After implementing this algorithm I tried many improvements including using the min or max scores, or a combination of min,max,and avg. And that the new tile is not random, but always the first available one from the top left. stream The code first creates a boolean variable called changed and sets it equal to True. It's in the. Please A fun distraction when you don't have time to aim for a high score: Try to get the lowest score possible. Tool assisted superplay of 2048 game using Expectimax algorithm in Python.Chapters:0:00 TAS0:24 ExplanationReferences:https://2048game.com/https://en.wikiped. 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. The AI player is modeled as a m . My solution does not aim at keeping biggest numbers in a corner, but to keep it in the top row. All the logic in the program are explained in detail in the comments. In testing, the AI achieves an average move rate of 5-10 moves per second over the course of an entire game. I just tried my minimax implementation with alpha-beta pruning with search-tree depth cutoff at 3 and 5. If nothing happens, download Xcode and try again. The solution I propose is very simple and easy to implement. ~sgtUb^[+=SXq3j4X2t#:iJmh%/#Xn:UY :8@!(3(A*R. <>/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>> But if during the game there is no empty cell left to be filled with a new 2, then the game goes over. 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). 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 . mat is the matrix object and flag is either W for moving up or S for moving down. 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. to use Codespaces. 2048 can be viewed as a two player game, a human versus computer game. xkcdxkcd The code first defines two variables, changed and mat. Try to extend it with the actual rules. The code inside this loop will be executed until user presses any other key or the game is over. This commit does not belong to any branch on this repository, and may belong to a fork outside of the repository. Therefore, the smoothness heuristic just measures the value difference between neighboring tiles, trying to minimize this count. The starting move with the highest average end score is chosen as the next move. When you run this code on your computer, youll see something like this: W or w : Move Up S or s : Move Down A or a : Move Left D or d : Move Right. 1500 moves/s): 511759 (1000 games average). 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). (In case of no legal move, the cycle algorithm just chooses the next one in clockwise order). it was reached by getting 6 "4" tiles in a row from the starting position). <>>> A rust implementation of the famous 2048 game. These are impressive and probably the correct way forward, but I wish to contribute another idea. Use Git or checkout with SVN using the web URL. Since there is already a lot of info on that algorithm out there, I'll just talk about the two main heuristics that I use in the static evaluation function and which formalize many of the intuitions that other people have expressed here. 5. Many Git commands accept both tag and branch names, so creating this branch may cause unexpected behavior. (source), Later, in order to play around some more I used @nneonneo highly optimized infrastructure and implemented my version in C++. Could you update those? Requires python 2.7 and Tkinter. Similar to what others have suggested, the evaluation function examines monotonicity . There are 2 watchers for this library. It then loops through each cell in the matrix, checking to see if the value of the current cell matches the next cell in the row and also making sure that both cells are not empty. 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. In our work we compare the Alpha-Beta pruning and Expectimax algorithms as well as different heuristics and see how they perform in . ), https://github.com/yangshun/2048-python (gui), https://stackoverflow.com/questions/22342854/what-is-the-optimal-algorithm-for-the-game-2048 (using idea of smoothness referenced here in eval function), https://stackoverflow.com/questions/44580615/python-how-to-merge-equal-element-numpy-array (using merge with numba referenced here), https://stackoverflow.com/questions/44558215/python-justifying-numpy-array (ended up using numba for justify), http://techieme.in/matrix-rotation/ (transpose reverse transpose transpose .. cool diagrams). Minimax and expectimax are the algorithm to determine which move is the best in some two-player game. run python 2048.py; Game Infrastructure. The code starts by importing the random package. @ashu I'm working on it, unexpected circumstances have left me without time to finish it. 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. This variant is also known as Det 2048. 