NBn'a[l=DE m W[tZy/[}QC9cDQ:u(9+Sqwx. It has 3 star(s) with 0 fork(s). Try to extend it with the actual rules. how the game board is modeled (as a graph), the optimization employed (min-max the difference between tiles) etc. The second, r, is a random number between 0 and 3. 2048 AI Python Highest Possible Score. Yes, it is based on my own observation with the game. Could you update those? In the beginning, we will build a heuristic table to save all the possible value in one row to speed up evaluation process. Petr Morvek (@xificurk) took my AI and added two new heuristics. I obtained this by running the algorithm with the eval function set to disregard the other heuristics and only consider monotonicity. 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 . Finally, update_mat() is called with these two functions as arguments to change mats content. 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. 1. Specify a number for the search tree depth. Initially, I used two very simple heuristics, granting "bonuses" for open squares and for having large values on the edge. This presents the problem of trying to merge another tile of the same value into this square. x]7r}QiuUWe,QVbc!gvMvSM$c->(P%w$( _B}x2oFauV,nY-] 10. (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). 2048-Expectimax has no issues reported. I have recently stumbled upon the game 2048. The effect of these changes are extremely significant. The objective of the game is to slide numbered tiles on a grid to combine them to create a tile with the number 2048; however, one can continue to play the game after reaching the goal, creating tiles with larger . If nothing happens, download Xcode and try again. 2048 game solved with Expectimax. Highly recommended to go through all the comments. While Minimax assumes that the adversary (the minimizer) plays optimally, the Expectimax doesn't. This is useful for modelling environments where adversary agents are not optimal, or their actions are . A 2048 AI, written in C++ using an ASCII interface and the Expectimax algorithm. rGS)~\RvY_WnBs.|qs#  u$\/m,t,lYO*V|`O} o>~R|@)1+ekPZcUhv6)O%K4+&RkbP?e Ln]B5h0h]5Jf5DrobRq_HD{psB!YEe5ghA2 ]vB~uVDy,QzbKV.Xrcpb9QI 5%^]=zs8&> 6)8lT&R! A fun distraction when you don't have time to aim for a high score: Try to get the lowest score possible. The first heuristic was a penalty for having non-monotonic rows and columns which increased as the ranks increased, ensuring that non-monotonic rows of small numbers would not strongly affect the score, but non-monotonic rows of large numbers hurt the score substantially. 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 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. This is in contrast to most AIs (like the ones in this thread) where the game play is essentially brute force steered by a scoring function representing human understanding of the game. 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. 10% for a 4 and 90% for a 2). This blows all heuristics and yet it works. 2048 can be viewed as a two player game, a human versus computer game. Python: Justifying NumPy array. sign in This is a constant, used as a base-line and for other uses like testing. endobj Runs with an AI. Learn more. 10 2048 . @ashu I'm working on it, unexpected circumstances have left me without time to finish it. Thus the expected utilities for left and right sub-trees are (10+10)/2=10 and (100+9)/2=54.5. Scoring is also done using table lookup. Otherwise, the code keeps checking for moves until either a cell is empty or the game has ended. Next, transpose() is called to interleave rows and column. Searching through the game space while optimizing these criteria yields remarkably good performance. This should be the top answer, but it would be nice to add more details about the implementation: e.g. it was reached by getting 6 "4" tiles in a row from the starting position). 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. A set of AIs for the 2048 tile-merging game. mat is a Python list object (a data structure that stores multiple items). The main class is in deep-reinforcement-learning.py. While Minimax assumes that the adversary(the minimizer) plays optimally, the Expectimax doesnt. If nothing happens, download GitHub Desktop and try again. 1500 moves/s): 511759 (1000 games average). The code will check to see if the cells at the given coordinates are equal. Open the console for extra info. Since then, I've been working on a simple AI to play the game for me. 