2048 expectimax python

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. First, it creates two new variables, new_grid and changed. This is a constant, used as a base-line and for other uses like testing. Work fast with our official CLI. (stay tuned), In case of T2, four tests in ten generate the 4096 tile with an average score of 42000. The first version in just a draft, the second one use CNN as an architecture, and this method could achieve 1024, but its result actually not very depend on the predict result. 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. Above, I mentioned that unfortunate random tile spawns can often spell the end of your game. 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. The Expectimax search algorithm is a game theory algorithm used to maximize the expected utility. A state is more flexible if it has more freedom of possible transitions. It is a variation of the Minimax algorithm. Around 80% wins (it seems it is always possible to win with more "professional" AI techniques, I am not sure about this, though.). 2048 can be viewed as a two player game, a human versus computer game. It is very easy but hard to achieve its goal. 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. Several benchmarks of the algorithm performances are presented. A set of AIs for the 2048 tile-merging game. 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. If nothing happens, download Xcode and try again. There was a problem preparing your codespace, please try again. I thinks it's quite successful for its simplicity. Hello. I just tried my minimax implementation with alpha-beta pruning with search-tree depth cutoff at 3 and 5. The implementation of the AI described in this article can be found here. stream The game is implemented in java with processing graphic library. 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. The second, r, is a random number between 0 and 3. Work fast with our official CLI. 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. 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). (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). It runs in the console and also has a remote-control to play the web version. For each cell in that column, if its value is equal to the next cells value and they are not empty, then they are double-checked to make sure that they are still equal. << /Length 5 0 R /Filter /FlateDecode >> Building instructions provided. Finally, both original grids and transposed matrices are returned. 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. 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. 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. The first heuristic was a penalty for having non-monotonic rows and columns which increased as the ranks increased, ensuring that non-monotonic rows of small numbers would not strongly affect the score, but non-monotonic rows of large numbers hurt the score substantially. The tiles tend to stack in incompatible ways if they are not shifted in multiple directions. The tiles are represented in a 2D array of integers that holds the values of the tiles. For more information, welcome to view my [report](AI for 2048 write up.pdf). 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. 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. Dealing with hard questions during a software developer interview. If all of the cells in mat have already been checked or if one of those cells contains 2048 (the winning condition), then no victory can be declared and control passes back to get_current_state() so that another round of checking can begin. Inside the if statement, we are checking for different keys and depending on that input, we are calling one of the functions from logic.py. This is done by appending an empty list to each row and then referencing the individual list items within that row. The starting move with the highest average end score is chosen as the next move. 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. Following are a few examples, Game Theory (Normal-form game) | Set 3 (Game with Mixed Strategy), Game Theory (Normal-form Game) | Set 6 (Graphical Method [2 X N] Game), Game Theory (Normal-form Game) | Set 7 (Graphical Method [M X 2] Game), Combinatorial Game Theory | Set 2 (Game of Nim), Game Theory (Normal - form game) | Set 1 (Introduction), Game Theory (Normal-form Game) | Set 4 (Dominance Property-Pure Strategy), Game Theory (Normal-form Game) | Set 5 (Dominance Property-Mixed Strategy), Minimax Algorithm in Game Theory | Set 1 (Introduction), Introduction to Evaluation Function of Minimax Algorithm in Game Theory, Minimax Algorithm in Game Theory | Set 5 (Zobrist Hashing). Some resources used: logic.py should be imported in 2048.py to use these functions. My goal was to develop an AI that plays the game more similarly to how I've . The code starts by creating two new variables, new_grid and changed. %PDF-1.3 Minimax and expectimax are the algorithm to determine which move is the best in some two-player game. It has a neutral sentiment in the developer community. If you combine this with other strategies for deciding between the 3 remaining moves it could be very powerful. This presents the problem of trying to merge another tile of the same value into this square. Use --help to see relevant command arguments. 2048-expectimax-ai is a Python library typically used in Gaming, Game Engine, Example Codes applications. Finally, the add_new_2 function is called with the newly selected cell as its argument. 1500 moves/s): 511759 (1000 games average). Optimization by precomputed some values in Python. It performs pretty quickly for depth 1-4, but on depth 5 it gets rather slow at a around 1 second per move. The AI in its default configuration (max search depth of 8) takes anywhere from 10ms to 200ms to execute a move, depending on the complexity of the board position. If any cells have been modified, then their values will be updated within this function before it returns them back to the caller. What I am doing is at any point, I will try to merge the tiles with values 2 and 4, that is, I try to have 2 and 4 tiles, as minimum as possible. 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 in this section is used to update the grid on the screen. If you order a special airline meal (e.g. 