search trees strategies (Minimax, Expectimax) and an attempt on reinforcement learning to achieve higher scores. Finally, the update_mat() function will use these two functions to change the contents of mat. Could you update those? The human's turn is moving the board to one of the four directions, while the computer's will use minimax and expectimax algorithm. Expectimax Algorithm. The result: sheer impossibleness. By far, the most interesting solution here. rev2023.3.1.43269. Next, the start_game() function is declared. Watching this playing is calling for an enlightenment. 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. A 2048 AI, written in C++ using an ASCII interface and the Expectimax algorithm. A rust implementation of the famous 2048 game. A-143, 9th Floor, Sovereign Corporate Tower, We use cookies to ensure you have the best browsing experience on our website. (You can see this for yourself by running the AI and opening the debug console.). Finally, both original grids and transposed matrices are returned. I developed a 2048 AI using expectimax optimization, instead of the minimax search used by @ovolve's algorithm. The first list has 0 elements, the second list has 1 element, the third list has 2 elements, and so on. Open the console for extra info. However randomization in Haskell is not that bad, you just need a way to pass around the `seed'. Contribute to Lesaun/2048-expectimax-ai development by creating an account on GitHub. The code first checks to see if the user has moved their finger (or swipe) right or left. Besides the online version the game is available to use Codespaces. If it has not, then the code checks to see if any cells have been merged. 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. I believe there's still room for improvement on the heuristics. stream 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. View the heuristic score of any possible board state. Model the sort of strategy that good players of the game use. In our work we compare the Alpha-Beta pruning and Expectimax algorithms as well as different heuristics and see how they perform in . 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. Several AI algorithms also exist to play the game automatically, . The code starts by creating two new variables, new_grid and changed. Then it calls the reverse() function to reverse the matrix. This variant is also known as Det 2048. 1500 moves/s): 511759 (1000 games average). The code begins by compressing the grid, which will result in a smaller grid. 2048 bot using AI. A multi-agent implementation of the game Connect-4 using MCTS, Minimax and Exptimax algorithms. Then it moves down using the move_down function. Initially two random cells are filled with 2 in it. In ExpectiMax strategy, we tried 4 different heuristic functions and combined them to improve the performance of this method. Final project of the course Introduction to Artificial Intelligence of NCTU. This is in contrast to most AIs (like the ones in this thread) where the game play is essentially brute force steered by a scoring function representing human understanding of the game. The levels of the tree . If you watch it run, it will often make surprising but effective moves, like suddenly switching which wall or corner it's building up against. The code uses expectimax search to evaluate each move, and chooses the move that maximizes the search as the next move to execute. Includes an expectimax strategy that reaches 16384 with 34.6% success and an ML model trained with temporal difference learning. I also tried the corner heuristic, but for some reason it makes the results worse, any intuition why? It performs pretty quickly for depth 1-4, but on depth 5 it gets rather slow at a around 1 second per move. In testing, the AI achieves an average move rate of 5-10 moves per second over the course of an entire game. game.exe -a Expectimax. If nothing happens, download GitHub Desktop and try again. 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. For example, 4 is a moderate speed, decent accuracy search to start at. topic, visit your repo's landing page and select "manage topics.". 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. Finally, the code compresses this merged cell again to create a smaller grid once again. This version allows for up to 100000 runs per move and even 1000000 if you have the patience. To run program without Python, download dist/game/ and run game.exe. Next, the code loops through each column in turn. But, when I actually use this algorithm, I only get around 4000 points before the game terminates. the entire board filled with 4 .. 65536 each once - 15 fields occupied) and the board has to be set up at that moment so that you actually can combine. @ashu I'm working on it, unexpected circumstances have left me without time to finish it. 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). Stochastic Two-Player This intuition will give you also the upper bound for a tile value: where n is the number of tile on the board. https://www.edx.org/micromasters/columbiax-artificial-intelligence (knowledge), https://courses.cs.washington.edu/courses/cse473/11au/slides/cse473au11-adversarial-search.pdf (more knowledge), https://web.uvic.ca/~maryam/AISpring94/Slides/06_ExpectimaxSearch.pdf (even more knowledge! vegan) just to try it, does this inconvenience the caterers and staff? Not bad, your illustration has given me an idea, of taking the merge vectors into evaluation. The code first randomly selects a row and column index. This file contains all the functions used in this project. It's really effective for it's simplicity. This variable will track whether any changes have occurred since the last time compress() was called. Learn more. 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. Next, it updates the grid matrix based on the inputted direction. In a separate repo there is also the code used for training the controller's state evaluation function. The tiles tend to stack in incompatible ways if they are not shifted in multiple directions. If you combine this with other strategies for deciding between the 3 remaining moves it could be very powerful. This is a simplified check of the possibility of having merges within that state, without making a look-ahead. There is no type of pruning that can be done, as the value of a single unexplored utility can change the expectimax value drastically. stream
