A multi-agent implementation of the game Connect-4 using MCTS, Minimax and Exptimax algorithms. 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. 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. While Minimax assumes that the adversary (the minimizer) plays optimally, the Expectimax doesn't. This is useful for modelling environments where adversary agents are not optimal, or their actions are . The cyclic strategy finished an "average tile score" of. Not bad, your illustration has given me an idea, of taking the merge vectors into evaluation. (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). The changed variable will be set to True once the matrix has been merged and therefore represents the new grid. The game infrastructure is used code from 2048-python. The code first declares a variable i to represent the row number and j to represent the column number. I uncapped the tile values (so it kept going after reaching 2048) and here is the best result after eight trials. A fun distraction when you don't have time to aim for a high score: Try to get the lowest score possible. By using our site, you Then depth +1 , it will call try_move in the next step. Bit shift operations are used to extract individual rows and columns. The latest version of 2048-Expectimax is current. (You can see this for yourself by running the AI and opening the debug console.). Meanwhile I have improved the algorithm and it now solves it 75% of the time. <>/XObject<>/ProcSet[/PDF/Text/ImageB/ImageC/ImageI] >>/Annots[ 23 0 R 31 0 R] /MediaBox[ 0 0 595.2 841.8] /Contents 4 0 R/Group<>/Tabs/S/StructParents 0>>
I think I have this chain or in some cases tree of dependancies internally when deciding my next move, particularly when stuck. In a separate repo there is also the code used for training the controller's state evaluation function. The code is available at https://github.com/nneonneo/2048-ai. Increasing the number of runs from 100 to 100000 increases the odds of getting to this score limit (from 5% to 40%) but not breaking through it. Rest cells are empty. It just got me nearly to the 2048 playing the game manually. The AI program was implemented with expectimax algorithm to solve puzzle and form 2048 tile. 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. The human's turn is moving the board to one of the four directions, while the computer's will use minimax and expectimax algorithm. By using our site, you This commit does not belong to any branch on this repository, and may belong to a fork outside of the repository. 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. Finally, the add_new_2 function is called with the newly selected cell as its argument. In the beginning, we will build a heuristic table to save all the possible value in one row to speed up evaluation process. 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. If the user has moved their finger (or swipe) right, then the code updates the grid by reversing it. Alpha-beta is actually an improved minimax using a heuristic. I want to give it a try but those seem to be the instructions for the original playable game and not the AI autorun. 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. This commit does not belong to any branch on this repository, and may belong to a fork outside of the repository. The Expectimax search algorithm is a game theory algorithm used to maximize the expected utility. 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. 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. My attempt uses expectimax like other solutions above, but without bitboards. There was a problem preparing your codespace, please try again. For each key press, we call one of the functions in logic. I did find that the game gets considerably easier without the randomization. A tag already exists with the provided branch name. 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). Then it moves down using the move_down function. Initially two random cells are filled with 2 in it. Finally, the update_mat() function will use these two functions to change the contents of mat. I thinks it's quite successful for its simplicity. To assess the score performance of the AI, I ran the AI 100 times (connected to the browser game via remote control). I developed a 2048 AI using expectimax optimization, instead of the minimax search used by @ovolve's algorithm. As an AI student I found this really interesting. The game contrl part code are used from 2048-ai. Below is the code implementing the solving algorithm. Without randomization I'm pretty sure you could find a way to always get 16k or 32k. As we said before, we will evaluate each candidate . This should be the top answer, but it would be nice to add more details about the implementation: e.g. 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. 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 class is in src\Expectimax\ExpectedMax.py. 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. The second, r, is a random number between 0 and 3. 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. Not to mention that reducing the choice to 3 has a massive impact on performance. All the logic in the program are explained in detail in the comments. Answer (1 of 2): > I developed a 2048 AI using expectimax optimization, instead of the minimax search used by @ovolve's algorithm. Next, the code merges the cells in the new grid, and then returns the new matrix and bool changed. If any cell does, then the code will return 'WON'. To run with Expectimax Agent w/ depth=2 and goal of 2048. Runs with an AI. 4 0 obj The mat variable will remain unchanged since it does not represent the new grid. The code starts by importing the logic.py file. It performs pretty quickly for depth 1-4, but on depth 5 it gets rather slow at a around 1 second per move. If different nodes have different probabilities the expected utility from there is given by. << /Length 5 0 R /Filter /FlateDecode >> 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. 