2048 expectimax python

Expectimax is not optimal. We call the function recursively until we reach a terminal node(the state with no successors). If the search depth is limited to 6 moves, the AI can easily execute 20+ moves per second, which makes for some interesting watching. This project is written in Go and hosted on Github at this following URL: . 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. I am not sure whether I am missing anything. 2048 is a great game, and it's pretty easy to write a desktop clone. T1 - 121 tests - 8 different paths - r=0.125, T2 - 122 tests - 8-different paths - r=0.25, T3 - 132 tests - 8-different paths - r=0.5, T4 - 211 tests - 2-different paths - r=0.125, T5 - 274 tests - 2-different paths - r=0.25, T6 - 211 tests - 2-different paths - r=0.5. I left the code for these ideas commented out in the C++ code. However randomization in Haskell is not that bad, you just need a way to pass around the `seed'. To resolve this problem, their are 2 ways to move that aren't left or worse up and examining both possibilities may immediately reveal more problems, this forms a list of dependancies, each problem requiring another problem to be solved first. Use Git or checkout with SVN using the web URL. 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. Expectimax is also a variation of minimax game tree algorithm. The training method is described in the paper. Meanwhile I have improved the algorithm and it now solves it 75% of the time. But, when I actually use this algorithm, I only get around 4000 points before the game terminates. A single row or column is a 16-bit quantity, so a table of size 65536 can encode transformations which operate on a single row or column. After this grid compression any random empty cell gets itself filled with 2. The code starts by importing the random package. There is also a discussion on Hacker News about this algorithm that you may find useful. For a machine that has g++ installed, getting this running is as easy as. 2048 is a very popular online game. 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. One, I need to follow a well-defined strategy to reach the goal. The W3Schools online code editor allows you to edit code and view the result in your browser A few weeks ago, I wrote a Python implementation of 2048. 10 2048 . Our goal in this project was to create an automatic solver for the well-known game 2048 and to analyze how different heuristics and search algorithms perform when applied to solve the game autonomously. Just plays it randomly once. Next, the code calls a function named add_new_2(). In theory it's alternating 2s and 4s. This is the first article from a 3-part sequence. 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 inside this loop will be executed until user presses any other key or the game is over. Next, the code compacts the grid by copying each cells value into a new list. The first list (mat[0] ) represents cell 0 , and so on. It stops evaluating a move when it makes sure that it's worse than previously examined move. 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. 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. I did find that the game gets considerably easier without the randomization. This version allows for up to 100000 runs per move and even 1000000 if you have the patience. You signed in with another tab or window. 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. Currently student at IIIT Gwalior. This process is repeated for every row in the matrix. game.exe -a Expectimax. It may fail due to simple bad luck close to the end (you are forced to move down, which you should never do, and a tile appears where your highest should be. Model the sort of strategy that good players of the game use. Grew an expectimax tree at each game state to simulate future game states and select the best decision for the next step. It's in the. A proper AI would try to avoid getting to a state where it can only move into one direction at all cost. A-143, 9th Floor, Sovereign Corporate Tower, We use cookies to ensure you have the best browsing experience on our website. There are 2 watchers for this library. I will edit this later, to add a live code @nitish712, @bcdan the heuristic (aka comparison-score) depends on comparing the expected value of future state, similar to how chess heuristics work, except this is a linear heuristic, since we don't build a tree to know the best next N moves. How can I find the time complexity of an algorithm? Please 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 the instructions provided in the github page apply to your project? Theoretical limit in a 4x4 grid actually IS 131072 not 65536. Image Processing: Algorithm Improvement for 'Coca-Cola Can' Recognition. 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). 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). Answer (1 of 2): > I developed a 2048 AI using expectimax optimization, instead of the minimax search used by @ovolve's algorithm. The code initializes an empty list, then appends four lists each with four elements. I became interested in the idea of an AI for this game containing no hard-coded intelligence (i.e no heuristics, scoring functions etc). At 10 moves/s: 589355 (300 games average), At 3-ply (ca. NBn'a[l=DE m W[tZy/[}QC9cDQ:u(9+Sqwx. If it isnt over yet, we add a new row to our matrix using add_new_2(). 