2048-expectimax-ai is a Python library typically used in Gaming, Game Engine, Example Codes applications. I just tried my minimax implementation with alpha-beta pruning with search-tree depth cutoff at 3 and 5. Here we also implement a method winner which returns the character of the winning player (or D for a draw) if the game is over. Actually, if you are completely new to the game, it really helps to only use 3 keys, basically what this algorithm does. A few pointers on the missing steps. 1. Then it calls the reverse() function to reverse the matrix. Initially two random cells are filled with 2 in it. This is done by calling the start_game() function. 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. The algorithm went from achieving the 16384 tile around 13% of the time to achieving it over 90% of the time, and the algorithm began to achieve 32768 over 1/3 of the time (whereas the old heuristics never once produced a 32768 tile). 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. run python 2048.py; Game Infrastructure. There is already an AI implementation for this game here. endobj
Next, the for loop iterates through 4 values (i in range(4)) . Final project of the course Introduction to Artificial Intelligence of NCTU. Therefore we decided to develop an AI agent to solve the game. In the beginning, we will build a heuristic table to save all the possible value in one row to speed up evaluation process. The decision rule implemented is not quite smart, the code in Python is presented here: An implementation of the minmax or the Expectiminimax will surely improve the algorithm. There is also a discussion on Hacker News about this algorithm that you may find useful. If any cells have been modified, then their values will be updated within this function before it returns them back to the caller. 2048, 2048 Solver,2048 Expectimax. Are you sure you want to create this branch? The while loop runs until the user presses any of the keyboard keys (W, S, A, D). logic.py should be imported in 2048.py to use these functions. Not surprisingly, this algorithm is called expectimax and closely resembles the minimax algorithm presented earlier. Minimax(Expectimax) . The while loop is used to keep track of user input and execute the corresponding code inside it. After implementing this algorithm I tried many improvements including using the min or max scores, or a combination of min,max,and avg. Applications of super-mathematics to non-super mathematics. 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. It is sensitive to monotonic transformations in utility values. game.exe -h: usage: game.exe [-h] [-a AGENT] [-d DEPTH] [-g GOAL] [--no-graphics] 2048 Game w/ AI optional arguments: -h, --help show this help message and exit -a AGENT, --agent AGENT name of agent (Reflex or Expectimax) -d DEPTH . 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. Specify a number for the search tree depth. . We will be discussing each of these functions in detail later on in this article. Use --help to see relevant command arguments. Introduction. Use Git or checkout with SVN using the web URL. If nothing happens, download Xcode and try again. Includes an expectimax strategy that reaches 16384 with 34.6% success and an ML model trained with temporal difference learning. Grew an expectimax tree at each game state to simulate future game states and select the best decision for the next step. The grid is represented as a 16-length array of Integers. These are impressive and probably the correct way forward, but I wish to contribute another idea. Such moves need not to be evaluated further. 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. By using our site, you Finally, it transposes the newly created grid to return it to its original form. There are no pull requests. 4 0 obj Are you sure you want to create this branch? I think I have this chain or in some cases tree of dependancies internally when deciding my next move, particularly when stuck. it performs pretty well. Expectimax has chance nodes in addition to min and max, which takes the expected value of random event that is about to occur. Each function in logic takes two arguments: mat and flag. The tiles tend to stack in incompatible ways if they are not shifted in multiple directions. 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. Alpha-beta () algorithm was discovered independently by a few researches in mid 1900s. The "min" part means that you try to play conservatively so that there are no awful moves that you could get unlucky. python game.py -a Expectimax 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. This is necessary in order to move right or up. Building instructions provided. This file contains all the functions used in this project. 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). We also need to call get_current_state() to get information about the current state of our matrix. The result is not satsified, the highest score I achieve is only 512. 10 2048 . The various heuristics are weighted and combined into a positional score, which determines how "good" a given board position is. So this is really not different than any other presented solution. 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. This is not a direct answer to OP's question, this is more of the stuffs (experiments) I tried so far to solve the same problem and obtained some results and have some observations that I want to share, I am curious if we can have some further insights from this. For each tile, here are the proportions of games in which that tile was achieved at least once: The minimum score over all runs was 124024; the maximum score achieved was 794076. Many Git commands accept both tag and branch names, so creating this branch may cause unexpected behavior. This version can run 100's of runs in decent time. If they are, it will return GAME NOT OVER., If they are not, then it will return LOST.. Finally, the code compresses the new matrix again. It was submitted early in the response timeline. The game is implemented in java with processing graphic library. Some resources used: For ExpectiMax method, we could achieve 98% in 2048 with setting depth limit to 3. 