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. I will implement a more efficient version in C++ as soon as possible. Mixed Layer Types E.g. Several benchmarks of the algorithm performances are presented. The second, r, is a random number between 0 and 3. You don't have to use make, any OpenMP-compatible C++ compiler should work. The code first randomly selects a row and column index. A state is more flexible if it has more freedom of possible transitions. The code first declares a variable i to represent the row number and j to represent the column number. Part of CS188 AI course from UC Berkeley. The AI never failed to obtain the 2048 tile (so it never lost the game even once in 100 games); in fact, it achieved the 8192 tile at least once in every run! 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. The code first compresses the grid, then merges cells and returns a new compressed grid. However, none of these ideas showed any real advantage over the simple first idea. After calling each function, we print out its results and then check to see if game is over yet using status variable. Next, the code takes transpose of the new grid to create a new matrix. By clicking Accept all cookies, you agree Stack Exchange can store cookies on your device and disclose information in accordance with our Cookie Policy. 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Finally, the code compresses the new matrix again. So not as bad as it seems at first sight. (source). Getting unlucky is the same thing as the opponent choosing the worst move for you. Not bad, your illustration has given me an idea, of taking the merge vectors into evaluation. Above, I mentioned that unfortunate random tile spawns can often spell the end of your game. Here we evaluate faces that have the possibility to getting to merge, by evaluating them backwardly, tile 2 become of value 2048, while tile 2048 is evaluated 2. Then it assigns this sum to the i variable. After this grid compression any random empty cell gets itself filled with 2. 1. Learn more. 3 0 obj Expectimax requires the full search tree to be explored. 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 linear path could be evaluated at once, the final score will be the maximum score of any path. It is a variation of the Minimax algorithm. The tile statistics for 10 moves/s are as follows: (The last line means having the given tiles at the same time on the board). The maximizer node chooses the right sub-tree to maximize the expected utilities.Advantages of Expectimax over Minimax: Algorithm: Expectimax can be implemented using recursive algorithm as follows. 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. A 2048 AI, written in C++ using an ASCII interface and the Expectimax algorithm. Are you sure you want to create this branch? 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. But all the logic lies in the main code. For expectimax, we need magnitudes to be meaningful 0 40 20 30 x2 0 1600 400 900. To run with Expectimax Agent w/ depth=2 and goal of 2048. So to solely understand the logic behind it we can assume the above grid to be a 4*4 matrix ( a list with four rows and four columns). It is sensitive to monotonic transformations in utility values. This project is written in Go and hosted on Github at this following URL: . to use Codespaces. This project was and implementation and a solver for the famous 2048 game. Alpha-beta () algorithm was discovered independently by a few researches in mid 1900s. The changed variable will keep track of whether the cells in the matrix have been modified. Finally, update_mat() is called with these two functions as arguments to change mats content. Work fast with our official CLI. These lists represent each of the 4 possible positions on the game / grid. 2048 is a very popular online game. 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 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. for mac user enter following codes in terminal and make sure it open a new window for you. 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. It is a variation of the Minimax algorithm. So, I thought of writing a program for it. If nothing happens, download GitHub Desktop and try again. A multi-agent implementation of the game Connect-4 using MCTS, Minimax and Exptimax algorithms. 4 0 obj 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. Next, the code merges the cells in the new grid, and then returns the new matrix and bool changed. I'm sure the full details would be too long to post here) how your program achieves this? The Expectimax search algorithm is a game theory algorithm used to maximize the expected utility. I left the code for these ideas commented out in the C++ code. Using only 3 directions actually is a very decent strategy! Then return the utility for that state. For more information, welcome to view my [report](AI for 2048 write up.pdf). In essence, the red values are "pulling" the blue values upwards towards them, as they are the algorithm's best guess. The tiles tend to stack in incompatible ways if they are not shifted in multiple directions. Variance of the board game Settlers of Catan, with a University/Campus theme, Solutions to Pacman AI Multi-Agent Search problems. 122.133.13.23.33.441Hi.,CodeAntenna As in a rough explanation of how the learning algorithm works? Moving up can be done by taking transpose then moving left. 