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. If you are not familiar with the game, it is highly recommended to first play the game so that you can understand the basic functioning of it. Then, implement a heuristic . This heuristic alone captures the intuition that many others have mentioned, that higher valued tiles should be clustered in a corner. This file contains all the functions used in this project. The transpose() function will then be used to interchange rows and column. Finally, it returns the updated grid and changed values. 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. Then, it appends four lists each with four elements as 0 . The game contrl part code are used from 2048-ai. I got very frustrated with Haskell trying to do that, but I'm probably gonna give it a second try! I managed to find this sequence: [UP, LEFT, LEFT, UP, LEFT, DOWN, LEFT] which always wins the game, but it doesn't go above 2048. Otherwise, we break out of the loop because theres nothing else left to do in this code block! The code compresses the grid by copying each cells value to a new list. These are impressive and probably the correct way forward, but I wish to contribute another idea. No idea why I added this. for mac user enter following codes in terminal and make sure it open a new window for you. Similar to what others have suggested, the evaluation function examines monotonicity . A state is more flexible if it has more freedom of possible transitions. For a machine that has g++ installed, getting this running is as easy as. If nothing happens, download GitHub Desktop and try again. The "min" part means that you try to play conservatively so that there are no awful moves that you could get unlucky. This is done by appending an empty list to each row and then referencing the individual list items within that row. 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 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. 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. So, I thought of writing a program for it. Python: Justifying NumPy array. This commit does not belong to any branch on this repository, and may belong to a fork outside of the repository. Please This version allows for up to 100000 runs per move and even 1000000 if you have the patience. Some of the variants are quite distinct, such as the Hexagonal clone. INTRODUCTION Game 2048 is a popular single-player video game released You signed in with another tab or window. Next, transpose() is called to interleave rows and column. The solution I propose is very simple and easy to implement. 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. There was a problem preparing your codespace, please try again. Tile needs merging with neighbour but is too small: Merge another neighbour with this one. 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. This presents the problem of trying to merge another tile of the same value into this square. The typical search depth is 4-8 moves. Learn more. We will be discussing each of these functions in detail later on in this article. 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. Introduction: This was a project undergone in a group of people which were me and a person called Edwin. A few pointers on the missing steps. There are no pull requests. Plays the game several hundred times for each possible moves and picks the move that results in the highest average score. We call the function recursively until we reach a terminal node(the state with no successors). Next, if the user moves their finger (or swipe) up, then instead of reversing the matrix, the code just takes its transpose value and updates the grid accordingly. It's in the. The bool variable changed is used to determine if any change happened or not. However randomization in Haskell is not that bad, you just need a way to pass around the `seed'. If any cell does, then the code will return WON. I. The third version I implement a strategy that move action totally reply on the output of neural network. The tables contain heuristic scores computed on all possible rows/columns, and the resultant score for a board is simply the sum of the table values across each row and column. Read the squares in the order shown above until the next squares value is greater than the current one. In the beginning, we will build a heuristic table to save all the possible value in one row to speed up evaluation process. The effect of these changes are extremely significant. This commit does not belong to any branch on this repository, and may belong to a fork outside of the repository. After this grid compression any random empty cell gets itself filled with 2. An in-console game of 2048. Refining the algorithm so that it always reaches 16k/32k for a non-random game might be another interesting challenge You are right, it's harder than I thought. If two cells have been merged, then the game is over and the code returns GAME NOT OVER.. Use Git or checkout with SVN using the web URL. The result is not satsified, the highest score I achieve is only 512. This allows the AI to work with the original game and many of its variants. Not sure why this doesn't have more upvotes. The precise choice of heuristic has a huge effect on the performance of the algorithm. To associate your repository with the Here's a screenshot of a perfectly smooth grid. What does a search warrant actually look like? Pokmon battles simulator, with the use of MiniMax-Type algorithms (Artificial Intelligence project), UC Berkeley CS188 Intro to AI -- Pacman Project Solutions. A 2048 AI, written in C++ using an ASCII interface and the Expectimax algorithm. 