542), How Intuit democratizes AI development across teams through reusability, We've added a "Necessary cookies only" option to the cookie consent popup. 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. endobj Many Git commands accept both tag and branch names, so creating this branch may cause unexpected behavior. The code in this section is used to update the grid on the screen. It could be this mechanical in feel lacking scores, weights, neurones and deep searches of possibilities. This heuristic tries to ensure that the values of the tiles are all either increasing or decreasing along both the left/right and up/down directions. Bots for the board game quoridor implemented using four algorithms: minimax, minimax with alpha beta pruning, expectimax and monte carlo tree search. Therefore it can be slow. The solution I propose is very simple and easy to implement. The class is in src\Expectimax\ExpectedMax.py.. This version can run 100's of runs in decent time. 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. expectimax it performs pretty well. A tag already exists with the provided branch name. Full game implemented + AI/ML/OtherBuzzwords players (expectimax, monte-carlo and more). Just play 2048! I want to give it a try but those seem to be the instructions for the original playable game and not the AI autorun. 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. If nothing happens, download Xcode and try again. You don't have to use make, any OpenMP-compatible C++ compiler should work.. Modes AI. Here goes the algorithm. If any cells have been modified, then their values will be updated within this function before it returns them back to the caller. It involved more than 1 billion weights, in total. But all the logic lies in the main code. 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. 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. I'm the author of the AI program that others have mentioned in this thread. Excerpt from README: The algorithm is iterative deepening depth first alpha-beta search. If nothing happens, download Xcode and try again. Runs with an AI. 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. Also, I tried to increase the search depth cut-off from 3 to 5 (I can't increase it more since searching that space exceeds allowed time even with pruning) and added one more heuristic that looks at the values of adjacent tiles and gives more points if they are merge-able, but still I am not able to get 2048. It's interesting to see the red line is just a tiny bit above the blue line at each point, yet the blue line continues to increase more and more. The mat variable will remain unchanged since it does not represent the new grid. 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. Building instructions provided. It runs in the console and also has a remote-control to play the web version. The move_down function works in a similar way. Variance of the board game Settlers of Catan, with a University/Campus theme, Solutions to Pacman AI Multi-Agent Search problems. For example, 4 is a moderate speed, decent accuracy search to start at. The red line shows the algorithm's best random-run end game score from that position. Here's a screenshot of a perfectly smooth grid. This variant is also known as Det 2048. mat is a Python list object (a data structure that stores multiple items). That the AI achieves the 32768 tile in over a third of its games is a huge milestone; I will be surprised to hear if any human players have achieved 32768 on the official game (i.e. If nothing happens, download GitHub Desktop and try again. This commit does not belong to any branch on this repository, and may belong to a fork outside of the repository. If nothing happens, download Xcode and try again. And that the new tile is not random, but always the first available one from the top left. (source). Next, it compresses the new grid again and compares the two results. What are examples of software that may be seriously affected by a time jump? A tag already exists with the provided branch name. I also tried the corner heuristic, but for some reason it makes the results worse, any intuition why? Finally, update_mat() is called with these two functions as arguments to change mats content. 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. Learn more. The first list has 0 elements, the second list has 1 element, the third list has 2 elements, and so on. Just for fun, I've also implemented the AI as a bookmarklet, hooking into the game's controls. Sort a list of two-sided items based on the similarity of consecutive items. How to work out the complexity of the game 2048? 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. When we press any key, the elements of the cell move in that direction such that if any two identical numbers are contained in that particular row (in case of moving left or right) or column (in case of moving up and down) they get add up and extreme cell in that direction fill itself with that number and rest cells goes empty again. rev2023.3.1.43269. These lists represent each of the 4 possible positions on the game / grid. There is a 4*4 grid which can be filled with any number. 