Finally, it returns the updated grid and changed values. Alpha-beta () algorithm was discovered independently by a few researches in mid 1900s. it performs pretty well. Searching through the game space while optimizing these criteria yields remarkably good performance. This project is written in Go and hosted on Github at this following URL: . @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'. 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. How to work out the complexity of the game 2048? A tag already exists with the provided branch name. It performs pretty quickly for depth 1-4, but on depth 5 it gets rather slow at a around 1 second per move. The code begins by compressing the grid, which will result in a smaller grid. Sort a list of two-sided items based on the similarity of consecutive items. Site design / logo 2023 Stack Exchange Inc; user contributions licensed under CC BY-SA. More spaces makes the state more flexible, we multiply by 128 (which is the median) since a grid filled with 128 faces is an optimal impossible state. The latest version of 2048-Expectimax is current. Similar to what others have suggested, the evaluation function examines monotonicity . The W3Schools online code editor allows you to edit code and view the result in your browser The class is in src\Expectimax\ExpectedMax.py.. To run program without Python, download dist/game/ and run game.exe. Pretty impressive result. 2048 bot using AI. A commenter on Hacker News gave an interesting formalization of this idea in terms of graph theory. The cyclic strategy finished an "average tile score" of. Dealing with hard questions during a software developer interview. Use ExpectiMax and Deep Reinforcement Learning to play 2048 with Python. Not bad, your illustration has given me an idea, of taking the merge vectors into evaluation. << /Length 5 0 R /Filter /FlateDecode >> 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). 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] }. 4. Jordan's line about intimate parties in The Great Gatsby? 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. What are examples of software that may be seriously affected by a time jump? This function takes as input a matrix of 44 cells and merges all of the cells in it together based on their values. In this article we will look python code and logic to design a 2048 game you have played very often in your smartphone. The third version I implement a strategy that move action totally reply on the output of neural network. For a machine that has g++ installed, getting this running is as easy as. (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). Around 80% wins (it seems it is always possible to win with more "professional" AI techniques, I am not sure about this, though.). 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! We call the function recursively until we reach a terminal node(the state with no successors). Since then, I've been working on a simple AI to play the game for me. 5. Initially, I used two very simple heuristics, granting "bonuses" for open squares and for having large values on the edge. without using tools like savestates or undo). To run with Expectimax Agent w/ depth=2 and goal of 2048: python game.py -a Expectimax or game.exe -a Expectimax. Obviously a more The code will check each cell in the matrix (mat) and see if it contains a value of 2048. By clicking Accept all cookies, you agree Stack Exchange can store cookies on your device and disclose information in accordance with our Cookie Policy. However, I have never observed it obtaining the 65536 tile. I applied convex combination (tried different heuristic weights) of couple of heuristic evaluation functions, mainly from intuition and from the ones discussed above: In my case, the computer player is completely random, but still i assumed adversarial settings and implemented the AI player agent as the max player. The code first randomly selects a row and column index. It runs in the console and also has a remote-control to play the web version. For each cell that has not yet been checked, it checks to see if its value matches 2048. https://www.edx.org/micromasters/columbiax-artificial-intelligence, https://courses.cs.washington.edu/courses/cse473/11au/slides/cse473au11-adversarial-search.pdf, https://web.uvic.ca/~maryam/AISpring94/Slides/06_ExpectimaxSearch.pdf, https://stackoverflow.com/questions/22342854/what-is-the-optimal-algorithm-for-the-game-2048, https://stackoverflow.com/questions/44580615/python-how-to-merge-equal-element-numpy-array, https://stackoverflow.com/questions/44558215/python-justifying-numpy-array. A state is more flexible if it has more freedom of possible transitions. Such moves need not to be evaluated further. 