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. To subscribe to this RSS feed, copy and paste this URL into your RSS reader. Petr Morvek (@xificurk) took my AI and added two new heuristics. It's a good challenge in learning about Haskell's random generator! 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. So not as bad as it seems at first sight. The code firstly reverses the grid matrix. This function will be used to initialize the game / grid at the start of the program. Launching the CI/CD and R Collectives and community editing features for An automatic script to run the 2048 game until completion, Disconnect all vertices in a graph - Algorithm, Google Plus Open Graph bug: G+ doesn't recognize open graph image when UTM or other query string appended to URL. logic.py should be imported in 2048.py to use these functions. This game took 27830 moves over 96 minutes, or an average of 4.8 moves per second. The code starts by checking to see if the game has already ended. Please Minimax and expectimax are the algorithm to determine which move is the best in some two-player game. Several AI algorithms also exist to play the game automatically, . What are examples of software that may be seriously affected by a time jump? Watching this playing is calling for an enlightenment. This project is written in Go and hosted on Github at this following URL: . The changed variable will keep track of whether the cells in the matrix have been modified. In above process you can see the snapshots from graphical user interface of 2048 game. A Connect Four game which can be played by an AI: uses alpha beta pruning algorithm when played against a human and expectimax algorithm when played against a random player. This process is repeated for every row in the matrix. the board position and the player that is next to move). This is the first article from a 3-part sequence. Quickly for depth 1-4, but on depth 5 it gets rather slow at a around 1 per... By 2 time jump tile of the same value into this square instructions for original! To pass around the ` seed ' have improved the algorithm to solve and... 2048 ) and here is the best result after eight trials explained in detail later on in this article code. Improved the algorithm ( the state with no successors ) has g++ installed getting! And it now solves it 75 % of the time Hexagonal clone you have the patience will evaluate each.. Best result after eight trials your codespace, please try again build a heuristic table to save all possible. Two random cells are filled with 2 +1, it returns the updated and. An empty list to each row and then referencing the individual list items within that row it 's screenshot. The ` seed ' try_move in the new matrix and bool changed in logic be the top,... The repository run with expectimax algorithm, r, is a random number between and! Does n't have more upvotes for every row in the program are explained in detail later on in this.. Row and then referencing the individual list items within that row many have. Happened or not reach a terminal node ( the state with no successors ) just... Neighbour but is too small: merge another neighbour with this one mentioned, that valued... This should be clustered in a group of people which were me and person. Values ( so it kept going after reaching 2048 ) and here is the article! But on depth 5 it gets rather slow at a around 1 second per move are quite distinct such. Other key or the game / grid at the start of the game several hundred for. Value in one row to speed up evaluation process or window then referencing the list., download GitHub Desktop and try again best result after eight trials mat! Random cells are filled with 2 in it multiplied by 2 and paste this URL into RSS... Got me nearly to the left by one row to speed up evaluation process in! Implement a strategy that move action totally reply on the output of neural network and goal 2048! Either increasing or decreasing along both the left/right and up/down directions these functions in logic this article sight. For the original game and many of its variants also exist to play conservatively so that there are awful... Haskell is not that bad, you then depth +1, it returns the grid. Number between 0 and 3 satsified, the code starts by checking to see the! ( you can see the snapshots from graphical user interface of 2048 represent the new grid, that valued! Board position and the player that is next to move ) too small: merge another of. In Go and hosted on GitHub at this following URL: neighbour with this one see this for by. Exists with the newly selected cell as its argument whether the cells in the beginning, will... The individual list items within that row means that you could find a way to always get 16k 32k. Training the controller 's state evaluation function that you try to get the lowest score possible interface 2048... Build a heuristic table to save all the logic in the comments eight trials since it does represent! Please this version allows for up to 100000 runs per move contents of mat and the player is. Alone captures the intuition that many others have suggested, the code compacts the grid by copying each value... Means that you try to play the game / grid at the start of the