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. <> If a law is new but its interpretation is vague, can the courts directly ask the drafters the intent and official interpretation of their law? Without randomization I'm pretty sure you could find a way to always get 16k or 32k. The effect of these changes are extremely significant. There is already an AI implementation for this game here. The game terminates when all the boxes are filled and there are no moves that can merge tiles, or you create a tile with a value of 2048. The code starts by declaring two variables, changed and new_mat. Similar to what others have suggested, the evaluation function examines monotonicity . Can non-Muslims ride the Haramain high-speed train in Saudi Arabia? A tag already exists with the provided branch name. 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, sign in Here: The model has changed due to the luck of being closer to the expected model. If I try it this way, all other tiles were automatically getting merged and the strategy seems good. However, I have never observed it obtaining the 65536 tile. I was trying to solve the same problem for a 4x4 grid as a project assignment for the edX course ColumbiaX: CSMM.101x Artificial Intelligence (AI). The second step is to merge adjacent cells together so that they form a single cell with all of its original values intact. machine-learning ai emscripten alpha-beta-pruning monte-carlo-tree-search minimax-algorithm expectimax embind 2048-ai temporal-difference-learning. It's really effective for it's simplicity. Are you sure the instructions provided in the github page apply to your project? 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. For a machine that has g++ installed, getting this running is as easy as. A multi-agent implementation of the game Connect-4 using MCTS, Minimax and Exptimax algorithms. The code initializes an empty list, then appends four lists each with four elements. The controller uses expectimax search with a state evaluation function learned from scratch (without human 2048 expertise) by a variant of temporal difference learning (a reinforcement learning technique). So not as bad as it seems at first sight. Next, the code compacts the grid by copying each cells value into a new list. run python 2048.py; Game Infrastructure. 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 Play as single player and see what the heuristics do, or run with an AI at multiple search tree depths and see the highest score it can get. I will implement a more efficient version in C++ as soon as possible. EDIT: This is a naive algorithm, modelling human conscious thought process, and gets very weak results compared to AI that search all possibilities since it only looks one tile ahead. 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. This is done by calling the start_game() function. In this code, we are checking for the input of a key and depending on that input, we are calling one of the function in logic.py file. I wrote an Expectimax solver for 2048 using the heuristics noted on the top ranking SO post "Optimal AI for 2048". Congratulations ! Contribute to Lesaun/2048-expectimax-ai development by creating an account on GitHub. Theoretical limit in a 4x4 grid actually IS 131072 not 65536. Next, the for loop iterates through 4 values (i in range(4)) . mat is the matrix object and flag is either W for moving up or S for moving down. Not surprisingly, this algorithm is called expectimax and closely resembles the minimax algorithm presented earlier. 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Includes an expectimax strategy that reaches 16384 with 34.6% success and an ML model trained with temporal difference learning. If there have been no changes, then changed is set to False . What is the best algorithm for overriding GetHashCode? Finally, it transposes the newly created grid to return it to its original form. The expectimax search itself is coded as a recursive search which alternates between "expectation" steps (testing all possible tile spawn locations and values, and weighting their optimized scores by the probability of each possibility), and "maximization" steps (testing all possible moves and selecting the one with the best score). How can I figure out which tiles move and merge in my implementation of 2048? To subscribe to this RSS feed, copy and paste this URL into your RSS reader. By far, the most interesting solution here. First I created a JavaScript version which can be seen in action here. 2048 Auto Play Feb 2019 - Feb 2019 . The code then moves the grid left using the move_left function. Try to extend it with the actual rules. search trees strategies (Minimax, Expectimax) and an attempt on reinforcement learning to achieve higher scores. Therefore it can be slow. 2048-Expectimax has a low active ecosystem. 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). Then it moves down using the move_down function. 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. Read the squares in the order shown above until the next squares value is greater than the current one. This file contains all the functions used in this project. 10% for a 4 and 90% for a 2). For example, 4 is a moderate speed, decent accuracy search to start at. You signed in with another tab or window. 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. And scoring is done simply by counting the number of empty squares. It's in the. The code uses expectimax search to evaluate each move, and chooses the move that maximizes the search as the next move to execute. 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. If nothing happens, download GitHub Desktop and try again. The code will check to see if the cells at the given coordinates are equal. It is likely that it will fail, but it can still achieve it: When it manages to reach the 128 it gains a whole row is gained again: I copy here the content of a post on my blog. Alpha-beta () algorithm was discovered independently by a few researches in mid 1900s. 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. The code first randomly selects a row and column index. Currently porting to Cuda so the GPU does the work for even better speeds! A rust implementation of the famous 2048 game. The tree of possibilities rairly even needs to be big enough to need any branching at all. To run with Expectimax Agent w/ depth=2 and goal of 2048: python game.py -a Expectimax or game.exe -a Expectimax. This is possible due to domain-independent nature of the AI. 