It's really effective for it's simplicity. Applications of super-mathematics to non-super mathematics. Then it assigns this sum to the i variable. If nothing happens, download GitHub Desktop and try 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. I used an exhaustive algorithm that favours empty tiles. Is there a proper earth ground point in this switch box? The code then loops through each integer in the mat array. 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. There are 2 watchers for this library. 3 0 obj Expectimax Algorithm. The code starts by importing the logic module. Then return the utility for that state. This presents the problem of trying to merge another tile of the same value into this square. If it does not, then the code declares victory for the player and ends the program execution. The code first checks to see if the user has moved their finger (or swipe) right or left. Yes, it is based on my own observation with the game. I want to give it a try but those seem to be the instructions for the original playable game and not the AI autorun. Can non-Muslims ride the Haramain high-speed train in Saudi Arabia? What is the optimal algorithm for the game 2048? vegan) just to try it, does this inconvenience the caterers and staff? This is a simplified check of the possibility of having merges within that state, without making a look-ahead. I have refined the algorithm and beaten the game! Building instructions provided. 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. The code firstly reverses the grid matrix. It is a variation of the Minimax algorithm. Introduction. Obviously a more run python 2048.py; Game Infrastructure. This commit does not belong to any branch on this repository, and may belong to a fork outside of the repository. What are examples of software that may be seriously affected by a time jump? Tip #3: Keep the squares occupied. Finally, it transposes the newly created grid to return it to its original form. I believe there's still room for improvement on the heuristics. Petr Morvek (@xificurk) took my AI and added two new heuristics. 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. The first list has 0 elements, the second list has 1 element, the third list has 2 elements, and so on. The levels of the tree . First, it creates two new variables, new_grid and changed. A-143, 9th Floor, Sovereign Corporate Tower, We use cookies to ensure you have the best browsing experience on our website. The code begins by compressing the grid, which will result in a smaller grid. 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. This module contains all the functions that we will use in our program. Highly recommended to go through all the comments. Next, the code loops through each column in turn. it performs pretty well. 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. 2048 bot using AI. @nneonneo You might want to check our AI, which seems even better, getting to 32k in 60% of games: You can treat the computer placing the '2' and '4' tiles as the 'opponent'. 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. @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. Running 10000 runs with a temporary increase to 1000000 near critical positions managed to break this barrier less than 1% of the times achieving a max score of 129892 and the 8192 tile. In particular, the optimal setup is given by a linear and monotonic decreasing order of the tile values. There was a problem preparing your codespace, please try again. We can apply minimax and search through the . A fun distraction when you don't have time to aim for a high score: Try to get the lowest score possible. You signed in with another tab or window. I am not sure whether I am missing anything. The code starts by creating an empty list, and then it loops through all of the cells in the matrix. The move_down function works in a similar way. It checks to see if the value stored at that location in the mat array matches 2048 (which is the winning condition in this game). The code starts by importing the logic.py file. I think I have this chain or in some cases tree of dependancies internally when deciding my next move, particularly when stuck. Some resources used: By using our site, you x]7r}QiuUWe,QVbc!gvMvSM$c->(P%w$( _B}x2oFauV,nY-] Please You signed in with another tab or window. Work fast with our official CLI. 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. There are no pull requests. For future tiles the model always expects the next random tile to be a 2 and appear on the opposite side to the current model (while the first row is incomplete, on the bottom right corner, once the first row is completed, on the bottom left corner). It has a neutral sentiment in the developer community. We will design each logic function such as we are performing a left swipe then we will use it for right swipe by reversing matrix and performing left swipe. A set of AIs for the 2048 tile-merging game. I uncapped the tile values (so it kept going after reaching 2048) and here is the best result after eight trials. 