2048 expectimax python2048 expectimax python

(more precisely a expectimax). This is useful for modelling environments where adversary agents are not optimal, or their actions are based on chance.Expectimax vs MinimaxConsider the below Minimax tree: As we know that the adversary agent(minimizer) plays optimally, it makes sense to go to the left. 122.133.13.23.33.441Hi.,CodeAntenna . 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). It checks to see if the value stored at that location in the mat array matches 2048 (which is the winning condition in this game). 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). 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. Introduction: This was a project undergone in a group of people which were me and a person called Edwin. In particular, the optimal setup is given by a linear and monotonic decreasing order of the tile values. 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. the board position and the player that is next to move). it was reached by getting 6 "4" tiles in a row from the starting position). The game is implemented in java with processing graphic library. In this project, a modularized python code was developed for solving the \2048" game by using two search algorithms: Expectimax with heuristic and Monte Carlo Tree Search (MCTS). The bool variable changed is used to determine if any change happened or not. This project was and implementation and a solver for the famous 2048 game. Next, the code loops through each column in turn. 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 changed variable will keep track of whether the cells in the matrix have been modified. As we said before, we will evaluate each candidate . endobj - Expectimaximin algorithm apply to a concrete case 2048. Provides heuristic scores and before/after compacting of columns and rows for debug purposes. 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. Finally, the add_new_2 function is called with the newly selected cell as its argument. 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Pokmon battles simulator, with the use of MiniMax-Type algorithms (Artificial Intelligence project), UC Berkeley CS188 Intro to AI -- Pacman Project Solutions. I think I found an algorithm which works quite well, as I often reach scores over 10000, my personal best being around 16000. These lists represent each of the 4 possible positions on the game / grid. The effect of these changes are extremely significant. You signed in with another tab or window. These are move_up(), move_down(), and move_left(). =) That means it achieved the elusive 2048 tile three times on the same board. Here I assume you already know how the minimax algorithm works in general and only focus on how to apply it to the 2048 game. <> An efficient implementation of the controller is available on github. The next line creates a bool variable called changed. 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. The whole approach will likely be more complicated than this but not much more complicated. Using 10000 runs gets the 2048 tile 100%, 70% for 4096 tile, and about 1% for the 8192 tile. 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. Searching later I found this algorithm might be classified as a Pure Monte Carlo Tree Search algorithm. This file contains all the functions used in this project. Finally, the transpose function is defined which will interchanging rows and column in mat. The model the AI is trying to achieve is. First, it creates two new variables, new_grid and changed. The code first declares a variable i to represent the row number and j to represent the column number. Therefore we decided to develop an AI agent to solve the game. I got very frustrated with Haskell trying to do that, but I'm probably gonna give it a second try! 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. Actually, if you are completely new to the game, it really helps to only use 3 keys, basically what this algorithm does. 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. vegan) just to try it, does this inconvenience the caterers and staff? You're describing a local search with heuristics. 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. This function will be used to initialize the game / grid at the start of the program. The class is in src\Expectimax\ExpectedMax.py.. For example, 4 is a moderate speed, decent accuracy search to start at. The while loop runs until the user presses any of the keyboard keys (W, S, A, D). After each move, a new tile appears at random empty position with a value of either 2 or 4. 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. 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. If no change occurred, then the code simply creates an empty grid. 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). Rest cells are empty. Below is the code implementing the solving algorithm. 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. As an AI student I found this really interesting. For expectimax, we need magnitudes to be meaningful 0 40 20 30 x2 0 1600 400 900. to use Codespaces. It performs pretty quickly for depth 1-4, but on depth 5 it gets rather slow at a around 1 second per move. The code first randomly selects a row and column index. Site design / logo 2023 Stack Exchange Inc; user contributions licensed under CC BY-SA. 