We have two python files below, one is 2048.py which contains main driver code and the other is logic.py which contains all functions used. In deep reinforcement learning, we used sum of grid as reward and trained two hidden layers neural network. run python 2048.py; Game Infrastructure. The solution I propose is very simple and easy to implement. Such moves need not to be evaluated further. Thanks. Unlike Minimax, Expectimax can take a risk and end up in a state with a higher utility as opponents are random(not optimal). Fork me! For each cell that has not yet been checked, it checks to see if its value matches 2048. There is also a discussion on Hacker News about this algorithm that you may find useful. It is very easy but hard to achieve its goal. 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. A simplified version of Go game in Python, with AI agents built-in and GUI to play. For example, 4 is a moderate speed, decent accuracy search to start at. A few weeks ago, I wrote a Python implementation of 2048. This one will consist of planning our game-playing program at a conceptual level, and in the next 2 articles, we'll see the actual Python implementation. At what point of what we watch as the MCU movies the branching started? The result it reaches when starting with an empty grid and solving at depth 5 is: Source code can be found here: https://github.com/popovitsj/2048-haskell. Abstract. Runs with an AI. My solution does not aim at keeping biggest numbers in a corner, but to keep it in the top row. Runs with an AI. However, my expectimax algorithm performs maximization correctly but when it hits the expectation loop where it should be simulating all of the possible tile spawns for a move (90% 2, 10% 4) - it does not seem to function as . For example, moves are implemented as 4 lookups into a precomputed "move effect table" which describes how each move affects a single row or column (for example, the "move right" table contains the entry "1122 -> 0023" describing how the row [2,2,4,4] becomes the row [0,0,4,8] when moved to the right). If it does not, then the code declares victory for the player and ends the program execution. There was a problem preparing your codespace, please try again. If nothing happens, download Xcode and try again. Expectimax Search In expectimax search, we have a probabilistic model of how the opponent (or environment) will behave in any state Model could be a simple uniform distribution (roll a die) Model could be sophisticated and require a great deal of computationrequire a great deal of computation We have a node for every outcome Introduction: This was a project undergone in a group of people which were me and a person called Edwin. 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. Just plays it randomly once. The AI simply performs maximization over all possible moves, followed by expectation over all possible tile spawns (weighted by the probability of the tiles, i.e. We will be discussing each of these functions in detail later on in this article. Introduction. There was a problem preparing your codespace, please try again. topic page so that developers can more easily learn about it. You can try the AI for yourself. Obviously a more This is necessary in order to move right or up. Maximum points AFAIK is slightly more than 20,000 points which is way larger than my current score. A tag already exists with the provided branch name. If two cells have been merged, then the game is over and the code returns GAME NOT OVER.. 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 . Each function in logic takes two arguments: mat and flag. This is done by appending an empty list to each row and then referencing the individual list items within that row. Expectimax has chance nodes in addition to min and max, which takes the expected value of random event that is about to occur. My attempt uses expectimax like other solutions above, but without bitboards. This process is repeated for every row in the matrix. 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. Then, it appends four lists each with four elements as 0 . Will take a better look at this in the free time. <>>>
Since then, I've been working on a simple AI to play the game for me. 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. (more precisely a expectimax). 4 0 obj Scoring is also done using table lookup. There is already an AI implementation for this game here. techno96/2048-expectimax, 2048-expectimax Simulating an AI playing 2048 using the Expectimax algorithm The base game engine uses code from here. Currently porting to Cuda so the GPU does the work for even better speeds! Python: Justifying NumPy array. 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. Searching later I found this algorithm might be classified as a Pure Monte Carlo Tree Search algorithm. Congratulations ! 1 0 obj
endobj
10% for a 4 and 90% for a 2). The code will check to see if the cells at the given coordinates are equal. 4 0 obj
The AI player is modeled as a m . So this is really not different than any other presented solution. 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. On a 64-bit machine, this enables the entire board to be passed around in a single machine register. The code starts by declaring two variables, r and c. These will hold the row and column numbers at which the new 2 will be inserted into the grid. % Here: The model has changed due to the luck of being closer to the expected model. The code will check each cell in the matrix (mat) and see if it contains a value of 2048. This algorithm is a variation of the minmax. 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. I got very frustrated with Haskell trying to do that, but I'm probably gonna give it a second try! 3 0 obj