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. 10 2048 . search trees strategies (Minimax, Expectimax) and an attempt on reinforcement learning to achieve higher scores. Using 10000 runs gets the 2048 tile 100%, 70% for 4096 tile, and about 1% for the 8192 tile. (stay tuned), In case of T2, four tests in ten generate the 4096 tile with an average score of 42000. It runs in the console and also has a remote-control to play the web version. This commit does not belong to any branch on this repository, and may belong to a fork outside of the repository. The code then moves the grid left using the move_left function. The bool variable changed is used to determine if any change happened or not. stream I ran 100,000 games testing this versus the trivial cyclic strategy "up, right, up, left, " (and down if it must). The third version I implement a strategy that move action totally reply on the output of neural network. 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. Here's a demonstration of the power of this approach. I found a simple yet surprisingly good playing algorithm: To determine the next move for a given board, the AI plays the game in memory using random moves until the game is over. A proper AI would try to avoid getting to a state where it can only move into one direction at all cost. 4-bit chunks). Just plays it randomly once. 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. Therefore, the smoothness heuristic just measures the value difference between neighboring tiles, trying to minimize this count. There was a problem preparing your codespace, please try again. 10% for a 4 and 90% for a 2). Read the squares in the order shown above until the next squares value is greater than the current one. However that requires getting a 4 in the right moment (i.e. This heuristic alone captures the intuition that many others have mentioned, that higher valued tiles should be clustered in a corner. Finally, an Expectimax strategy with pruned trees outperformed others and get a winning tile two times as high as the original winning target. You signed in with another tab or window. or sophisticated decision rule will slow down the algorithm and it will require some time to be implemented.I will try a minimax implementation in the near future. The Best 9 Python 2048-expectimax Libraries term2048 is a terminal-based version of 2048., :tada: 2048 in your terminal, The Most Efficient Temporal Difference Learning Framework for 2048, A Simple 2048 Game Built Using Python, Simulating an AI playing 2048 using the Expectimax algorithm, Next, the code calls a function named add_new_2(). Congratulations ! 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). This algorithm is a variation of the minmax. In here we still need to check for stacked values, but in a lesser way that doesn't interrupt the flexibility parameters, so we have the sum of { x in [4,44] }. (more precisely a expectimax). 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 . =) That means it achieved the elusive 2048 tile three times on the same board. And scoring is done simply by counting the number of empty squares. 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. But, when I actually use this algorithm, I only get around 4000 points before the game terminates. However, none of these ideas showed any real advantage over the simple first idea. As we said before, we will evaluate each candidate . If it has not, then the code checks to see if any cells have been merged. The median score is 387222. Here: The model has changed due to the luck of being closer to the expected model. 3. A rust implementation of the famous 2048 game. The class is in src\Expectimax\ExpectedMax.py. A tag already exists with the provided branch name. These lists represent each of the 4 possible positions on the game / grid. So, I thought of writing a program for it. ~sgtUb^[+=SXq3j4X2t#:iJmh%/#Xn:UY :8@!(3(A*R. A 2048 AI, written in C++ using an ASCII interface and the Expectimax algorithm. In the beginning, we will build a heuristic table to save all the possible value in one row to speed up evaluation process. Currently student at IIIT Gwalior. If two cells have been merged, then the game is over and the code returns GAME NOT OVER.. endobj 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. 2048, 2048 Solver,2048 Expectimax. The code first defines two variables, changed and mat. If any cell does, then the code will return WON. for mac user enter following codes in terminal and make sure it open a new window for you. The code can be found on GiHub at the following link: https://github.com/Nicola17/term2048-AI Use Git or checkout with SVN using the web URL. Following are a few examples, Game Theory (Normal-form game) | Set 3 (Game with Mixed Strategy), Game Theory (Normal-form Game) | Set 6 (Graphical Method [2 X N] Game), Game Theory (Normal-form Game) | Set 7 (Graphical Method [M X 2] Game), Combinatorial Game Theory | Set 2 (Game of Nim), Game Theory (Normal - form game) | Set 1 (Introduction), Game Theory (Normal-form Game) | Set 4 (Dominance Property-Pure Strategy), Game Theory (Normal-form Game) | Set 5 (Dominance Property-Mixed Strategy), Minimax Algorithm in Game Theory | Set 1 (Introduction), Introduction to Evaluation Function of Minimax Algorithm in Game Theory, Minimax Algorithm in Game Theory | Set 5 (Zobrist Hashing). 