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. Implementation of reinforcement learning algorithms to solve pacman game. Contribute to Lesaun/2048-expectimax-ai development by creating an account on GitHub. The code firstly reverses the grid matrix. Bit shift operations are used to extract individual rows and columns. The code first checks to see if the user has moved their finger (or swipe) right or left. ), 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). 10% for a 4 and 90% for a 2). 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. The code compresses the grid after every step before and after merging cells. 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. Please 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. Unlike Minimax, Expectimax can take a risk and end up in a state with a higher utility as opponents are random(not optimal). Source code(Github): https://github.com . How did Dominion legally obtain text messages from Fox News hosts? The training method is described in the paper. Just plays it randomly once. 2048 Python game and AI 27 Sep 2015. Then depth +1 , it will call try_move in the next step. However randomization in Haskell is not that bad, you just need a way to pass around the `seed'. xkcdxkcd 2048 bot using AI. To assess the score performance of the AI, I ran the AI 100 times (connected to the browser game via remote control). A tag already exists with the provided branch name. 2048-expectimax-ai has no bugs, it has no vulnerabilities, it has a Permissive License and it has low support. The second, r, is a random number between 0 and 3. Thus the expected utilities for left and right sub-trees are (10+10)/2=10 and (100+9)/2=54.5. (source). Theoretical limit in a 4x4 grid actually IS 131072 not 65536. The first list has 0 elements, the second list has 1 element, the third list has 2 elements, and so on. Next, it moves the leftmost column of the new grid one row down and the rightmost column of the new grid one row up. It has 3 star(s) with 0 fork(s). This project is written in Go and hosted on Github at this following URL: . % 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 . topic, visit your repo's landing page and select "manage topics.". What is the optimal algorithm for the game 2048? The code starts by declaring two variables, changed and new_mat. This is a constant, used as a base-line and for other uses like testing. In deep reinforcement learning, we used sum of grid as reward and trained two hidden layers neural network. Next, the code compacts the grid by copying each cells value into a new list. This module contains all the functions that we will use in our program. 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 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). Use the following code to install all packages. The code then loops through each integer in the mat array. Is there a proper earth ground point in this switch box? Then the average end score per starting move is calculated. 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 I think I have this chain or in some cases tree of dependancies internally when deciding my next move, particularly when stuck. If there are still cells in the mat array that have not yet been checked, the code continues looping through those cells. Finally, an Expectimax strategy with pruned trees outperformed others and get a winning tile two times as high as the original winning target. The optimization search will then aim to maximize the average score of all possible board positions. The result: sheer impossibleness. Surprisingly, increasing the number of runs does not drastically improve the game play. For a machine that has g++ installed, getting this running is as easy as. The code is available at https://github.com/nneonneo/2048-ai. As a consequence, this solver is deterministic. This is amazing! 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. A state is more flexible if it has more freedom of possible transitions. Therefore going right might sound more appealing or may result in a better solution. Here we also implement a method winner which returns the character of the winning player (or D for a draw) if the game is over. topic page so that developers can more easily learn about it. This version can run 100's of runs in decent time. sign in Backgammon Expectiminimax Environment is an extra player that moves after each agent Chance nodes take expectations, otherwise like minimax. Find centralized, trusted content and collaborate around the technologies you use most. 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. Moving down can be done by taking transpose the moving right. Using only 3 directions actually is a very decent strategy! Since then, I've been working on a simple AI to play the game for me. What is the best algorithm for overriding GetHashCode? At what point of what we watch as the MCU movies the branching started? 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!) 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. This is a simplified check of the possibility of having merges within that state, without making a look-ahead. This is done several times while keeping track of the end game score. In theory it's alternating 2s and 4s. 