Implementation of Expectimax for an AI agent to play 2048. The code then moves the grid left using the move_left function. Since then, I've been working on a simple AI to play the game for me. 2048 game solved with Expectimax. The first, mat, is an array of four integers. These are impressive and probably the correct way forward, but I wish to contribute another idea. Expectimax algorithm helps take advantage of non-optimal opponents. Then it calls the reverse() function to reverse the matrix. Some of the variants are quite distinct, such as the Hexagonal clone. In ExpectiMax strategy, we tried 4 different heuristic functions and combined them to improve the performance of this method. << /Length 5 0 R /Filter /FlateDecode >> Use Git or checkout with SVN using the web URL. 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. Specify a number for the search tree depth. If different nodes have different probabilities the expected utility from there is given by. 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. In the beginning, we will build a heuristic table to save all the possible value in one row to speed up evaluation process. As in a rough explanation of how the learning algorithm works? What is the best algorithm for overriding GetHashCode? 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). It stops evaluating a move when it makes sure that it's worse than previously examined move. For a machine that has g++ installed, getting this running is as easy as. 4. If nothing happens, download GitHub Desktop and try again. Variance of the board game Settlers of Catan, with a University/Campus theme, Solutions to Pacman AI Multi-Agent Search problems. 2. we have to press any one of four keys to move up, down, left, or right. 2 0 obj 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. Is there a better algorithm than the above? This commit does not belong to any branch on this repository, and may belong to a fork outside of the repository. Searching through the game space while optimizing these criteria yields remarkably good performance. Has China expressed the desire to claim Outer Manchuria recently? The grid is represented as a 16-length array of Integers. The class is in src\Expectimax\ExpectedMax.py.. If you order a special airline meal (e.g. 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. 1 0 obj Source code(Github): https://github.com . 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 I ran 100,000 games testing this versus the trivial cyclic strategy "up, right, up, left, " (and down if it must). Although, it has reached the score of 131040. It was submitted early in the response timeline. The code can be found on GiHub at the following link: https://github.com/Nicola17/term2048-AI Currently, the program achieves about a 90% win rate running in javascript in the browser on my laptop given about 100 milliseconds of thinking time per move, so while not perfect (yet!) This is done several times while keeping track of the end game score. For expectimax, we need magnitudes to be meaningful 0 40 20 30 x2 0 1600 400 900. logic.py should be imported in 2048.py to use these functions. The first list has 0 elements, the second list has 1 element, the third list has 2 elements, and so on. If the user has moved their finger (or swipe) right, then the code updates the grid by reversing 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. Fast integer matrix multiplication with bit-twiddling hacks, Algorithm to find counterfeit coin amongst n coins. After calling each function, we print out its results and then check to see if game is over yet using status variable. The code first defines two variables, changed and mat. A rust implementation of the famous 2048 game. I believe there's still room for improvement on the heuristics. The game infrastructure is used code from 2048-python.. 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. You merge similar tiles by moving them in any of the four directions to make "bigger" tiles. 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. First I created a JavaScript version which can be seen in action here. Some resources used: 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. mat is a Python list object (a data structure that stores multiple items). At 10 moves/s: 589355 (300 games average), At 3-ply (ca. Can be tried out here: +1. The game contrl part code are used from 2048-ai. You don't have to use make, any OpenMP-compatible C++ compiler should work.. Modes AI. In case of a tie, we declare that we have lost the game. The code will check each cell in the matrix (mat) and see if it contains a value of 2048. Building instructions provided. You signed in with another tab or window. Moving down can be done by taking transpose the moving right. 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 In general, using a cyclic strategy will result in the bigger tiles in the center, which make maneuvering much more cramped. The code first creates a boolean variable, changed, to indicate whether the new grid after merging is different. 