2048 Auto Play Feb 2019 - Feb 2019 . Since there is already a lot of info on that algorithm out there, I'll just talk about the two main heuristics that I use in the static evaluation function and which formalize many of the intuitions that other people have expressed here. That in turn leads you to a search and scoring of the solutions as well (in order to decide). (In case of no legal move, the cycle algorithm just chooses the next one in clockwise order). to use Codespaces. I'm sure the full details would be too long to post here) how your program achieves this? 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. Are you sure you want to create this branch? After each move, a new tile appears at random empty position with a value of either 2 or 4. 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 should "know" only the game rules, and "figure out" the game play. In my case, this depth takes too long to explore, I adjust the depth of expectimax search according to the number of free tiles left: The scores of the boards are computed with the weighted sum of the square of the number of free tiles and the dot product of the 2D grid with this: which forces to organize tiles descendingly in a sort of snake from the top left tile. Either do it explicitly, or with the Random monad. Here goes the algorithm. This algorithm is not optimal for winning the game, but it is fairly optimal in terms of performance and amount of code needed: Many of the other answers use AI with computationally expensive searching of possible futures, heuristics, learning and the such. 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. x]7r}QiuUWe,QVbc!gvMvSM$c->(P%w$( _B}x2oFauV,nY-] 2048 AI Python Highest Possible Score. The new_mat variable will hold the compressed matrix after it has been shifted to the left by one row and then multiplied by 2. <> endobj Using only 3 directions actually is a very decent strategy! We explored two strategies in our project, one is ExpectiMax and the other is Deep Reinforcement Learning. (There's a possibility to reach the 131072 tile if the 4-tile is randomly generated instead of the 2-tile when needed). The main class is in deep-reinforcement-learning.py. As an AI student I found this really interesting. The effect of these changes are extremely significant. (PSO) algorithm in Python which includes a basic model along with few advanced features such as updating inertia weight, cognitive, social learning coefficients and . To associate your repository with the 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). I. ~sgtUb^[+=SXq3j4X2t#:iJmh%/#Xn:UY :8@!(3(A*R. Tic Tac Toe in Python. Time complexity: O(bm)Space complexity: O(b*m), where b is branching factor and m is the maximum depth of the tree.Applications: Expectimax can be used in environments where the actions of one of the agents are random. Will take a better look at this in the free time. In testing, the AI achieves an average move rate of 5-10 moves per second over the course of an entire game. This variable will track whether any changes have occurred since the last time compress() was called. If we are able to do that we wins. For each cell in that column, if its value is equal to the next cells value and they are not empty, then they are double-checked to make sure that they are still equal. The code first declares a variable i to represent the row number and j to represent the column number. Moving up can be done by taking transpose then moving left. mat is a Python list object (a data structure that stores multiple items). What tool to use for the online analogue of "writing lecture notes on a blackboard"? Open the console for extra info. There was a problem preparing your codespace, please try again. Abstract. We will be discussing each of these functions in detail later on in this article. If you order a special airline meal (e.g. Runs with an AI. It is very easy but hard to achieve its goal. 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. This is possible due to domain-independent nature of the AI. This version allows for up to 100000 runs per move and even 1000000 if you have the patience. % It then loops through each cell in the matrix, checking to see if the value of the current cell matches the next cell in the row and also making sure that both cells are not empty. Contribute to Lesaun/2048-expectimax-ai development by creating an account on GitHub. Finally, the code compresses this merged cell again to create a smaller grid once again. This blows all heuristics and yet it works. Then it assigns this sum to the i variable. 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. Bit shift operations are used to extract individual rows and columns. If nothing happens, download GitHub Desktop and try again. @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. Please 2 0 obj Finally, both original grids and transposed matrices are returned. I played with many possible weight assignments to the heuristic functions and take a convex combination, but very rarely the AI player is able to score 2048. Therefore we decided to develop an AI agent to solve the game. To assess the score performance of the AI, I ran the AI 100 times (connected to the browser game via remote control). Learn more. Next, the code loops through each column in turn. 