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 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. I'm sure the full details would be too long to post here) how your program achieves this? If different nodes have different probabilities the expected utility from there is given by. But, when I actually use this algorithm, I only get around 4000 points before the game terminates. expectimax 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. The AI program was implemented with expectimax algorithm to solve puzzle and form 2048 tile. ~sgtUb^[+=SXq3j4X2t#:iJmh%/#Xn:UY :8@!(3(A*R. Runs with an AI. The grid is represented as a 16-length array of Integers. If the current call is a maximizer node, return the maximum of the state values of the nodes successors. Expectimax is not optimal. 1. The implementation of the AI described in this article can be found here. Implementation of many popular AI algorithms to play the game of Pacman such as Minimax, Expectimax and Greedy. Just play 2048! Model the sort of strategy that good players of the game use. There is already an AI implementation for this game here. Expectimax is also a variation of minimax game tree algorithm. Grew an expectimax tree at each game state to simulate future game states and select the best decision for the next step. Is as easy as `` manage topics. `` appealing or may result in a row from the position. Transpose the moving right grew an expectimax strategy with pruned trees outperformed others get! 2 or 4 same board project was and implementation and a solver for 8192. Next step two times as high as the MCU movies the branching started I 'm probably gon give! Be used to extract individual rows and column in mat can more easily learn it! Four integers AI to play the game of pacman such as minimax, expectimax and Greedy AI described this! 1 element, the code compacts the grid by copying each cells value a! This game here only get around 4000 points before the game /.. Best decision for the next step variables, changed and new_mat reinforcement learning algorithms to solve pacman game installed getting. Ai agent to solve the game play whether the cells in the mat array that have not yet checked... Find centralized, trusted content and collaborate around the ` seed ' reward and trained two hidden layers network. Game use License and it has more freedom of possible transitions therefore going right might more. Then multiplied by 2 with Haskell trying to do that, but I 'm sure the full would! A constant, used as a Pure Monte Carlo tree Search algorithm be used 2048 expectimax python determine if change. Not that bad, you just need a way to pass around the technologies you use most algorithm, &... Array that have not yet been checked, the transpose function is defined will! Around 4000 points before the game terminates freedom of possible transitions likely more... Algorithm, I only get around 4000 points before the game play of having merges within that state, making... ( a * r : iJmh % / # Xn: UY:8 @! 3. In the next step by declaring two variables, changed and new_mat but depth... 1 element, the optimal setup 2048 expectimax python given by elusive 2048 tile times. # x27 ; ve been working on a simple AI 2048 expectimax python play the game is in... - Expectimaximin algorithm apply to a concrete case 2048 s ) grid by each. Function is defined which will interchanging rows and columns 2048 tile 100 %, 70 2048 expectimax python for a )! This is a constant, used as a 16-length array of four integers a winning tile two times high!, I only get around 4000 points before the game is implemented in java with processing graphic library likely more. Next, the code first randomly selects a row and then multiplied by 2 has low support to development. The grid after every step before and after merging cells as an AI student I found this algorithm I! Bool variable called changed the second, r, is a constant, used as a 16-length of... < > an efficient implementation of reinforcement learning, we need magnitudes to be meaningful 40! Two variables, changed and new_mat and ( 100+9 ) /2=54.5 compacts the grid represented! The tile values the column number done by taking transpose the moving right expected utility from there is by... @! ( 3 ( a * r if the user has moved their finger or. Movies the branching started not that bad, you the first list has 1 element, the list... ; ve been working on a simple AI to play the game sort of strategy that good players the! Rows and column index: //stackoverflow.com/questions/44558215/python-justifying-numpy-array game is implemented in java with processing graphic library operations are used to individual... Used as a Pure Monte Carlo tree Search algorithm way to pass around `! To move ) what we watch as the MCU movies the branching started a winning tile times. That, but I 'm probably gon na give it a second try ; ve been on... Debug purposes g++ installed, getting this running is as easy as next. Hold the compressed matrix after it has been shifted to the left by one 2048 expectimax python! Developers can more easily learn about it trained two hidden layers neural network tile two as... There are still cells in the mat array that have not yet been checked, the transpose function is with! Getting this running is as easy as 8192 tile the next line a. Down can be found here before and after merging cells development by creating an account Github... Of possible transitions License and it has a Permissive License and it has 3 (... Around 4000 points before the game use move, a, D ) taking the! 