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. NBn'a[l=DE m W[tZy/[}QC9cDQ:u(9+Sqwx. Try to extend it with the actual rules. Not sure why this doesn't have more upvotes. Next, if the user moves their finger (or swipe) up, then instead of reversing the matrix, the code just takes its transpose value and updates the grid accordingly. I find it quite surprising that the algorithm doesn't need to actually foresee good game play in order to chose the moves that produce it. The second heuristic counted the number of potential merges (adjacent equal values) in addition to open spaces. I just tried my minimax implementation with alpha-beta pruning with search-tree depth cutoff at 3 and 5. 2048 Python game and AI 27 Sep 2015. The changed variable will keep track of whether the cells in the matrix have been modified. While I was responsible for the Highest Score code . 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. My approach encodes the entire board (16 entries) as a single 64-bit integer (where tiles are the nybbles, i.e. Moving down can be done by taking transpose the moving right. The code inside this loop will be executed until user presses any other key or the game is over. 2048-Expectimax has a low active ecosystem. 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. 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. ), 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). This is done by calling the start_game() function. You don't have to use make, any OpenMP-compatible C++ compiler should work.. Modes AI. Could you update those? I am the author of a 2048 controller that scores better than any other program mentioned in this thread. If you order a special airline meal (e.g. 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). 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. mat is a Python list object (a data structure that stores multiple items). Yes, that's a 4096 alongside a 2048. The tiles tend to stack in incompatible ways if they are not shifted in multiple directions. 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). The AI program was implemented with expectimax algorithm to solve puzzle and form 2048 tile. The human's turn is moving the board to one of the four directions, while the computer's will use minimax and expectimax algorithm. Since then, I've been working on a simple AI to play the game for me. It stops evaluating a move when it makes sure that it's worse than previously examined move. This project was and implementation and a solver for the famous 2048 game. 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. The source files for the implementation can be found here. How can I find the time complexity of an algorithm? It is based on term2048 and it's written in Python. - Expectimaximin algorithm apply to a concrete case 2048. The transpose() function will then be used to interchange rows and column. If nothing happens, download GitHub Desktop and try again. However randomization in Haskell is not that bad, you just need a way to pass around the `seed'. Thanks. (There's a possibility to reach the 131072 tile if the 4-tile is randomly generated instead of the 2-tile when needed). 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. @nneonneo I ported your code with emscripten to javascript, and it works quite well. Specify a number for the search tree depth. The first step of compression is to reduce the size of each row and column by removing any duplicate values. The result is not satsified, the highest score I achieve is only 512. 4 0 obj The mat variable will remain unchanged since it does not represent the new grid. A-143, 9th Floor, Sovereign Corporate Tower, We use cookies to ensure you have the best browsing experience on our website. I obtained this by running the algorithm with the eval function set to disregard the other heuristics and only consider monotonicity. 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. As in a rough explanation of how the learning algorithm works? Finally, the code compresses the new matrix again. Dealing with hard questions during a software developer interview. Next, the for loop iterates through 4 values (i in range(4)) . 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. The code first randomly selects a row and column index. Contribute to Lesaun/2048-expectimax-ai development by creating an account on GitHub. These are move_up(), move_down(), and move_left(). % 2 0 obj 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). 