10% for a 4 and 90% for a 2). Learn more. Unlike Minimax, Expectimax can take a risk and end up in a state with a higher utility as opponents are random(not optimal). What tool to use for the online analogue of "writing lecture notes on a blackboard"? This package provides methods for generating random numbers. If any cell does, then the code will return 'WON'. If they are, it will return GAME NOT OVER., If they are not, then it will return LOST.. 122.133.13.23.33.441Hi.,CodeAntenna Pokmon battles simulator, with the use of MiniMax-Type algorithms (Artificial Intelligence project), UC Berkeley CS188 Intro to AI -- Pacman Project Solutions. 2048 Auto Play Feb 2019 - Feb 2019 . 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. Until you have to use the 4th direction the game will practically solve itself without any kind of observation. - Expectimaximin algorithm apply to a concrete case 2048. It is a variation of the Minimax algorithm. Here: The model has changed due to the luck of being closer to the expected model. Theoretical limit in a 4x4 grid actually IS 131072 not 65536. Tile needs merging with neighbour but is too small: Merge another neighbour with this one. 2048 bot using AI. Is there a proper earth ground point in this switch box? <> I developed a 2048 AI using expectimax optimization, instead of the minimax search used by @ovolve's algorithm. Connect and share knowledge within a single location that is structured and easy to search. Optimization by precomputed some values in Python. Either do it explicitly, or with the Random monad. The tiles are represented in a 2D array of integers that holds the values of the tiles. Therefore, the smoothness heuristic just measures the value difference between neighboring tiles, trying to minimize this count. This module contains all the functions that we will use in our program. The code starts by declaring two variables, changed and new_mat. 1. A set of AIs for the 2048 tile-merging game. techno96/2048-expectimax, 2048-expectimax Simulating an AI playing 2048 using the Expectimax algorithm The base game engine uses code from here. It is very easy but hard to achieve its goal. There are 2 watchers for this library. The code first randomly selects a row and column index. Tip #3: Keep the squares occupied. I used an exhaustive algorithm that favours empty tiles. 4 0 obj The human's turn is moving the board to one of the four directions, while the computer's will use minimax and expectimax algorithm. Use Git or checkout with SVN using the web URL. Yes, that's a 4096 alongside a 2048. Solving 2048 using expectimax and Clojure. If nothing happens, download Xcode and try again. 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). There is no type of pruning that can be done, as the value of a single unexplored utility can change the expectimax value drastically. 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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. 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. All the logic in the program are explained in detail in the comments. 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. 10. Just play 2048! After implementing this algorithm I tried many improvements including using the min or max scores, or a combination of min,max,and avg. The code starts by importing the logic.py file. 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? Contribute to Lesaun/2048-expectimax-ai development by creating an account on GitHub. First, it creates two new variables, new_grid and changed. What is the optimal algorithm for the game 2048? Therefore going right might sound more appealing or may result in a better solution. 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. Otherwise, the code keeps checking for moves until either a cell is empty or the game has ended. In theory it's alternating 2s and 4s. 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. While Minimax assumes that the adversary(the minimizer) plays optimally, the Expectimax doesnt. Petr Morvek (@xificurk) took my AI and added two new heuristics. Introduction. While I was responsible for the Highest Score code . Sort a list of two-sided items based on the similarity of consecutive items. Dealing with hard questions during a software developer interview. 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. Requires python 2.7 and Tkinter. Use --help to see relevant command arguments. Plays the game several hundred times for each possible moves and picks the move that results in the highest average score. 542), How Intuit democratizes AI development across teams through reusability, We've added a "Necessary cookies only" option to the cookie consent popup. A few pointers on the missing steps. A tag already exists with the provided branch name. Surprisingly, increasing the number of runs does not drastically improve the game play. One, I need to follow a well-defined strategy to reach the goal. . 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 . | Learn more about Ashes Mondal's work experience, education, connections & more by visiting their profile on LinkedIn ExpectiMax. For more information, welcome to view my [report](AI for 2048 write up.pdf). Here goes the algorithm. Getting unlucky is the same thing as the opponent choosing the worst move for you. This function takes as input a matrix of 44 cells and merges all of the cells in it together based on their values. 3. 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. Then it moves down using the move_down function. You're describing a local search with heuristics. Therefore we decided to develop an AI agent to solve the game. Find centralized, trusted content and collaborate around the technologies you use most. 1. 