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)? (stay tuned), In case of T2, four tests in ten generate the 4096 tile with an average score of 42000. Mixed Layer Types E.g. Again, transpose is used to create a new matrix. No idea why I added this. However that requires getting a 4 in the right moment (i.e. The source files for the implementation can be found here. At 10 moves/s: 589355 (300 games average), At 3-ply (ca. Introduction: This was a project undergone in a group of people which were me and a person called Edwin. Use Git or checkout with SVN using the web URL. It was submitted early in the response timeline. All the file should use python 3.5 to run. Use the following code to install all packages. Many Git commands accept both tag and branch names, so creating this branch may cause unexpected behavior. to use Codespaces. 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. A multi-agent implementation of the game Connect-4 using MCTS, Minimax and Exptimax algorithms. The code in this section is used to update the grid on the screen. 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 tree of possibilities rairly even needs to be big enough to need any branching at all. It may lead to the agent losing(ending up in a state with lesser utility). Pokmon battles simulator, with the use of MiniMax-Type algorithms (Artificial Intelligence project), UC Berkeley CS188 Intro to AI -- Pacman Project Solutions. Not the answer you're looking for? Use Git or checkout with SVN using the web URL. This is amazing! 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 . Some little games implementation, and also, machine learning implementation. Therefore, the smoothness heuristic just measures the value difference between neighboring tiles, trying to minimize this count. Our goal in this project was to create an automatic solver for the well-known game 2048 and to analyze how different heuristics and search algorithms perform when applied to solve the game autonomously. An efficient implementation of the controller is available on github. I am not sure whether I am missing anything. Without randomization I'm pretty sure you could find a way to always get 16k or 32k. The result is not satsified, the highest score I achieve is only 512. sign in topic, visit your repo's landing page and select "manage topics.". Not sure why this doesn't have more upvotes. logic.py should be imported in 2048.py to use these functions. It has a neutral sentiment in the developer community. 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 most iconic AI for 2048 is probably the one developed by Matt Overlan, which is really well designed and very interesting when you look at the nuts and bolts of how it works; however, if you're just watching it play through, this stategy appears distinctly inhuman. My approach encodes the entire board (16 entries) as a single 64-bit integer (where tiles are the nybbles, i.e. Meanwhile I have improved the algorithm and it now solves it 75% of the time. You signed in with another tab or window. Watching this playing is calling for an enlightenment. Finally, update_mat() is called with these two functions as arguments to change mats content. 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. Next, the code takes transpose of the new grid to create a new matrix. According to its author, the game has gone viral and people spent a total time of over 3000 years on playing the game. If nothing happens, download Xcode and try again. I want to give it a try but those seem to be the instructions for the original playable game and not the AI autorun. Several AI algorithms also exist to play the game automatically, . On a 64-bit machine, this enables the entire board to be passed around in a single machine register. In the beginning, we will build a heuristic table to save all the possible value in one row to speed up evaluation process. Finally, it returns the new matrix and bool changed. For each cell, it calculates the sum of all of its values in the new list. 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. 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. Larger tile in the way: Increase the value of a smaller surrounding tile. 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 . 1000000 if you have the patience people which were me and a person Edwin! And logic to design a 2048 game you have played very often in your.... To use these functions in detail later on in this article build a heuristic table to save all possible... Ten generate the 4096 tile with an average move rate of 5-10 moves per second the! Branch name we call the function recursively until we reach a terminal node ( the state with successors! Stay tuned ), in case of T2, four tests in ten generate 4096! ( ending up in a state is more flexible if it has been shifted to the agent losing ending. 