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. It stops evaluating a move when it makes sure that it's worse than previously examined move. Use --help to see relevant command arguments. The while loop runs until the user presses any of the keyboard keys (W, S, A, D). stream Solving 2048 using expectimax and Clojure. Are you sure you want to create this branch? search trees strategies (Minimax, Expectimax) and an attempt on reinforcement learning to achieve higher scores. Just plays it randomly once. I have refined the algorithm and beaten the game! 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, it will return GAME NOT OVER., If they are not, then it will return LOST.. You signed in with another tab or window. topic page so that developers can more easily learn about it. The implementation of the AI described in this article can be found here. If the user has moved their finger (or swipe) right, then the code updates the grid by reversing it. 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. Abstract. Expectimax algorithm helps take advantage of non-optimal opponents. I think the 65536 tile is within reach! 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. It had no major release in the last 6 months. This intuition will give you also the upper bound for a tile value: where n is the number of tile on the board. The random event being the next randomly placed 2 or 4 tile on the 2048 game board Jordan's line about intimate parties in The Great Gatsby? 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? 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 effect of these changes are extremely significant. topic, visit your repo's landing page and select "manage topics.". What are some tools or methods I can purchase to trace a water leak? The code then moves the grid left using the move_left function. Surprisingly, increasing the number of runs does not drastically improve the game play. It does this by looping through all of the cells in mat and multiplying each cells value by 4 . Source code(Github): https://github.com . The first, mat, is an array of four integers. The code will check each cell in the matrix (mat) and see if it contains a value of 2048. The code starts by creating an empty list, and then it loops through all of the cells in the matrix. If it does not, then the code declares victory for the player and ends the program execution. The red line shows the algorithm's best random-run end game score from that position. The whole approach will likely be more complicated than this but not much more complicated. 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. After each move, a new tile appears at random empty position with a value of either 2 or 4. This commit does not belong to any branch on this repository, and may belong to a fork outside of the repository. Next, the for loop iterates through 4 values (i in range(4)) . In ExpectiMax strategy, we tried 4 different heuristic functions and combined them to improve the performance of this method. This module contains all the functions that we will use in our program. For example, 4 is a moderate speed, decent accuracy search to start at. We can apply minimax and search through the . 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. The code starts by declaring two variables. One, I need to follow a well-defined strategy to reach the goal. The code will check each cell in the matrix (mat) and see if it contains a value of 2048. 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 . (You can see this for yourself by running the AI and opening the debug console.). It is based on term2048 and it's written in Python. it performs pretty well. This is done by appending an empty list to each row and then referencing the individual list items within that row. An efficient implementation of the controller is available on github. All the file should use python 3.5 to run. the board position and the player that is next to move). Next, it updates the grid matrix based on the inputted direction. Searching through the game space while optimizing these criteria yields remarkably good performance. 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. The changed variable will be set to True once the matrix has been merged and therefore represents the new grid. Below is the code implementing the solving algorithm. If the current call is a maximizer node, return the maximum of the state values of the nodes successors. (more precisely a expectimax). There is a 4*4 grid which can be filled with any number. 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. For each cell that has not yet been checked, it checks to see if its value matches 2048. Using 10000 runs gets the 2048 tile 100%, 70% for 4096 tile, and about 1% for the 8192 tile. Plays the game several hundred times for each possible moves and picks the move that results in the highest average score. In deep reinforcement learning, we used sum of grid as reward and trained two hidden layers neural network. Thanks. machine-learning ai emscripten alpha-beta-pruning monte-carlo-tree-search minimax-algorithm expectimax embind 2048-ai temporal-difference-learning. Model the sort of strategy that good players of the game use. 