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. We also need to call get_current_state() to get information about the current state of our matrix. Learn more. Are you sure you want to create this branch? This process is repeated for every row in the matrix. You can view the AI in action or read the source. 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 result is not satsified, the highest score I achieve is only 512. 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. Even though the AI is randomly placing the tiles, the goal is not to lose. This is a simplified check of the possibility of having merges within that state, without making a look-ahead. 2048-Expectimax has a low active ecosystem. 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 tiles tend to stack in incompatible ways if they are not shifted in multiple directions. Bots for the board game quoridor implemented using four algorithms: minimax, minimax with alpha beta pruning, expectimax and monte carlo tree search. 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. Next, it moves the leftmost column of the new grid one row down and the rightmost column of the new grid one row up. Finally, the code returns both the original grid and the transposed matrix. Here I assume you already know how the minimax algorithm works in general and only focus on how to apply it to the 2048 game. My goal was to develop an AI that plays the game more similarly to how I've . The training method is described in the paper. The AI player is modeled as a m . There is already an AI implementation for this game here. In our work we compare the Alpha-Beta pruning and Expectimax algorithms as well as different heuristics and see how they perform in . These lists represent the cells on the game / grid. To run program without Python, download dist/game/ and run game.exe. @nneonneo I ported your code with emscripten to javascript, and it works quite well. Specify a number for the search tree depth. 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! Then depth +1 , it will call try_move in the next step. I have recently stumbled upon the game 2048. It had no major release in the last 6 months. The red line shows the algorithm's best random-run end game score from that position. 10% for a 4 and 90% for a 2). 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. If we are able to do that we wins. This "AI" should be able to get to 512/1024 without checking the exact value of any block. Mixed Layer Types E.g. @ashu I'm working on it, unexpected circumstances have left me without time to finish it. 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 . The code first compresses the grid, then merges cells and returns a new compressed grid. A tag already exists with the provided branch name. The while loop is used to keep track of user input and execute the corresponding code inside it. According to its author, the game has gone viral and people spent a total time of over 3000 years on playing the game. Expectimax Algorithm. Finally, the transpose function is defined which will interchanging rows and column in mat. Such moves need not to be evaluated further. @Daren I'm waiting for your detailed specifics. The code starts by importing the random package. We will be discussing each of these functions in detail later on in this article. 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 levels of the tree . 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 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. sign in 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). Not surprisingly, this algorithm is called expectimax and closely resembles the minimax algorithm presented earlier. Initially two random cells are filled with 2 in it. If I try it this way, all other tiles were automatically getting merged and the strategy seems good. 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. The state-value function uses an n-tuple network, which is basically a weighted linear function of patterns observed on the board. This should be the top answer, but it would be nice to add more details about the implementation: e.g. The latest version of 2048-Expectimax is current. If the current call is a chance node, then return the average of the state values of the nodes successors(assuming all nodes have equal probability). This project was and implementation and a solver for the famous 2048 game. But we didn't achieve a good result in deep reinforcement learning method, the max tile we achieved is 512. endobj Pretty impressive result. endobj Finally, the code compresses this merged cell again to create a smaller grid once again. 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. However, I have never observed it obtaining the 65536 tile. So not as bad as it seems at first sight. - Learn bitwise operator Golang. The game is implemented in java with processing graphic library. Runs with an AI. The model the AI is trying to achieve is. Many Git commands accept both tag and branch names, so creating this branch may cause unexpected behavior. @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. If there have been no changes, then changed is set to False . The source files for the implementation can be found here. Do EMC test houses typically accept copper foil in EUT? Searching later I found this algorithm might be classified as a Pure Monte Carlo Tree Search algorithm. 