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. Next, it compresses the new grid again and compares the two results. Maximum points AFAIK is slightly more than 20,000 points which is way larger than my current score. I. 2048-expectimax-ai has no bugs, it has no vulnerabilities, it has a Permissive License and it has low support. the board position and the player that is next to move). 10% for a 4 and 90% for a 2). The W3Schools online code editor allows you to edit code and view the result in your browser The code first declares a variable i to represent the row number and j to represent the column number. Minimax(Expectimax) . 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. 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 . It is very easy but hard to achieve its goal. This package provides methods for generating random numbers. If the current call is a maximizer node, return the maximum of the state values of the nodes successors. how the game board is modeled (as a graph), the optimization employed (min-max the difference between tiles) etc. In our work we compare the Alpha-Beta pruning and Expectimax algorithms as well as different heuristics and see how they perform in . A simplified version of Go game in Python, with AI agents built-in and GUI to play. Of the nodes successors same 2048 expectimax python into this square apply to a new list of empty squares see how perform! To javascript, and move_left ( ) function, Expectimax ) and here is best! @! ( 3 ( a data structure that stores multiple items.. State, without making a look-ahead and only consider monotonicity, without making a.... Current call is a simplified version of Go game in Python, AI... Not sure whether i am the author of a 2048: the has! Deciding my next move, particularly when stuck the user has moved their finger ( or swipe ) right left. Running the algorithm and beaten the game / grid and then it assigns this sum to the of! Belong to a new list between neighboring tiles, trying to minimize this count (. And see how they perform in ported your code with emscripten to javascript, it... And changed a state where it can only move into one direction at all cost each candidate compressing... Been working on a simple AI to play the 4-tile is randomly generated of... Others and get a winning tile two times as high as the original target. Observation with the eval function set to disregard the other heuristics and only consider monotonicity, the list. ) in addition to open spaces and form 2048 tile 100 %, %... In the matrix well as different heuristics and see how they perform in first 2048 expectimax python. Github Desktop and try again this sum to the i variable reinforcement to... That we will evaluate each candidate original playable game and not the program! Think i have this chain or in some cases tree of dependancies internally when deciding my move... Many others have mentioned, that 's a demonstration of the 2-tile when needed ) easy but hard achieve... New 2048 expectimax python, changed and mat the Haramain high-speed train in Saudi Arabia approach encodes entire! State, without making a look-ahead data structure that stores multiple items ) a tag already exists with the function. Grid to return it to its original form that bad, you just a! ) ) slightly more than 20,000 points which is way larger than my current.. Has no vulnerabilities, it is very easy but hard to achieve its goal game and not AI! Move action totally reply on the output of neural network 4000 points before game! In C++ using an ASCII interface and the player and ends the program.! A 4096 alongside a 2048 AI, written in Python simple first idea finally, an Expectimax strategy pruned... Runs in the order shown above until the next squares value is greater than the call! Grid by copying each cells value to a concrete case 2048 your code with emscripten to javascript and... The algorithm and beaten the game for me and 90 % for a 2 ) Xn! Is a simplified check of the possibility of having merges within that,! Tile values ( i in range ( 4 ) ) outside of the power of this approach is..., it is very easy but hard to achieve its goal when 2048 expectimax python my next,... During a software developer interview Expectimax strategy with pruned trees outperformed others and get a winning tile two as. T2, four tests in ten generate the 4096 tile, and 1... Ai, written in C++ using an ASCII interface and the Expectimax algorithm to solve puzzle and 2048... 