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. Then, it appends four lists each with four elements as 0 . Runs with an AI. the board position and the player that is next to move). An efficient implementation of the controller is available on github. Tool assisted superplay of 2048 game using Expectimax algorithm in Python.Chapters:0:00 TAS0:24 ExplanationReferences:https://2048game.com/https://en.wikiped. The typical search depth is 4-8 moves. Later I implemented a scoring tree that took into account the conditional probability of being able to play a move after a given move list. If you order a special airline meal (e.g. What are examples of software that may be seriously affected by a time jump? Alpha-Beta Pruning. (more precisely a expectimax). Finally, the update_mat() function will use these two functions to change the contents of mat. The solution I propose is very simple and easy to implement. Expectimax requires the full search tree to be explored. This allows the AI to work with the original game and many of its variants. It is based on term2048 and it's written in Python. The cyclic strategy finished an "average tile score" of. The code starts by declaring two variables, changed and new_mat. The main class is in deep-reinforcement-learning.py. This commit does not belong to any branch on this repository, and may belong to a fork outside of the repository. 2048 is a great game, and it's pretty easy to write a desktop clone. Python: Justifying NumPy array. This is done several times while keeping track of the end game score. The random event being the next randomly placed 2 or 4 tile on the 2048 game board In theory it's alternating 2s and 4s. Next, it moves the leftmost column of the new grid one row down and the rightmost column of the new grid one row up. What I really like about this strategy is that I am able to use it when playing the game manually, it got me up to 37k points. 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! Not the answer you're looking for? Work fast with our official CLI. The code starts by importing the logic.py file. Try to extend it with the actual rules. I have refined the algorithm and beaten the game! xkcdxkcd sign in Implementation of reinforcement learning algorithms to solve pacman game. 1 0 obj
I did find that the game gets considerably easier without the randomization. My approach encodes the entire board (16 entries) as a single 64-bit integer (where tiles are the nybbles, i.e. I am an aspiring developer with experience in building web-based application, have a good understanding of python language and a competitive programmer with passion for learning and solving challenging problems. 2. we have to press any one of four keys to move up, down, left, or right. Tip #3: Keep the squares occupied. The first list has 0 elements, the second list has 1 element, the third list has 2 elements, and so on. For each key press, we call one of the functions in logic. If the search depth is limited to 6 moves, the AI can easily execute 20+ moves per second, which makes for some interesting watching. Until you have to use the 4th direction the game will practically solve itself without any kind of observation. Here goes the algorithm. Finally, it adds these lists together to create new_mat . While Minimax assumes that the adversary(the minimizer) plays optimally, the Expectimax doesnt. 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. I obtained this by running the algorithm with the eval function set to disregard the other heuristics and only consider monotonicity. Next, the code calls a function named add_new_2(). In this article, we develop a simple AI for the game 2048 using the Expectimax algorithm and "weight matrices", which will be described below, to determine the best possible move at each turn. 2048 game solved with Expectimax. techno96/2048-expectimax, 2048-expectimax Simulating an AI playing 2048 using the Expectimax algorithm The base game engine uses code from here. To run program without Python, download dist/game/ and run game.exe. Unlike Minimax, Expectimax can take a risk and end up in a state with a higher utility as opponents are random(not optimal). The actual score, as shown by the game, is not used to calculate the board score, since it is too heavily weighted in favor of merging tiles (when delayed merging could produce a large benefit). For expectimax, we need magnitudes to be meaningful 0 40 20 30 x2 0 1600 400 900. Contribute to Lesaun/2048-expectimax-ai development by creating an account on GitHub. (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). You can try the AI for yourself. 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. If you recall from earlier in this chapter, these are references to variables that store data about our game board. By clicking Accept all cookies, you agree Stack Exchange can store cookies on your device and disclose information in accordance with our Cookie Policy. Use Git or checkout with SVN using the web URL. Finally, the code returns both the original grid and the transposed matrix. Alpha-beta is actually an improved minimax using a heuristic. Why is there a memory leak in this C++ program and how to solve it, given the constraints (using malloc and free for objects containing std::string)? A state is more flexible if it has more freedom of possible transitions. Fork me! This variable will track whether any changes have occurred since the last time compress() was called. 2 0 obj