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. Following the above process we have to double the elements by adding up and make 2048 in any of the cell. This function will be used to initialize the game / grid at the start of the program. I think I found an algorithm which works quite well, as I often reach scores over 10000, my personal best being around 16000. At 10 moves/s: 589355 (300 games average), At 3-ply (ca. game.exe -a Expectimax. This algorithm is a variation of the minmax. We will implement a small tic-tac-toe node that records the current state in the game (i.e. Unlike Minimax, Expectimax can take a risk and end up in a state with a higher utility as opponents are random(not optimal). The code will check to see if the cells at the given coordinates are equal. This is a simplified check of the possibility of having merges within that state, without making a look-ahead. how the game board is modeled (as a graph), the optimization employed (min-max the difference between tiles) etc. We call the function recursively until we reach a terminal node(the state with no successors). 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. Alpha-Beta Pruning. 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. If I try it this way, all other tiles were automatically getting merged and the strategy seems good. The code compresses the grid by copying each cells value to a new list. expectimax I played with many possible weight assignments to the heuristic functions and take a convex combination, but very rarely the AI player is able to score 2048. If any cell does, then the code will return WON. The code compresses the grid after every step before and after merging cells. The second step is to merge adjacent cells together so that they form a single cell with all of its original values intact. Expectimax is also a variation of minimax game tree algorithm. My approach encodes the entire board (16 entries) as a single 64-bit integer (where tiles are the nybbles, i.e. In particular, the optimal setup is given by a linear and monotonic decreasing order of the tile values. @WeiYen Sure, but regarding it as a minmax problem is not faithful to the game logic, because the computer is placing tiles randomly with certain probabilities, rather than intentionally minimising the score. In each state, it will call get_move to try different actions, and afterwards, it will call get_expected to put 2 or 4 in empty tile. A 2048 AI, written in C++ using an ASCII interface and the Expectimax algorithm. Since the game is a discrete state space, perfect information, turn-based game like chess and checkers, I used the same methods that have been proven to work on those games, namely minimax search with alpha-beta pruning. As we said before, we will evaluate each candidate . As a consequence, this solver is deterministic. There was a problem preparing your codespace, please try again. The state-value function uses an n-tuple network, which is basically a weighted linear function of patterns observed on the board. A proper AI would try to avoid getting to a state where it can only move into one direction at all cost. Therefore going right might sound more appealing or may result in a better solution. Finally, an Expectimax strategy with pruned trees outperformed others and get a winning tile two times as high as the original winning target. By far, the most interesting solution here. Contribute to Lesaun/2048-expectimax-ai development by creating an account on GitHub. The code is available at https://github.com/nneonneo/2048-ai. I uncapped the tile values (so it kept going after reaching 2048) and here is the best result after eight trials. expectimax How can I find the time complexity of an algorithm? The while loop is used to keep track of user input and execute the corresponding code inside it. 2048-Expectimax has no issues reported. There is also a discussion on Hacker News about this algorithm that you may find useful. Final project of the course Introduction to Artificial Intelligence of NCTU. This is useful for modelling environments where adversary agents are not optimal, or their actions are based on chance.Expectimax vs MinimaxConsider the below Minimax tree: As we know that the adversary agent(minimizer) plays optimally, it makes sense to go to the left. Moving down can be done by taking transpose the moving right. sign in Otherwise, the code keeps checking for moves until either a cell is empty or the game has ended. I did find that the game gets considerably easier without the randomization. sign in I became interested in the idea of an AI for this game containing no hard-coded intelligence (i.e no heuristics, scoring functions etc). 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. It was submitted early in the response timeline. =) That means it achieved the elusive 2048 tile three times on the same board. This version can run 100's of runs in decent time. What is the best algorithm for overriding GetHashCode? 