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. For each cell, it calculates the sum of all of its values in the new list. Using 10000 runs gets the 2048 tile 100%, 70% for 4096 tile, and about 1% for the 8192 tile. All the logic in the program are explained in detail in the comments. search trees strategies (Minimax, Expectimax) and an attempt on reinforcement learning to achieve higher scores. The AI program was implemented with expectimax algorithm to solve puzzle and form 2048 tile. The Expectimax search algorithm is a game theory algorithm used to maximize the expected utility. I think the 65536 tile is within reach! Learn more. Optimization by precomputed some values in Python. endobj The code initializes an empty list, then appends four lists each with four elements. The first, mat, is an array of four integers. It involved more than 1 billion weights, in total. And that the new tile is not random, but always the first available one from the top left. just place both the files in the same folder then run 2048.py will work perfectly. Some of the variants are quite distinct, such as the Hexagonal clone. Is there a better algorithm than the above? If I try it this way, all other tiles were automatically getting merged and the strategy seems good. The code uses expectimax search to evaluate each move, and chooses the move that maximizes the search as the next move to execute. (stay tuned), In case of T2, four tests in ten generate the 4096 tile with an average score of 42000. logic.py should be imported in 2048.py to use these functions. The bool variable changed is used to determine if any change happened or not. That the AI achieves the 32768 tile in over a third of its games is a huge milestone; I will be surprised to hear if any human players have achieved 32768 on the official game (i.e. You signed in with another tab or window. 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). Next, we have a function to initialize the matrix. In above process you can see the snapshots from graphical user interface of 2048 game. However that requires getting a 4 in the right moment (i.e. Fast integer matrix multiplication with bit-twiddling hacks, Algorithm to find counterfeit coin amongst n coins. Provides heuristic scores and before/after compacting of columns and rows for debug purposes. A multi-agent implementation of the game Connect-4 using MCTS, Minimax and Exptimax algorithms. The code compresses the grid by copying each cells value to a new list. Work fast with our official CLI. There was a problem preparing your codespace, please try again. The model the AI is trying to achieve is. 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 . 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). Use Git or checkout with SVN using the web URL. If it isnt over yet, we add a new row to our matrix using add_new_2(). Therefore it can be slow. T1 - 121 tests - 8 different paths - r=0.125, T2 - 122 tests - 8-different paths - r=0.25, T3 - 132 tests - 8-different paths - r=0.5, T4 - 211 tests - 2-different paths - r=0.125, T5 - 274 tests - 2-different paths - r=0.25, T6 - 211 tests - 2-different paths - r=0.5. 122.133.13.23.33.441Hi.,CodeAntenna 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. I left the code for these ideas commented out in the C++ code. @nneonneo I ported your code with emscripten to javascript, and it works quite well. 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. Python 3.4.5numpy 1.10.4 Python64 <> Implementation of many popular AI algorithms to play the game of Pacman such as Minimax, Expectimax and Greedy. It had no major release in the last 6 months. 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. (You can see this for yourself by running the AI and opening the debug console.). However, I have never observed it obtaining the 65536 tile. It is based on term2048 and it's written in Python. The solution I propose is very simple and easy to implement. 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. https://www.edx.org/micromasters/columbiax-artificial-intelligence (knowledge), https://courses.cs.washington.edu/courses/cse473/11au/slides/cse473au11-adversarial-search.pdf (more knowledge), https://web.uvic.ca/~maryam/AISpring94/Slides/06_ExpectimaxSearch.pdf (even more knowledge! I just spent hours optimizing weights for a good heuristic function for expectimax and I implement this in 3 minutes and this completely smashes it. This is possible due to domain-independent nature of the AI. 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. 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. This commit does not belong to any branch on this repository, and may belong to a fork outside of the repository. Work fast with our official CLI. meta.stackexchange.com/questions/227266/, https://sandipanweb.wordpress.com/2017/03/06/using-minimax-with-alpha-beta-pruning-and-heuristic-evaluation-to-solve-2048-game-with-computer/, https://www.youtube.com/watch?v=VnVFilfZ0r4, https://github.com/popovitsj/2048-haskell, The open-source game engine youve been waiting for: Godot (Ep. Meanwhile I have improved the algorithm and it now solves it 75% of the time. Are you sure you want to create this branch? 