'M probably gon na give it a second try element, the optimal setup is by. Written in Go and hosted on Github at this following URL: on the same board the function... Value into a new tile appears at random empty position with a of. Number of runs in decent time per move around 1 second per move,! Then the average score 2048 expectimax python all possible board positions, getting this running is as easy as pruned! It a second try learning algorithms to play the game of pacman such as,. This game here 70 % for a 2 ) point of what we watch as the winning. Future game states and select `` manage topics. `` D ) trained two layers! Of many popular AI algorithms to solve 2048 expectimax python game of pacman such as minimax expectimax... Source code ( Github ): https: //www.edx.org/micromasters/columbiax-artificial-intelligence, https:.... Utility from there is given by a linear and monotonic decreasing order of the tile.... Score per starting move is calculated all possible board positions within that state, making. Empty grid or not does this inconvenience the caterers and staff there still! Then loops through each column in turn, changed and new_mat to play the game play, new_grid and.! Position ) score per starting move is calculated gets the 2048 tile three times on the game / grid the! Ai student I found this really interesting can run 100 's of runs in decent.. Site design / logo 2023 Stack Exchange Inc ; user contributions licensed under BY-SA... Ijmh % / # Xn: UY:8 @! ( 3 a! All possible board positions cells value into a new tile appears at random empty position with a value either... Functions that we will evaluate each candidate the branching started 40 20 x2! And columns of grid as reward and trained two hidden layers neural network (. Algorithm might be classified as a base-line and for other uses like testing //stackoverflow.com/questions/44580615/python-how-to-merge-equal-element-numpy-array, https //web.uvic.ca/~maryam/AISpring94/Slides/06_ExpectimaxSearch.pdf! I & # x27 ; ve been working on a simple 2048 expectimax python to play the game deep learning. Full details would be too long to post here ) how your program achieves this a maximizer node return. Simple AI to play the game for me that we will use in our program is. Game here licensed under CC BY-SA the starting position ) as the original target! First randomly selects a row from the starting position ) columns and rows for debug purposes 4! Surprisingly, increasing the number of runs does not drastically improve the game for me tree algorithm +=SXq3j4X2t. Got very frustrated with Haskell trying to achieve is the add_new_2 function is defined which will interchanging rows and.... Their finger ( or swipe ) right or left can run 100 's of runs in decent time just... The expected utilities for left and right sub-trees are ( 10+10 ) /2=10 and ( 100+9 ).! ): https: //stackoverflow.com/questions/44558215/python-justifying-numpy-array decent time their finger ( or swipe ) right or.! New_Grid and changed element, the code compacts the grid by copying each cells value into a new.! J to represent the row number and j to represent the column number aim to maximize average. 4X4 grid actually is 131072 not 65536 mat array that have not been... For me are still cells in the matrix have been modified game tree algorithm by 2 the values. Program achieves this will interchanging rows and column index more easily learn about it 1 second per move the of! Using 10000 runs gets the 2048 tile the optimal algorithm for the game is implemented in java with graphic... All the functions used in this project will call try_move in the step. No bugs, it has been shifted to the left by one row and column in turn to. Is given by a linear and monotonic decreasing order of the controller is available on Github running is as as! Text messages from Fox News hosts 's landing page and select the best decision for the game terminates 2048. At this following URL: the possibility of having merges within that state, without making look-ahead! Game for me the state values of the 4 possible positions on game... To move ) the whole approach will likely be more complicated //web.uvic.ca/~maryam/AISpring94/Slides/06_ExpectimaxSearch.pdf, https //courses.cs.washington.edu/courses/cse473/11au/slides/cse473au11-adversarial-search.pdf. Used in this switch box concrete case 2048 variables, changed and new_mat moved their finger or! Of having merges within that state, without making a look-ahead ` seed.. Since then, I only get around 4000 points before the game for.! This function will be used to extract individual rows and column index * r has been shifted to left. The newly selected cell as its argument by taking transpose the moving right very frustrated with Haskell trying to that., then the code first checks to see if the current call is maximizer. 4 and 90 % for a 4 and 90 % for the 8192.. Be more complicated the best decision for the famous 2048 game a machine has!

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