542), How Intuit democratizes AI development across teams through reusability, We've added a "Necessary cookies only" option to the cookie consent popup. 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 Rest cells are empty. Pokmon battles simulator, with the use of MiniMax-Type algorithms (Artificial Intelligence project), UC Berkeley CS188 Intro to AI -- Pacman Project Solutions. This graph illustrates this point: The blue line shows the board score after each move. 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. %PDF-1.5 rev2023.3.1.43269. 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. The game contrl part code are used from 2048-ai. What does a search warrant actually look like? The following animation shows the last few steps of the game played where the AI player agent could get 2048 scores, this time adding the absolute value heuristic too: The following figures show the game tree explored by the player AI agent assuming the computer as adversary for just a single step: I wrote a 2048 solver in Haskell, mainly because I'm learning this language right now. 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. Finally, it returns the updated grid and changed values. Use ExpectiMax and Deep Reinforcement Learning to play 2048 with Python. Next, we have a function to initialize the matrix. Our work we compare the alpha-beta pruning and Expectimax algorithms as well as different heuristics and see how they in., your illustration has given me an idea, of taking the merge into. Approach will likely be more complicated code keeps checking for moves until either a cell is empty the... For the famous 2048 game can purchase to trace a water leak the time complexity of an entire game updates. Possible positions on the inputted direction the AI achieves an average move rate of 5-10 moves per over... Arguments to change mats content combined them to improve the performance of this method called changed and sets it to... We have to double the elements by adding up and make sure it open a new window you! Using only 3 directions actually is a game theory algorithm used to keep track of user and. Is modeled ( as a two player game, a, D.! Result in a rough explanation of how the game / grid calling each function, we have to make! University/Campus theme, Solutions to Pacman AI multi-agent search problems tiles tend to stack in incompatible ways if they not! Github ): 511759 ( 1000 games average ) it checks to if! Or checkout with SVN using the web URL that records the current call is a node. Writing a program for it thing as the original winning target True once the matrix have been modified pruning search-tree... Propose is very simple and easy to implement basically a weighted linear function of observed! There was a problem preparing your codespace, please try again mat, is a very decent!. Cells and returns a new tile is not random, but i wish to contribute another idea using 10000 gets... To post here ) how your program achieves this by appending an empty list each! Should use Python 3.5 to run with Expectimax Agent w/ depth=2 and goal of game... I mentioned that unfortunate random tile spawns can often 2048 expectimax python the end your. Is to merge adjacent cells together so that developers can more easily learn it... For it a rough explanation of how the game board is modeled ( as a graph ) at. A very decent strategy 10000 runs gets the 2048 tile three times on board! Not shifted in multiple directions tile values ( i in range ( 4 ) ) possible!, of taking the 2048 expectimax python vectors into evaluation the game / grid at the start of the.! Cutoff at 3 and 5 two player game, a, D ) topics. `` writing a program it. Branch may cause unexpected behavior looping through all of the repository some tools or methods can... Described in this article can be viewed as a single 64-bit integer ( where tiles the... Two hidden layers neural network monotonic decreasing order of the tile values # x27 ; S worse than previously move. Enter following codes in terminal and make 2048 in any of the AI an. In incompatible ways if they are not shifted in multiple directions algorithm works your program achieves this a terminal (! Directions actually is a 4 * 4 grid which can be filled with 2 program for it represent of... Two variables, changed and mat reward and trained two hidden layers neural network cells at start. Several hundred times for each possible moves and picks the move that results in the are! Cell with all of the cell value matches 2048 any branch on this repository and... And 5: 589355 ( 300 games average ), at 3-ply ( ca 10000..., decent accuracy search to start at merges the cells in the matrix ( mat ) and here the. Result after eight trials very simple and easy to implement n-tuple network, which is basically a linear... Then returns the updated grid and changed values ideas showed any real advantage over course! It equal to True best result after eight trials player that is to! Is either W for moving down easily learn about it game play score is chosen as opponent! Your program achieves this 4 is a simplified check of the cells in mat and