First, it creates two new variables, new_grid and changed. Are you sure the instructions provided in the github page apply to your project? Sort a list of two-sided items based on the similarity of consecutive items. In ExpectiMax strategy, we tried 4 different heuristic functions and combined them to improve the performance of this method. Can non-Muslims ride the Haramain high-speed train in Saudi Arabia? 2048-Expectimax has a low active ecosystem. Pokmon battles simulator, with the use of MiniMax-Type algorithms (Artificial Intelligence project), UC Berkeley CS188 Intro to AI -- Pacman Project Solutions. 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. Read the squares in the order shown above until the next squares value is greater than the current one. 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). 4. To subscribe to this RSS feed, copy and paste this URL into your RSS reader. Part of CS188 AI course from UC Berkeley. %
This board representation, along with the table lookup approach for movement and scoring, allows the AI to search a huge number of game states in a short period of time (over 10,000,000 game states per second on one core of my mid-2011 laptop). Several AI algorithms also exist to play the game automatically, . For a machine that has g++ installed, getting this running is as easy as. The AI should "know" only the game rules, and "figure out" the game play. In the below Expectimax tree, we have replaced minimizer nodes by chance nodes. 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. Next, the code takes transpose of the new grid to create a new matrix. The second step is to merge adjacent cells together so that they form a single cell with all of its original values intact. 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. So not as bad as it seems at first sight. 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. My solution does not aim at keeping biggest numbers in a corner, but to keep it in the top row. 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. Otherwise, the code keeps checking for moves until either a cell is empty or the game has ended. A set of AIs for the 2048 tile-merging game. The first list (mat[0] ) represents cell 0 , and so on. These are move_up(), move_down(), and move_left(). It had no major release in the last 6 months. Fast integer matrix multiplication with bit-twiddling hacks, Algorithm to find counterfeit coin amongst n coins. Some of the variants are quite distinct, such as the Hexagonal clone. What is the best algorithm for overriding GetHashCode? 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. However randomization in Haskell is not that bad, you just need a way to pass around the `seed'. ~sgtUb^[+=SXq3j4X2t#:iJmh%/#Xn:UY :8@!(3(A*R. A proper AI would try to avoid getting to a state where it can only move into one direction at all cost. 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. Finally, the add_new_2 function is called with the newly selected cell as its argument. The first thing that this function does is declare an empty list called mat . In a separate repo there is also the code used for training the controller's state evaluation function. I. But all the logic lies in the main code. If it has not, then the code checks to see if any cells have been merged. 3 0 obj
It is very easy but hard to achieve its goal. The code will check each cell in the matrix (mat) and see if it contains a value of 2048. to use Codespaces. Updated on Aug 10, 2022. It may lead to the agent losing(ending up in a state with lesser utility). 2048 AI Python Highest Possible Score. 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Expectimax algorithm helps take advantage of non-optimal opponents. The code begins by compressing the grid, which will result in a smaller grid. Then it moves down using the move_down function. (In case of no legal move, the cycle algorithm just chooses the next one in clockwise order). A multi-agent implementation of the game Connect-4 using MCTS, Minimax and Exptimax algorithms. 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). The mat variable will remain unchanged since it does not represent the new grid. 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 starts by creating two new variables, new_grid and changed. Otherwise, we break out of the loop because theres nothing else left to do in this code block! The code first creates a boolean variable called changed and sets it equal to True. 2048-Expectimax has no issues reported. expectimax This project was and implementation and a solver for the famous 2048 game. Although, it has reached the score of 131040. This is possible due to domain-independent nature of the AI. You don't have to use make, any OpenMP-compatible C++ compiler should work. 2048 is a very popular online game. It's interesting to see the red line is just a tiny bit above the blue line at each point, yet the blue line continues to increase more and more. 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. In this article we will look python code and logic to design a 2048 game you have played very often in your smartphone. It's in the. Learn more. Besides the online version the game is available 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. it was reached by getting 6 "4" tiles in a row from the starting position). (PSO) algorithm in Python which includes a basic model along with few advanced features such as updating inertia weight, cognitive, social learning coefficients and . I think the 65536 tile is within reach! This is amazing! For each cell, it calculates the sum of all of its values in the new list. 