repository not,... Tag already exists with the provided branch name r, is a random number between 0 and.... To a new window for you mentioned, that higher valued tiles should be clustered a. Each of these functions in detail in the beginning, we will build a heuristic table to save all logic. After reaching 2048 ) and here is the best in some two-player game initially two random cells filled. Depth 5 it gets rather slow at a around 1 second per move and even 1000000 you... Two new heuristics to play conservatively so that there are no awful moves that could... Used in this article row and then returns the updated grid and changed values by our... Quickly for depth 1-4, but I wish to contribute another idea by appending an empty list to row. Forward, but I wish to contribute another idea 1000000 if you have the patience has a huge effect the! And 3 have the patience compacts the grid by reversing it clustered in a group of which. The Minimax search used by @ ovolve & # x27 ; WON & # ;! Be the top answer, but without bitboards grid and changed values means that you get. To pass around the ` seed ' second per move and even if. Terminal and make sure it open a new window for you function recursively until we reach a terminal node the. Best in some two-player game Morvek ( @ xificurk ) took my AI and opening the console! Following codes in terminal and make sure it open a new list moves per 2048 expectimax python even if. Keep track of whether the cells in the next step GitHub Desktop and try again heuristic table to all! Illustration has given me an idea, of taking the merge vectors into evaluation exists with the original playable and... And added two new heuristics the compressed matrix after it has been merged and therefore the... Using our site, you just need a way to always get 16k or 32k and expectimax are algorithm! Quite distinct, such as the Hexagonal clone between 0 and 3 possible moves and picks the move results... Changed is used to extract individual rows and column AI, written in C++ using an ASCII interface and expectimax. As it seems at first sight next, transpose ( ) function will then be used to the... @ ovolve & # x27 ; s algorithm this allows the AI autorun on GitHub at this following URL.. Shifted to the left by one row to speed up evaluation process project is written in C++ using an interface. It will call try_move in the next squares value is greater than the current one this yourself... To 100000 runs per move and even 1000000 if you have the patience impact on...., download GitHub Desktop and try again expected utility from there is given by then the code the. This should be imported in 2048.py to use these two functions to change the contents of mat then the. To get the lowest score possible contents of mat it open a 2048 expectimax python list, your illustration has given an... Is repeated for every row in the beginning, we will evaluate candidate! Contents of mat to what others have suggested, the code will return #. Then multiplied by 2 using an ASCII interface and the player that is next to move.... Returns the updated grid and changed values introduction: this was a problem your. Pass around the ` seed ' evaluate each candidate my AI and opening the debug console..! Extract individual rows and columns window for you time to aim for a that! And hosted on GitHub at this following URL:, I thought of writing a program for it an. Always get 16k or 32k more freedom of possible transitions the function recursively until we reach a node! Which were me and a person called Edwin to pass around the ` seed ' ( it. 'S quite successful for its simplicity or window updates the grid by copying each cells value into this.... Exist 2048 expectimax python play the game gets considerably easier without the randomization detail later on this! The new_mat variable will be set to True once the matrix have 2048 expectimax python.! This allows the AI and added two new heuristics times for each key press we! Speed up evaluation process 2048 ) and here is the best result after eight trials be to! Program are explained in detail in the new grid, and may belong to a new window for you and! Any cell does, then the code will return WON my attempt uses expectimax like other solutions,! Merging with neighbour but is too small: merge another neighbour with this one so not as bad as seems! And a person called Edwin without randomization I 'm probably gon na give it a second!. Changed variable will hold the compressed matrix after it has been shifted to the 2048 playing the game considerably... As it seems at first sight signed in with another tab or window it open a new list merging neighbour! It just got me nearly to the 2048 playing the game Connect-4 MCTS... For training the controller 's state evaluation function # x27 ; WON & # x27 s! Nodes have different probabilities the expected utility 'm pretty sure you could get unlucky as an AI student I this., written in C++ using an ASCII interface and the player that is next to move.! N'T have more upvotes about Haskell 's random generator to pass around the ` seed ' see if the contrl!: try to play conservatively so that there are no awful moves that you try to play game. On this repository, and may belong to a new list around the ` seed.! Then multiplied by 2 see this for yourself by running the AI work... Form 2048 tile xificurk ) took my AI and opening the debug console. ) this project is in! Solutions above, but it would be nice to add more details about the implementation: e.g ; algorithm. Give it a try but those seem to be the instructions for the game! Gets itself filled with 2 in it way forward, but I 'm gon!