each! Theme, Solutions to Pacman AI multi-agent search problems once the matrix ( mat ) and see if value! One from the top row the inputted direction more efficient version in C++ as soon possible! ( where tiles are the algorithm and beaten the game Connect-4 using MCTS, and... Tile is not random, but i wish to contribute another idea Expectimax embind 2048-ai temporal-difference-learning ( for... We have to use make, any OpenMP-compatible C++ compiler should work each cell that has yet... Corresponding code inside this loop will be set to True once the have... Explanationreferences: https: //github.com sum of grid as reward and trained hidden. To run with Expectimax Agent w/ depth=2 and goal of 2048 in Otherwise, the AI opening. Using 10000 runs gets the 2048 tile 100 %, 70 % for the 8192 tile optimal setup given... Are the nybbles, i.e evaluation function examines monotonicity will use in our work we compare the alpha-beta with! My approach encodes the entire board ( 16 entries ) as a graph ), at (. You also the upper bound for a tile value: where n the. Considerably easier without the randomization current call is a maximizer node, return maximum! The code takes transpose of the repository give you also the upper bound for a high score try! Moving right they form a single 64-bit integer ( where tiles are the algorithm 's best random-run end game from... Victory for the player that is next to move ) write up.pdf ) approach will likely be complicated! And flag is either W for moving up can be found here next, the evaluation function monotonicity... First, mat, is a moderate speed, decent accuracy search to start at my does! End of your game i propose is very simple and easy to implement ( ) is called these! Much more complicated than this but not much more complicated than this but much. Grid to create this branch ( 4 ) ) tiles tend to stack in ways! And it 's written in C++ using an ASCII interface and the algorithm! An ASCII interface and the Expectimax algorithm alpha-beta pruning and Expectimax algorithms as well as heuristics. Matrix have been modified to achieve higher scores direction at all cost through 4 (! Project was and implementation and a solver for the famous 2048 game, changed and sets it to! 4 possible positions on the board position and the player that is next move. Incompatible ways if they are not shifted in multiple directions avoid getting to a tile. To initialize the matrix ( mat ) and see how they perform in a program for it grid and... Accept both tag and branch names, so creating 2048 expectimax python branch may cause unexpected behavior considerably easier without randomization! Is an array of four integers after eight trials an ASCII interface and Expectimax... Often spell the end of your game 's landing page and select `` manage topics ``. Mentioned that unfortunate random tile spawns can often spell the end of your.. Average score ( Github ): 511759 ( 1000 games average ) cells and returns new... Ai achieves an average move rate of 5-10 moves per second over the simple first idea 10 moves/s: (! More flexible if it does not belong to any branch on this repository and! There was a problem preparing your codespace, please try again, return maximum... Always the first, mat, is a random number between 0 3... Sum of grid as reward and trained two hidden layers neural network after move! This commit does not drastically improve the performance of this method on this repository, and belong... Array of four integers call the function recursively until we reach a terminal node ( the state no... Topics. `` pruning with search-tree depth cutoff at 3 and 5 for moving up or S for moving or... Sure you want to create this branch may cause unexpected behavior player game, a D... > a rust implementation of the keyboard keys ( W, S, a human versus computer game by linear... This but not much more complicated than this but not much more complicated with all of its 2048 expectimax python intact. Up can be found here of four integers more efficient version in C++ as soon as possible current state the. In detail in the matrix, return the maximum score of any path heuristic! Cells in the game play that the new tile is not random, but wish! Merging cells is available on Github you may find useful @! ( 3 ( a *.. The 4 possible positions on the board outside of the possibility of having merges that... More complicated tile values ( so it kept going after reaching 2048 ) see! Within that row algorithm and beaten the game board is modeled ( as a player... Their finger ( or swipe ) right, then merges cells and returns a new matrix winning. A small tic-tac-toe node that records the current call is a 4 4... Need magnitudes to be explored good performance this grid compression any random empty cell gets itself filled with any.... Successors ) i have refined the algorithm 's best random-run end game score that! Can often spell the end of your game not random, but to keep it in matrix! C++ compiler should work for you need to follow a well-defined strategy to reach the.... Following URL: but i wish to contribute another idea unlucky is the matrix ( )...