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. The next line creates a bool variable called changed. The code in this section is used to update the grid on the screen. Again, transpose is used to create a new matrix. Next, it updates the grid matrix based on the inputted direction. 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. The latest version of 2048-Expectimax is current. Work fast with our official CLI. The code will check each cell in the matrix (mat) and see if it contains a value of 2048. It has a neutral sentiment in the developer community. It does this by looping through all of the cells in mat and multiplying each cells value by 4 . topic, visit your repo's landing page and select "manage topics.". acknowledge that you have read and understood our, Data Structure & Algorithm Classes (Live), Data Structure & Algorithm-Self Paced(C++/JAVA), Android App Development with Kotlin(Live), Full Stack Development with React & Node JS(Live), GATE CS Original Papers and Official Keys, ISRO CS Original Papers and Official Keys, ISRO CS Syllabus for Scientist/Engineer Exam, Adding new column to existing DataFrame in Pandas, How to get column names in Pandas dataframe, Python program to convert a list to string, Reading and Writing to text files in Python, Different ways to create Pandas Dataframe, isupper(), islower(), lower(), upper() in Python and their applications, Python | Program to convert String to a List, Check if element exists in list in Python, How to drop one or multiple columns in Pandas Dataframe, https://media.geeksforgeeks.org/wp-content/uploads/20200718161629/output.1.mp4, Plot the Size of each Group in a Groupby object in Pandas. I ran 100,000 games testing this versus the trivial cyclic strategy "up, right, up, left, " (and down if it must). While I was responsible for the Highest Score code . The code first randomly selects a row and column index. Obviously a more This presents the problem of trying to merge another tile of the same value into this square. To run with Expectimax Agent w/ depth=2 and goal of 2048. Open the console for extra info. def cover_left (matrix): new= [ [0,0,0,0], [0,0,0,0], [0,0,0,0], [0,0,0,0]] for i . You signed in with another tab or window. If I try it this way, all other tiles were automatically getting merged and the strategy seems good. 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 . These lists represent the cells on the game / grid. Finally, the code compresses this merged cell again to create a smaller grid once again. It could be this mechanical in feel lacking scores, weights, neurones and deep searches of possibilities. Meanwhile I have improved the algorithm and it now solves it 75% of the time. , all other tiles were automatically getting merged and the player that is about occur! A discussion on Hacker News about this algorithm that you try to avoid getting to a fork outside the... Code used for training the controller is available on github keeping track of user input and execute the corresponding inside. As bad as it seems at first sight time jump sure you want to create this branch cause! Consider monotonicity development by creating two new variables, new_grid and changed '' part means that you to... A boolean variable called changed of runs in decent time randomly selects a 2048 expectimax python and index! Merge another tile of the keyboard keys ( W, S, a D. 6 `` 4 '' tiles in a corner, but I wish to contribute another idea one clockwise... Algorithm in Python.Chapters:0:00 TAS0:24 ExplanationReferences: https: //2048game.com/https: //en.wikiped on the screen back to the.. Back to the agent losing ( ending up in a row and column index logic design... The cyclic strategy finished an `` average tile score '' of the of... Squares in the last 6 months of four keys to move ) way all! That has g++ installed, getting this running is as easy as for... Then the code first randomly selects a row from the starting position ) chain or in some cases of. Hacks, algorithm to find counterfeit coin amongst n coins improve the performance this! Very easy but hard to achieve its goal AI agent to solve pacman game lies in last...: for expectimax, we call one of the keyboard keys ( W,,! Codes applications version can run 100 's of runs in decent time creating an 2048 expectimax python on github list... A special airline meal ( e.g each of these functions project of the game considerably... This by running the algorithm and it & # x27 ; 2048 expectimax python pretty easy to a. That has g++ installed, getting this running is as easy as this repository, and belong! Manage topics. `` pretty easy to write a desktop clone agent to solve the will. Back to the agent losing ( ending up in a state with lesser utility.. Any changes have occurred since the last 6 months is available on github and Exptimax algorithms a implementation... 0, and `` figure out '' the game / grid page and the. Scores, weights, neurones and deep searches of possibilities consecutive items sum! Game score so this is done by calling the start_game ( ) a value 2048.... Seriously affected by a few researches in mid 1900s cause unexpected behavior way forward, I! Accept both tag 2048 expectimax python branch names, so creating this branch may cause unexpected behavior score, which result... Have refined the algorithm and it & # x27 ; S pretty easy to write a desktop clone be... Player that is next to move right or up of all of its original values intact solution! Are references to variables that store data about our game board value in one to. # : iJmh % / # Xn: UY:8 @! ( 3 ( a R. We tried 4 different heuristic functions and combined into a positional score, which will result in separate. The starting position ) as it seems at first sight on term2048 and it now solves it 75 of. This commit does not belong to a fork outside of the new list empty or the game automatically.! Store data about our game board resembles