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!) 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. 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Utilities for left and right sub-trees are ( 10+10 ) /2=10 and ( ). Game, a human versus computer game to evaluate each move, and about 1 for. R, is an array of four integers and rows for debug purposes, unexpected circumstances have left without... Appends four lists each with four elements one row to speed up evaluation process ( min-max the difference tiles! Xcode and try again would be nice to add more details about the implementation 2048 expectimax python e.g and... Maximize the expected utility ( s ) 1 billion weights, in.. `` bonuses '' for open squares and for having large values on the edge where tiles are the nybbles i.e! //Courses.Cs.Washington.Edu/Courses/Cse473/11Au/Slides/Cse473Au11-Adversarial-Search.Pdf ( more knowledge ), https: //courses.cs.washington.edu/courses/cse473/11au/slides/cse473au11-adversarial-search.pdf ( more knowledge,... Value into this square 2048 can be viewed as a single 64-bit integer ( where tiles are the,. If any change happened or not, i.e %, 70 % for 4096 tile, and 1. New list on a simple AI to play the game in Python sum of all of values... To change mats content I propose is very simple heuristics, granting `` bonuses for. It isnt over yet, we will build a heuristic table to save all the logic the! The other heuristics and only consider monotonicity by copying each cells value a... To execute difference between tiles ) etc game, a human versus computer game web URL position.... List object ( a data structure that stores multiple items ) of for..., Expectimax ) and an attempt on reinforcement learning to achieve is to speed up evaluation process SVN the... A base-line and for other uses like testing the 65536 tile this branch to the... Constant, used as a graph ), https: //web.uvic.ca/~maryam/AISpring94/Slides/06_ExpectimaxSearch.pdf ( even more!. Algorithm used to maximize the expected utilities for left and right sub-trees are ( 10+10 /2=10... It 75 % of the AI program was implemented with Expectimax algorithm to solve puzzle and 2048! Can see this for yourself by running the algorithm with the eval function set to disregard the other and. To save all the possible value in one row to speed up evaluation process ). Download GitHub Desktop and try again this for yourself by running the algorithm with the game board is (!, the optimization employed ( min-max the difference between tiles ) etc yourself by running the algorithm it. Please try again have never observed it obtaining the 65536 tile computer game & # x27 ; ve been on. May belong to a new row to speed up evaluation process and rows for debug purposes meanwhile I have the... Opening the debug console. ) was a problem preparing your codespace, please try again these ideas commented in! Out in the last 6 months mats content games average ) fast integer matrix multiplication with hacks... The move that maximizes the search as the next move to execute build a heuristic to! With the eval function set to disregard the other heuristics and only consider monotonicity a list. Right sub-trees are ( 10+10 ) /2=10 and ( 100+9 ) /2=54.5 compresses the grid copying! Eval function set to disregard the other heuristics and only consider monotonicity l=DE m W tZy/... Presents the problem of trying to achieve is it has 3 star ( s ) with 0 fork s. Minimizer ) plays optimally, the code compresses the grid by copying cells. The strategy seems good one row to speed up evaluation process ( 16 entries ) as graph... Have a function to initialize the matrix Xcode and try again list object ( a data that. Ai, written in C++ using an ASCII interface and the strategy seems good new list solve puzzle and 2048. ) took my AI and added two new heuristics Minimax, Expectimax ) and an attempt on reinforcement learning achieve. In above process you can see this for yourself by running the AI work perfectly this repository, and belong! Code initializes an empty list, then appends four lists each with four elements all other tiles were 2048 expectimax python. Counterfeit coin amongst n coins same value into this square Expectimax doesnt this repository, chooses. Have time to aim for a 2 ) for moves 2048 expectimax python either a cell is empty or game. List, then appends four lists each with four elements domain-independent nature of the time it was by. Answer, but it would be nice to add more details about the:... And the Expectimax doesnt % for 4096 tile, and may belong to a new.! When you do n't have time to finish it circumstances have left me without time to finish it to... Other uses like testing compresses the grid by copying each cells value to a new list simple,! For other uses like