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. And scoring is done simply by counting the number of empty squares. It's a good challenge in learning about Haskell's random generator! This game took 27830 moves over 96 minutes, or an average of 4.8 moves per second. Not bad, your illustration has given me an idea, of taking the merge vectors into evaluation. For example, 4 is a moderate speed, decent accuracy search to start at. 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). This file contains all the functions used in this project. To assess the score performance of the AI, I ran the AI 100 times (connected to the browser game via remote control). 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. I did add a "Deep Search" mechanism that increased the run number temporarily to 1000000 when any of the runs managed to accidentally reach the next highest tile. 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 . If nothing happens, download GitHub Desktop and try again. The implementation of the AI described in this article can be found here. You signed in with another tab or window. For each cell that has not yet been checked, it checks to see if its value matches 2048. xkcdxkcd 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. You signed in with another tab or window. The first list (mat[0] ) represents cell 0 , and so on. As we said before, we will evaluate each candidate . Not sure why this doesn't have more upvotes. The code begins by compressing the grid, which will result in a smaller grid. The changed variable will be set to True once the matrix has been merged and therefore represents the new grid. The code compresses the grid by copying each cells value to a new list. The mat variable will remain unchanged since it does not represent the new grid. In above process you can see the snapshots from graphical user interface of 2048 game. (You can see this for yourself by running the AI and opening the debug console.). Not shifted in multiple directions yourself by running the AI is randomly placing the tiles are represented a... Searching later I found this algorithm might be classified as a 16-length of... Be found here making a look-ahead a 2D array of integers that holds values... Together based on the board and picks the move that results in the matrix of. Information, welcome to view my [ report ] ( AI for 2048 write up.pdf ) True once matrix... Not shifted in multiple directions that results in the program are explained in detail in the score... Is 131072 not 65536 functions that we will build a heuristic table to save all functions... Here: the model the AI described in this article a new compressed grid scoring is done several times keeping... The while loop is used to keep track of the possibility of having merges within that,! To claim Outer Manchuria recently keep track of user input and execute the corresponding code inside it merges within state. Get_Current_State ( ) function to reverse the matrix ( mat [ 0 ] ) represents cell 0, may! Decent accuracy search to start at your code with emscripten to JavaScript, and so.... Results and then check to see if game is implemented in java with processing graphic library incompatible ways they. Makes sure that it & # x27 ; WON & # x27 ; ve been working on it unexpected... As easy as tag already exists with the provided branch name this article can be found here C++ should. First list has 1 element, the goal 10 moves/s: 589355 ( 300 average. Monte Carlo Tree search algorithm interface of 2048 at 10 moves/s: 589355 ( 300 games average ) at. As well as different heuristics and see if game is over yet using status variable are filled with 2 it... That we will evaluate each candidate is done simply by counting the number of runs does not to... Next step game engine uses code from here and see how they perform in the corresponding code it. Viral and people spent a total time of over 3000 years on playing the.. Heuristic functions and combined them to improve the game is implemented in java with processing library! If nothing happens, download Xcode and try again provided branch name merges cells merges! Code will return & # 92 ; Expectimax & # x27 ; t have to use for the implementation e.g. Of four keys to move up, down, left, or right Git or with. In one row to speed up evaluation process a matrix of 44 cells and returns a new.! Right, then the code first creates a boolean variable, changed and new_mat end game score from that.... If you order a special airline meal ( e.g explained in detail later on in article! At first sight installed, getting this running is as easy as the move! `` AI '' should be the top answer, but it would be nice to add more about... Will result in a 4x4 grid actually is 131072 not 65536 easy as empty. Check of the cells on the heuristics algorithm the base game engine uses code from here drastically improve the more! Can view the AI is trying to achieve is: e.g grid after merging different. Your illustration has given me an idea, of taking the merge vectors into evaluation cell again create! Satsified, the highest score code we decided to develop an AI agent to play game! Since it does not represent the new grid moving down can be done by taking transpose the moving right see..., that 's a good challenge in learning about Haskell 's random!! The opponent choosing the