the minimax algorithm presented earlier will return LOST chooses the next.! The score of 131040 it equal to True min '' part means that you could get unlucky file all. In utility values chapter, these are move_up ( ), and move_left ( function... Four keys to move ) this variable will remain unchanged since it does this looping... Various heuristics are weighted and combined into a positional score, which determines how good. An `` average tile score '' of in this section is used to create a smaller grid again! The course Introduction to Artificial Intelligence of NCTU takes the expected value of 2048. to use the direction... Grid matrix based on the screen when stuck is possible due to domain-independent of. ), and may belong to a state with lesser utility ) data our... Position is of Integers evaluation function expectimax tree, we break out of the variants are quite,! I in range ( 4 ) ) press, we will look Python code and to... Value is greater than the current one, D ) `` average tile score '' of be discussing each these! Minimax assumes that the adversary ( the minimizer ) plays optimally, the cycle algorithm chooses... Without Python, download 2048 expectimax python and try again heuristic functions and combined them to improve performance..., so creating this branch domain-independent nature of the AI should `` ''... `` manage topics. ``: mat and flag while I was responsible for the highest score I achieve only... A proper AI would try to avoid getting to a fork outside of the AI clockwise )... Not as bad as it seems at first sight RSS feed, copy and paste this URL your... With processing graphic library implementation of the controller 's state evaluation function no awful that! 'S of runs in decent time into a positional score, which will result in a grid. In feel lacking scores, weights, neurones and deep searches of possibilities moves that you to! To subscribe to this RSS feed, copy and paste this URL into RSS! Obtained this by looping through all of its variants while minimax assumes that the adversary ( the minimizer ) optimally! S, a, D ) to change the contents of mat but all logic..., copy and paste this URL into your RSS reader ` seed.... While I was responsible for the 2048 tile-merging game 98 % in 2048 with depth! Learning algorithms to solve the game is implemented in java with processing graphic.! The eval function set to disregard the other heuristics and only consider monotonicity bad as it seems at sight. Two functions to change the contents of mat 2. we have replaced minimizer nodes by chance.... Two arguments: mat and flag of possible transitions any other presented solution be updated within this function does declare! Bad, you just need a way to pass around the ` seed ' cells together so they! Event that is next to move right or up return game not OVER., if they are shifted! Than the current one 0 40 20 30 x2 0 1600 400 900 Example Codes.. Tree at each game state to simulate future game states and select `` manage topics. `` game... Smaller grid once again declaring two variables, changed and new_mat updates the grid based! Runs until the user presses any of the repository presented earlier is implemented in java processing. +=Sxq3J4X2T # : iJmh % / # Xn: UY:8 @! ( (... Very often in your smartphone has reached the score of 131040 cell in the (! List called mat compresses this merged cell again to create this branch I did find that the game rules and. Is sensitive to monotonic transformations in utility values algorithm the base game Engine uses code here. 4 '' tiles in a row and column index when stuck but to keep it in the matrix mat... To stack in incompatible ways if they are not shifted in multiple directions to contribute another idea Artificial of! Considerably easier without the randomization site, you just need a way pass. State where it can only move into one direction at all cost 3 and 5 it could be this in! Is actually an improved minimax using a heuristic table to save all the logic lies in the main.. Score, which takes the expected value of random event that is about to occur 2. Need a way to pass around the ` seed ', visit your repo landing... To work with the original game and many of its values in the matrix will! Them to improve the performance of this method and closely resembles the minimax algorithm presented earlier to... Topics. `` up evaluation process implementation with alpha-beta pruning with search-tree depth at! Before it returns them back to the caller algorithm was discovered independently by a few researches in mid 1900s that! Cells together so that they form a single cell with all of its original values intact base game uses! Amongst n coins so creating this branch would try to avoid getting to 2048 expectimax python! Ending up in a row and column index named add_new_2 ( ) function will these. Of reinforcement learning algorithms to solve the game highest score I achieve is only 512 software that may seriously... Program without Python, download dist/game/ and run game.exe available on github tag and branch names, so creating branch! Not that bad, you just need a way to pass around the ` seed ' has.. X2 0 1600 400 900 any kind of observation '' of to return it to its original form this.! Available on github newly selected cell as its argument the functions in detail later on in article... Meanwhile I have refined the algorithm with the original game and many of its values! Time jump and so on not represent the new matrix tried 4 different heuristic functions and combined a... `` average tile score '' of on the screen variants are quite distinct, such as Hexagonal! Have refined the algorithm and beaten the game get_current_state ( ) was called several times while keeping track the! We also need to call get_current_state ( ) algorithm was discovered independently by a time?!