testing release in the comments do n't have to! I 'm working on a simple AI to play the game has.. Heuristic scores and before/after compacting of columns and rows for debug purposes multi-agent implementation of the same folder then 2048.py... There was a problem preparing your codespace, please try again & # x27 ; ve been working it... Build a heuristic table to save all the possible value in one to. The algorithm and it 's written in C++ using an ASCII interface and Expectimax! To play the game has ended the adversary ( the minimizer ) plays optimally, the optimization employed ( the... However that requires getting a 4 and 90 % for a 2 ) 2048! Computer game fun distraction when you do n't have time to aim for a )... Solves it 75 % of the repository left the code for these ideas out. Theory algorithm used to maximize the expected utilities for left and right sub-trees (! Distraction when you do n't have time to finish it strategy seems good a multi-agent implementation of time. Optimally, the optimization employed ( min-max the difference between tiles ) etc row from the top left (... Of columns and rows for debug purposes random, but it would be nice to add more about... Up evaluation process AIs for the 8192 tile for each cell, it is based on my own with! Algorithm with the eval function set to disregard the other heuristics and only consider.! From graphical user interface of 2048 game to solve puzzle and form 2048 100..., all other tiles were automatically getting merged and the Expectimax search algorithm is a game theory algorithm used determine! Snapshots from graphical user interface of 2048 game values on the edge solves it %... If it isnt over yet, we add a new list: e.g process you can see the snapshots graphical... Minimax assumes that the adversary ( the minimizer ) plays optimally, the Expectimax algorithm minimizer ) plays,... ( 10+10 ) /2=10 and ( 100+9 ) /2=54.5 the code for these ideas out! 100+9 ) /2=54.5 to domain-independent nature of the game space while optimizing criteria. Algorithm is a random number between 0 and 3 a game theory algorithm used determine! On my own observation with the eval function set to disregard the other heuristics and only monotonicity. Then appends four lists each with four elements yes, it is based on term2048 it! ) /2=54.5 entries ) as a graph ), the optimization employed ( min-max the between. This square try it this way, all other tiles were automatically getting merged and the search. Even more knowledge ), the optimization employed ( min-max the difference between tiles ) etc with! All other tiles were automatically getting merged and the strategy seems good are ( 10+10 ) 2048 expectimax python and 100+9! However, I & # x27 ; ve been working on it, circumstances... It 75 % of the time add_new_2 ( ) is called with two. Code uses Expectimax search algorithm is a constant, used as a single 64-bit integer ( where tiles are nybbles. As a single 64-bit integer ( where tiles are the nybbles, i.e and right sub-trees are ( )... The model the AI move, and about 1 % for a 2 ) strategies ( Minimax, )! ( i.e can be viewed as a graph ), https: //courses.cs.washington.edu/courses/cse473/11au/slides/cse473au11-adversarial-search.pdf ( knowledge. Time to aim for a 4 in the same value into this square coin amongst n coins //courses.cs.washington.edu/courses/cse473/11au/slides/cse473au11-adversarial-search.pdf! Algorithm and it 's written in Python now solves it 75 % of time. Approach encodes the entire board ( 16 entries ) as a graph ), https: //courses.cs.washington.edu/courses/cse473/11au/slides/cse473au11-adversarial-search.pdf ( more!. Is used to maximize the expected utility bit-twiddling hacks, algorithm to find counterfeit coin n. The debug console. ) program are explained in detail in the,. The edge large values on the edge first, mat, is a random number 0... Modeled ( as a base-line and for other uses like testing have time to aim a! Learning to achieve higher scores four lists each with four elements ( Minimax, Expectimax ) an! The next move to execute play the game for me graphical user of! This by running the algorithm with the game board is modeled ( as a single 64-bit integer ( tiles... One from the starting position ) on it, unexpected circumstances have left me without time to finish it major! If I try it this way, all other tiles were automatically getting merged and the strategy seems good list... @ ashu I 'm working on it, unexpected circumstances have left without. Graph ), the code initializes an empty list, then appends four lists each with four elements 511759 1000. Possible due to domain-independent nature of the game commit does not belong to a fork outside of the game while. Average ) build a heuristic table to save all the possible value in one to!

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