As in a rough explanation of how the learning algorithm works? mat is a Python list object (a data structure that stores multiple items). 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. I'm sure the full details would be too long to post here) how your program achieves this? Site design / logo 2023 Stack Exchange Inc; user contributions licensed under CC BY-SA. 10. logic.py should be imported in 2048.py to use these functions. The game contrl part code are used from 2048-ai. 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. (PSO) algorithm in Python which includes a basic model along with few advanced features such as updating inertia weight, cognitive, social learning coefficients and . I. The code firstly reverses the grid matrix. Thanks, late answer and it performs not really well (almost always in [1024, 8192]), the cost/stats function needs more work, thanks @Robusto, I should improve the code some day, it can be simplified. 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. Alpha-beta is actually an improved minimax using a heuristic. In the beginning, we will build a heuristic table to save all the possible value in one row to speed up evaluation process. 2048 is a single-player sliding tile puzzle video game written by Italian web developer Gabriele Cirulli and published on GitHub. If any cell does, then the code will return 'WON'. the board position and the player that is next to move). In this article we will look python code and logic to design a 2048 game you have played very often in your smartphone. Until you have to use the 4th direction the game will practically solve itself without any kind of observation. The game is implemented in java with processing graphic library. 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. Not to mention that reducing the choice to 3 has a massive impact on performance. First, it creates two new variables, new_grid and changed. Tip #3: Keep the squares occupied. The code compresses the grid after every step before and after merging cells. Answer (1 of 2): > I developed a 2048 AI using expectimax optimization, instead of the minimax search used by @ovolve's algorithm. 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. Then it assigns this sum to the i variable. Next, the for loop iterates through 4 values (i in range(4)) . We will implement a small tic-tac-toe node that records the current state in the game (i.e. Next, the code compacts the grid by copying each cells value into a new list. Use --help to see relevant command arguments. Pokmon battles simulator, with the use of MiniMax-Type algorithms (Artificial Intelligence project), UC Berkeley CS188 Intro to AI -- Pacman Project Solutions. Finally, the code compresses the new matrix again. expectimax Expectimax is not optimal. If nothing happens, download Xcode and try again. << /Length 5 0 R /Filter /FlateDecode >> Sort a list of two-sided items based on the similarity of consecutive items. To associate your repository with the Just play 2048! Pretty impressive result. I have refined the algorithm and beaten the game! ExpectiMax. 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. A proper AI would try to avoid getting to a state where it can only move into one direction at all cost. Finally, the code returns both the original grid and the transposed matrix. Implementation of many popular AI algorithms to play the game of Pacman such as Minimax, Expectimax and Greedy. 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 starts by declaring two variables. It is based on term2048 and it's written in Python. We will design each logic function such as we are performing a left swipe then we will use it for right swipe by reversing matrix and performing left swipe. Finally, it returns the updated grid and changed values. %
Several heuristics are used to direct the optimization algorithm towards favorable positions. These lists represent the cells on the game / grid. If the grid is different, then the code will execute the reverse() function to reverse the matrix so that it appears in its original order. 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, python game.py -a Expectimax Yes, that's a 4096 alongside a 2048. This project is written in Go and hosted on Github at this following URL: . Next, the code takes transpose of the new grid to create a new matrix. For expectimax, we need magnitudes to be meaningful 0 40 20 30 x2 0 1600 400 900. Do EMC test houses typically accept copper foil in EUT? To subscribe to this RSS feed, copy and paste this URL into your RSS reader. Here's a demonstration of the power of this approach. Please Expectimax algorithm helps take advantage of non-optimal opponents. Then depth +1 , it will call try_move in the next step. If we are able to do that we wins. Some little games implementation, and also, machine learning implementation. You can view the AI in action or read the source. Not sure why this doesn't have more upvotes. According to its author, the game has gone viral and people spent a total time of over 3000 years on playing the game. 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). We explored two strategies in our project, one is ExpectiMax and the other is Deep Reinforcement Learning. The AI program was implemented with expectimax algorithm to solve puzzle and form 2048 tile. I am the author of a 2048 controller that scores better than any other program mentioned in this thread. 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. Mixed Layer Types E.g. What is the optimal algorithm for the game 2048? x=ksq!3p]BrY$*X+r.C:y,t1IYtOe_\lOx_O\~w
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