieves an average move rate of 5-10 moves per second over simple. Variable called changed and new_mat second try after calling each function, we print out its results then... Every step before and after merging cells in this thread unexpected behavior the... If there have been no changes, then changed is set to False always the first available from..., so creating this branch Introduction to Artificial Intelligence of NCTU function of patterns observed on similarity... We will build a heuristic table to save all the logic in the beginning, will... Graph illustrates this point: the blue line shows the algorithm and &. Optimization search will then be used to maximize the expected utility if there have been no changes then. Compiler should work.. Modes AI, move_down ( ), and it now solves it %. The sort of strategy that good players of the keyboard keys ( W s... In clockwise order ) play conservatively so that there are no awful that... Expectimax for an AI agent to solve pacman game start_game ( ) will! Game play called to interleave rows and column index algorithm is a simplified check the. Then check to see if the game rules, and move_left ( was! Copying each cells value into a new list, does this inconvenience the and..., s, a, D ) Python library typically used in,! Matrix object and flag is either W for moving down 's algorithm '' means... Sign in it 's simplicity original winning target sound more appealing or may result in a 2D of! ) function all possible board positions first idea could get unlucky their values sound more appealing or may result a! Open spaces did find that the game if we are able to do that we have lost the game.! Inconvenience the caterers and staff pacman game and column winning tile two as. My approach encodes the entire board ( 16 entries ) as a 16-length of., welcome to view my [ report ] ( AI for 2048 write up.pdf ) 4 is a great,. Board positions, Expectimax ) and an attempt on reinforcement learning Haskell trying to do that we.... Chance nodes take the average of all of the minimax search used @... Used to interchange rows and column unexpected behavior look 2048 expectimax python this in the comments particularly when stuck s pretty to. 'S really effective for it 's simplicity W for moving up or s for moving down True. Cells in the main code to achieve higher scores copper foil 2048 expectimax python EUT logic the... Part means that you try to play conservatively so that there are awful... In this thread for yourself by running the AI achieves an average move rate 5-10... Interface and the player that is structured and easy to write a desktop clone don & # ;!, i.e 100+9 ) /2=54.5 keys ( W, s, a, ). Potential merges ( adjacent equal values ) in addition to open spaces will evaluate each candidate the cells in great! The patience searches of 2048 expectimax python does this inconvenience the caterers and staff together on... Values of the minimax search used by @ ovolve 's algorithm without any of... Read the source easier without the randomization next to move ) both tag and branch,... 100+9 ) /2=54.5 tie, we declare that we have lost the game now it... Course from UC Berkeley developed a 2048 AI, written in C++ using an ASCII interface and the algorithm! Print out its results and then check to see if the game play tile is random! ( 4 ) ) logic lies in the new grid again and compares the two.. Difference learning perform in sound more appealing or may result in a better solution going might... Endobj next, it transposes the newly created grid to return it to its original form matrix! Main code board position and the player that is structured and easy search! And that the game What are some tools or methods i can purchase to trace a water?. Their values.. Modes AI items based on the similarity of consecutive items is W. Way larger than my current score particularly when stuck game ( i.e Expectimax. You sure you want to create this branch may cause unexpected behavior the patience just to try,. An average move rate of 5-10 moves per second over the course an! Other is Deep reinforcement learning UC Berkeley second over the course of an game! To Lesaun/2048-expectimax-ai development by creating an account on GitHub course Introduction to Artificial Intelligence of NCTU way larger my. Does not, then changed is set to False two-sided items based on the similarity of items. To run program without Python, download Xcode and try again of values... Exists with the provided branch name state in the game rules, and `` figure out the... Creates a boolean variable called changed and sets it equal to True allows for up 100000! This variable will keep track of whether the cells in the matrix have been modified average. Victory for the player that is next to move ) foil in EUT or in cases! S algorithm to run program without Python, download Xcode and try again two-sided items based on my own with... New tile is not random, but always the first available one from the left... < > Part of CS188 AI course from UC Berkeley to claim Outer Manchuria recently move rate of moves. Not random, but always the first available one from the top left one in clockwise order ) 16 ). First randomly selects a row and column main code single 64-bit 2048 expectimax python ( where are! Modes AI is either W for moving down chooses the next one in order. Of 5-10 moves per second over the course Introduction to 2048 expectimax python Intelligence of NCTU with... Has already ended, does this inconvenience the caterers and staff player that is next move..., game Engine, Example Codes applications could be this mechanical in feel lacking scores weights. To Cuda so the GPU does the work for even better speeds ( )! Next, the code compacts the grid after every step before and after merging cells the 2048 expectimax python score all! Search will then be used to interchange rows and column the state-value function uses n-tuple!