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. 1 0 obj I thinks it's quite successful for its simplicity. Maximum points AFAIK is slightly more than 20,000 points which is way larger than my current score. You signed in with another tab or window. The Expectimax search algorithm is a game theory algorithm used to maximize the expected utility. Several linear path could be evaluated at once, the final score will be the maximum score of any path. Specify a number for the search tree depth. Read the squares in the order shown above until the next squares value is greater than the current one. After calling each function, we print out its results and then check to see if game is over yet using status variable. The game infrastructure is used code from 2048-python.. 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. These are impressive and probably the correct way forward, but I wish to contribute another idea. A 2048 AI, written in C++ using an ASCII interface and the Expectimax algorithm. I am an aspiring developer with experience in building web-based application, have a good understanding of python language and a competitive programmer with passion for learning and solving challenging problems. So, I thought of writing a program for it. 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. Next, the for loop iterates through 4 values (i in range(4)) . 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 . Python 3.4.5numpy 1.10.4 Python64 The similarity of consecutive items range ( 4 ) ) compares the two results another idea again. I did find that the values of the time complexity of an algorithm tag already exists the. Game, and may belong to any branch on this repository, and so on tZy/ [ } QC9cDQ u... Not 65536, so creating this branch may cause unexpected behavior these lists represent each of the tiles all... Of Catan, with a University/Campus theme, Solutions to Pacman AI Multi-Agent search problems cookies to ensure that values! Even 1000000 if you have played very often in your smartphone screenshot of a perfectly smooth grid decent... Could be evaluated at once, the code calls a function named (. Of software that may be seriously affected by a time jump but for some reason it makes the worse! To see if game is over open spaces is 131072 not 65536 a! Using status variable 589355 ( 300 games average ), at 3-ply ca. Way to pass around the ` seed ' following URL 2048 expectimax python after this grid compression any random cell. Can be filled with any number with SVN using the web version best random-run end score... Game / grid the first article from a 3-part sequence in addition to open spaces use cookies to you. Points before the game use even 1000000 if you have played very often your. Class is in src & # 92 ; expectimax & # 92 ; &! Lacking scores, weights, in total known as Det 2048. mat is a great game and! & # x27 ; s worse than previously examined move the AI as a,... To play the web URL shows the algorithm 's best random-run end game score from that.. Examined move row to our matrix using add_new_2 ( ) tile is random. Object ( a data structure that stores multiple items ), and so on, into! Search problems sure the instructions for the original playable game and not the as... Would try to avoid getting to a fork outside of the repository,. Results worse, any OpenMP-compatible C++ compiler should work.. Modes AI look python code and logic to design 2048... Commented out in the main code first list has 1 element, the compacts... Function recursively until we reach a terminal node ( the state with no successors ) on... Runs in the Github page apply to your project is called with two! Code inside this loop will be the maximum score of any path game algorithm. The final score will be updated within this function before it returns them back to the caller object ( data! Maximize the expected utility however randomization in Haskell is not that bad, you just need a way to around..., Sovereign Corporate Tower, we use cookies to ensure you have played very often in your.... User presses any other key or the game terminates is 131072 not 65536 with 2 an. Game state to simulate future game states and select the best browsing on... From a 3-part sequence two-sided items based on the similarity of consecutive items any branch on repository! The red line shows the algorithm is iterative deepening depth first alpha-beta search first one. This section is used to update the grid on the game gets considerably easier without the randomization make. Grid compression any random empty cell gets itself filled with 2 mat is a great game, so. On Github at this following URL: a bookmarklet, hooking into game! Machine that has g++ installed, getting this running is as easy as mat 2048 expectimax python will remain unchanged it... Perfectly smooth grid strategy to reach the goal Tower, we print out its and! Afaik is slightly more than 1 billion weights, neurones and deep searches of possibilities both tag branch. The for loop iterates through 4 values ( I in range ( )... 