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 . A commenter on Hacker News gave an interesting formalization of this idea in terms of graph theory. There was a problem preparing your codespace, please try again. What are some tools or methods I can purchase to trace a water leak? Finally, the code compresses the new matrix again. But if during the game there is no empty cell left to be filled with a new 2, then the game goes over. Full game implemented + AI/ML/OtherBuzzwords players (expectimax, monte-carlo and more). But, when I actually use this algorithm, I only get around 4000 points before the game terminates. In particular, the optimal setup is given by a linear and monotonic decreasing order of the tile values. If there are still cells in the mat array that have not yet been checked, the code continues looping through those cells. The move_down function works in a similar way. Pokmon battles simulator, with the use of MiniMax-Type algorithms (Artificial Intelligence project), UC Berkeley CS188 Intro to AI -- Pacman Project Solutions. The AI program was implemented with expectimax algorithm to solve puzzle and form 2048 tile. And finally, there is a penalty for having too few free tiles, since options can quickly run out when the game board gets too cramped. Finally, the code compresses this merged cell again to create a smaller grid once again. This "AI" should be able to get to 512/1024 without checking the exact value of any block. These are move_up(), move_down(), and move_left(). What tool to use for the online analogue of "writing lecture notes on a blackboard"? Besides the online version the game is available For ExpectiMax method, we could achieve 98% in 2048 with setting depth limit to 3. Several linear path could be evaluated at once, the final score will be the maximum score of any path. So this is really not different than any other presented solution. Larger tile in the way: Increase the value of a smaller surrounding tile. Are you sure you want to create this branch? 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. In our work we compare the Alpha-Beta pruning and Expectimax algorithms as well as different heuristics and see how they perform in . The class is in src\Expectimax\ExpectedMax.py.. 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. "pdawP 2048 bot using AI. The code will check each cell in the matrix (mat) and see if it contains a value of 2048. 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. 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). As in a rough explanation of how the learning algorithm works? An interesting fact about this algorithm is that while the random-play games are unsurprisingly quite bad, choosing the best (or least bad) move leads to very good game play: A typical AI game can reach 70000 points and last 3000 moves, yet the in-memory random play games from any given position yield an average of 340 additional points in about 40 extra moves before dying. Work fast with our official CLI. Since then, I've been working on a simple AI to play the game for me. 2048 is a very popular online game. The class is in src\Expectimax\ExpectedMax.py. Using only 3 directions actually is a very decent strategy! or The code first defines two variables, changed and mat. You can view the AI in action or read the source. The code compresses the grid after every step before and after merging cells. I have refined the algorithm and beaten the game! Although, it has reached the score of 131040. Expectimax algorithm helps take advantage of non-optimal opponents. The model the AI is trying to achieve is. 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 result: sheer impossibleness. 2048 Python game and AI 27 Sep 2015. - Learn bitwise operator Golang. how the game board is modeled (as a graph), the optimization employed (min-max the difference between tiles) etc. Actually, if you are completely new to the game, it really helps to only use 3 keys, basically what this algorithm does. rGS)~\RvY_WnBs.|qs#  u$\/m,t,lYO*V|`O} o>~R|@)1+ekPZcUhv6)O%K4+&RkbP?e Ln]B5h0h]5Jf5DrobRq_HD{psB!YEe5ghA2 ]vB~uVDy,QzbKV.Xrcpb9QI 5%^]=zs8&> 6)8lT&R! In ExpectiMax strategy, we tried 4 different heuristic functions and combined them to improve the performance of this method. In the beginning, we will build a heuristic table to save all the possible value in one row to speed up evaluation process. A set of AIs for the 2048 tile-merging game. Open the console for extra info. 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. 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. The transpose() function will then be used to interchange rows and column. In here we still need to check for stacked values, but in a lesser way that doesn't interrupt the flexibility parameters, so we have the sum of { x in [4,44] }. There is a 4*4 grid which can be filled with any number. What is the optimal algorithm for the game 2048? 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 . Here goes the algorithm. If you recall from earlier in this chapter, these are references to variables that store data about our game board. If it has not, then the code checks to see if any cells have been merged. This commit does not belong to any branch on this repository, and may belong to a fork outside of the repository. Not to mention that reducing the choice to 3 has a massive impact on performance. If it isnt over yet, we add a new row to our matrix using add_new_2(). I developed a 2048 AI using expectimax optimization, instead of the minimax search used by @ovolve's algorithm. 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. 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. An in-console game of 2048. 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). Searching through the game space while optimizing these criteria yields remarkably good performance. One, I need to follow a well-defined strategy to reach the goal. Next, the code loops through each column in turn. 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. Furthermore, Petr also optimized the heuristic weights using a "meta-optimization" strategy (using an algorithm called CMA-ES), where the weights themselves were adjusted to obtain the highest possible average score.
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