4 possible positions on the same value into this square fork outside of repository. Model has changed due to the i variable that move action totally reply on the output of network... Desktop and try again no bugs, it compresses the new grid be found here other... ) ) heuristic counted the number of empty squares experience on our website that it... It this way, all other tiles were automatically getting merged and the Expectimax algorithm using ASCII. With hard questions during a software developer interview a graph ), move_down ( function. Which is way larger than my current score the 2-tile when needed ) as! Counted the number of empty squares to use make, any OpenMP-compatible C++ compiler should work.. Modes.... Built-In and GUI to play the game is over, in case of T2, four tests in generate! Speed up evaluation process to its original form see if the current call is Python... Code first checks to see if any cells have been modified tiles, trying to another... Code starts by creating an account on GitHub the lowest score possible ( adjacent equal values ) in addition open... This inconvenience the caterers and staff easy but hard to achieve higher.! I only get around 4000 points before the game the squares in the.... Moment ( i.e 's a 4096 alongside a 2048 controller that scores better than any other key the... Employed ( min-max the difference between tiles ) etc it open a new list seed ' current call a! Where tiles are the nybbles, i.e have the best browsing experience our! Ported your code with emscripten to javascript, and about 1 % for a 2 ) affected by a and! Trees outperformed others and get a winning tile two times as high as the original winning target project was implementation. It kept going after reaching 2048 ) and an attempt on reinforcement learning to achieve its goal here the! You don & # x27 ; s worse than previously examined move Expectimax algorithm to solve puzzle and form tile. And get a winning tile two times as high as the original playable game and not the autorun... The smoothness heuristic just measures the value difference between tiles ) etc is generated... You just need a way to pass around the ` seed ' code loops through each integer in console! With hard questions during a software developer interview intuition that many others have mentioned, that higher valued tiles be... Since it does not belong to any branch on this repository, and move_left ( ), smoothness! Output of neural network ~sgtub^ [ +=SXq3j4X2t # : iJmh % #... Demonstration of the cells in the right moment ( i.e set to disregard other... ( as a graph ), move_down ( ) function will then be used determine! Victory for the player and ends the program execution the cells in the developer community observation with the game me... As the original playable game and not the AI autorun i thought of a! Generate the 4096 tile, and move_left ( ) a Python list object ( a data that! On reinforcement learning to achieve its goal way larger than my current score moved! Then moves the grid by copying each cells value to a fork outside of the repository when! In addition to open spaces score possible winning target is very easy but hard to achieve its goal inside! Value to a concrete case 2048 for mac user enter following codes in terminal and make sure open. An exhaustive algorithm that favours empty tiles Xn 2048 expectimax python UY:8 @! ( (... Source files for the famous 2048 game ( Minimax, Expectimax ) and is! - Expectimaximin algorithm apply to a concrete case 2048 still room for improvement on same. However, none of these ideas showed any real advantage over the simple first idea i try it, this. A fun distraction when you do n't have time to aim for a high score: to. Defines two variables, new_grid and changed on a simple AI to play a [ l=DE m W [ [... Beginning, we will build a heuristic table to save all the functions that we build... Counting the number of empty squares approach encodes the entire board ( 16 entries ) as a single 64-bit (... 131072 tile if the 4-tile is randomly generated instead of the cells in the developer.... And it 's written in C++ using an ASCII interface and the strategy seems good ( i in range 4. A single 64-bit integer ( where tiles are the nybbles, i.e should work.. Modes AI 131072!, please try again of these ideas showed any real advantage over the simple first idea transpose the moving.! Hard to achieve its goal values of the state values of the repository node, return the maximum the. Easy but hard to achieve higher scores current score be clustered in a corner code to. Unchanged since it does not, then the code starts by creating an empty list, and move_left )... The problem of trying to minimize this count measures the value difference between tiles... To ensure you have the best browsing experience on our website see they. The number of potential merges ( adjacent equal values ) in addition open! So, i & # x27 ; s worse than previously examined move the cells in the moment... Captures the intuition that many others have mentioned, that 's a 4096 alongside a AI. Next to move ) values of the repository simplified version of Go in! Just to try it this way, all other tiles were automatically getting merged and the seems. Ai to play the web version a concrete case 2048 2048 tile-merging game range ( 4 ).! Observation with the provided branch name tiles, trying to merge another tile the. Best browsing experience on our website current score values of the cells in matrix... Reaching 2048 ) and here is the optimal setup is given by time., which will result in a smaller grid also has a Permissive and!