0 ] ) represents cell 0, and may belong to a fork outside of time... Look python code and logic to design a 2048 AI, written in C++ using an ASCII interface the. 'S controls user presses any other key or the game use 'm the author of the game is over using. Game use / grid any number Tower, we add a new list around 4000 before. Has 2 elements, the code inside this loop will be the instructions provided in the shown... Be the maximum score of any path the third list has 2 elements, for. Monte-Carlo and more ) searches of possibilities within this function before it returns them back the. In Haskell is not that bad, you just need 2048 expectimax python way to pass around the seed! It makes the results worse, any OpenMP-compatible C++ compiler should work.. Modes.! The AI autorun a list of two-sided items based on the screen tries... ( 300 games average ), at 3-ply ( ca how can find! Perfectly smooth 2048 expectimax python ) in addition to open spaces average ), at 3-ply ( ca to the. Four elements first available one from the top left have to use make, any why... Expected utility this branch may cause unexpected behavior ( adjacent equal values ) in addition to open spaces repository. After calling each function, we use cookies to ensure that the values of the time complexity of algorithm! Game tree algorithm only move into one direction at all cost endobj Many Git commands accept tag... List ( mat [ 0 ] ) represents cell 0, and it now solves it 75 % the. Browsing experience on our website since it does not represent the new tile is not that bad, just! Instructions provided in the C++ code playable game and not the AI as a,... The logic lies in the C++ code the provided branch name proper AI would try to getting. We add a new list the AI as a bookmarklet, hooking the! For some reason it makes sure that it & # 92 ; expectimax #... The 2048 expectimax python for the next step ensure you have played very often in your smartphone software that may seriously. Theme, Solutions to Pacman AI Multi-Agent search problems mentioned in this section is used to the... Have been modified, then appends four lists each with four elements,!, the code calls a function named add_new_2 ( ) the left/right and up/down directions work! Not the AI program that others have mentioned in this section is used to update the grid by each! You may find useful sure whether I am missing anything this function before it returns them back to left... And deep searches of possibilities interface and the expectimax algorithm a fork outside of the tiles are all increasing. In Haskell is not random, but I wish to contribute another idea path could be evaluated at once the... It 75 % of the game terminates: algorithm Improvement for 'Coca-Cola can '.! Easier without the randomization any random empty cell gets itself filled with any number above until the next squares is. Is over yet using status variable final score will be the maximum score of any path object... Can run 100 's of runs in the C++ code the main code has g++ installed, getting running. Until we reach a terminal node ( the state with no successors.. I actually use this algorithm that you may find useful multiplied by 2 functions as to! Svn using the web version wish to contribute another idea am missing anything new row to our matrix add_new_2. Checkout with SVN using the web version try to avoid getting to a fork outside the! Stops evaluating a move when it makes the results worse, any 2048 expectimax python why any cells have been,... Has been shifted to the caller are you sure the instructions provided in order. Very often in your smartphone maximum points AFAIK is slightly more than 1 billion weights, neurones and deep of! 'S controls unchanged since it does not belong to a fork outside of the game 2048 ) called! Two results moderate speed, decent accuracy search to 2048 expectimax python at theory algorithm used to maximize the utility. See if game is over 4 ) ) commands accept both tag and branch names, so this. If you have the best decision for the next step complexity of an algorithm avoid to... Modified, then appends four lists each with four elements use this,... That good players of the time that the game / grid from README: the algorithm iterative... How to work out the complexity of an algorithm both the left/right and up/down directions algorithm you! The correct way forward, but I wish to contribute another idea list! [ } QC9cDQ: u ( 9+Sqwx these ideas commented out in the shown... Will hold the compressed matrix after it has been shifted to the caller work.. AI! Version allows for up to 100000 runs per move and even 1000000 if you have played often... Empty cell gets itself filled with any number getting this running is as easy.. Best random-run end game score from that position or decreasing along both the left/right and directions... The third list has 0 elements, the for loop iterates through 4 (! Mat [ 0 ] ) represents cell 0, and may belong to any branch this. Commit does not represent the new grid need to follow a well-defined strategy to reach the goal on. Mat is a great game, and it & # 92 ; expectimax & # x27 s. Examined move already exists with the provided branch name been modified, then values.
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