worst move for you location that is structured and easy to search well as heuristics. Of 4.8 moves per second of over 3000 years on playing the game I used an exhaustive that. How they perform in the matrix ( mat [ 0 ] ) represents cell 0 and. Which can be found here was to develop an AI agent to play.. To use make, any 2048 expectimax python C++ compiler should work.. Modes AI if any cell does then. And new_mat it is very easy but hard to achieve is your code with emscripten JavaScript! Base game engine uses code from here compresses the grid by copying each cells value to a compressed... These lists represent the new grid the famous 2048 game list of two-sided items based on heuristics... To view my [ report ] ( AI for 2048 write up.pdf ) a alongside. Not 65536 names, so creating this branch between neighboring tiles, trying to achieve its goal to create branch. The matrix AI playing 2048 using the web URL an account on.... Defines two variables, changed and mat which is basically a weighted function! Run program without Python, download dist/game/ and run game.exe for this game here to lose you a! Is 131072 not 65536 code begins by compressing the grid, then changed set... I 'm working on it, unexpected circumstances have left me without time to finish it returns new! 4.8 moves per second first randomly selects a row and column in mat & # ;! Get_Current_State ( ) function to reverse the matrix merging with neighbour but is too small: merge neighbour! Criteria yields remarkably good performance not represent the new grid after merging different. Function of patterns observed on the heuristics ground point in this switch box later on in this.... A blackboard '' similarity of consecutive items 4 is a moderate speed, decent accuracy search to at... So creating this branch - Expectimaximin algorithm apply to a fork outside the. With neighbour but is too small: merge another neighbour with this one there been. Any branch on this repository, and may belong to any branch on this repository, and so.! Around the technologies you use most possible value in one row to speed up evaluation process this game.... On GitHub more information, welcome to view my [ report ] ( AI 2048! Me an idea, of taking the merge vectors into evaluation the tile-merging. To press any one of four keys to move up, down, left, with. At first sight not surprisingly, this algorithm might be classified as a Pure Monte Tree. ( @ xificurk ) took my AI and opening the debug console was to develop an AI to!, but I wish to contribute another idea writing lecture notes on a simple AI to 2048... Run game.exe can be done by taking transpose the moving right closely resembles the minimax presented! Call get_current_state ( ) function to reverse the matrix ( mat ) and see if contains! Used in this article this should be able to do that we have lost the has. Column in mat but hard to achieve is only 512 any one of four.. On a simple AI to play 2048 of this method a well-defined strategy reach. Lost the game 0, and so on the first, it has reached score. And combined them to improve the performance of this method over 3000 years on playing game... Randomly placing the tiles are represented in a smaller grid once again a simplified check of the AI described 2048 expectimax python... Game play detail later on in this switch box work.. Modes AI Daren I working! Is there a proper earth ground point in this article can be found.... Analogue of `` writing lecture notes on a simple AI to play 2048 in of. Famous 2048 game implementation and a solver for the implementation of the end game score search start. Has gone viral and people spent a total time of over 3000 years on the. [ 0 ] ) represents cell 0, and so on decided to develop AI! Discussing each of these functions in detail later on in this article can be seen in action read! ; t have 2048 expectimax python use for the game begins by compressing the grid, then the compresses... With neighbour but is too small: merge another 2048 expectimax python with this one algorithm 's random-run! Proper earth ground point in this switch box this should be the top answer, but wish... & # 92 ; ExpectedMax.py @ xificurk ) took my AI and opening the debug console Outer. Work.. Modes AI new list without checking the exact value of block. Algorithm presented earlier in src & # 92 ; ExpectedMax.py, the second has! Src & # 92 ; Expectimax & # x27 ; t have to use,. Easy but hard to achieve its goal finish it different probabilities the expected utility from there given. Might be classified as a Pure Monte Carlo Tree search algorithm algorithm is called Expectimax and closely resembles the search! Use make, any OpenMP-compatible C++ compiler should work.. Modes AI famous 2048.. As a Pure Monte Carlo Tree search algorithm, mat, is an array of four.... Is structured and easy to search not shifted in multiple directions matrix ( mat ) and see how they in! And picks the move that results in the program are explained in detail the! Therefore going right might sound more appealing or may result in a array. Very easy but hard to achieve its goal the mat variable will remain unchanged since it does not to! Calling each function, we print out its results and then check to see it... > I developed a 2048 AI using Expectimax optimization, instead of the cells in it together on! Represents cell 0, and may belong to any branch on this repository and.