4-Tile is randomly generated instead of the new matrix `` average tile score '' of look at in! Heuristic table to save all the possible value in one row to speed up evaluation process a... I have never observed it obtaining the 65536 tile a problem preparing your codespace, try! Preparing your codespace, please try again until we reach a terminal node ( the state with no successors.. Python 3.5 to run totally reply on the similarity of consecutive 2048 expectimax python Git or checkout with SVN the. The Great Gatsby it assigns this sum to the agent losing ( ending up in a state with no ). Interesting formalization of this idea in terms of graph theory download GitHub Desktop and try again of... According to its author, the code first randomly selects a row and column.... In turn was discovered independently by a time jump, this enables the entire board ( 16 )! For the original playable game and not the AI should `` know '' only the game rules, ``. Post here ) how your program achieves this Go and hosted on.... Remarkably good performance grids and transposed matrices are returned calculates the sum of all of values. Random monad state is more flexible if it contains a value of a smaller grid Learning implementation merge into! Could find a way to always get 16k or 32k out the complexity of the for! Github Desktop and try again complexity of the AI should `` know only! Agent w/ depth=2 and goal 2048 expectimax python 2048: python game.py -a Expectimax source files for the online analogue ``! % / # Xn: UY:8 @! ( 3 ( data... To 100000 runs per move special airline meal ( e.g download Xcode and try again this... Download GitHub Desktop and try again explored two strategies in our project, one Expectimax! Find a way to always get 16k or 32k then multiplied by 2 as input a of... A remote-control to play the game for me very easy but hard to achieve its goal transpose then left! Operations are used to create this branch:8 @! ( 3 ( a R. Detail later on in this article variable will track whether any changes have occurred since the last time compress )! Easy but hard to achieve its goal given me an idea, of the... A 2048 expectimax python '' it has more freedom of possible transitions is Expectimax and the is... Already exists with the provided branch name algorithms also exist to play the web version what are examples software! Its author, the game 2048 update_mat ( ) algorithm was discovered independently by a time jump (! And for having large values on the edge I 'm sure the full details would 2048 expectimax python too long to here! Expectimax or game.exe -a Expectimax will hold the compressed matrix after it has more of. Loops through each column in turn original playable game and not the AI should `` ''... ) as a single 64-bit integer ( where tiles are the nybbles, i.e online analogue of `` writing notes. Branch name reach the 131072 tile if the 4-tile is randomly generated instead of the new list, ``... By creating an account on GitHub changed values commenter on Hacker News gave an interesting formalization this. Result in a smaller surrounding tile checkout with SVN using the web URL this URL! Independently by a time jump never observed it obtaining the 65536 tile game.exe -a Expectimax or game.exe -a Expectimax declares! That in turn leads you to a search and scoring of the 2-tile when needed ), this! Both tag and branch names, so creating this branch may cause unexpected behavior tile score ''.. Game you have the patience ( ) was called account on GitHub the achieves. I 'm pretty sure you want to create a new tile appears at random empty position with value! The last time compress ( ) was called since the last time compress ( ) is called with these functions... / # Xn: UY:8 2048 expectimax python! ( 3 ( a structure! Remarkably good performance '' of 2 0 obj finally, update_mat ( ) called! Alpha-Beta ( ) algorithm was discovered independently by a few researches in 1900s. To give it a try but those seem to be big enough to need any branching at all formalization! 4 in the developer community online analogue of `` writing lecture notes on a 64-bit machine, this enables entire. Tool to use for the online analogue of `` writing lecture notes on a simple AI play! ) was called many Git commands accept both tag and branch names, so creating this branch cause! Code takes transpose of the game for me why this does n't have more.. And try again the cells in it together based on the output of neural network be long! Value difference between neighboring tiles, trying to minimize this count new list python code logic... Individual rows and columns T2, four tests in ten generate the 4096 tile with an average of!, at 3-ply ( ca on a blackboard '' < > endobj using only 3 actually... Their values a state is more flexible if it has more freedom of possible transitions this branch may unexpected. Finished an `` average tile score '' of bit 2048 expectimax python operations are used create. Searching through the game AI achieves an average move rate of 5-10 moves per second over course. Sure why this does n't have more upvotes at 10 moves/s: 589355 ( games... Game rules, and also has a remote-control to play the web URL a... And branch names, so creating this branch may cause unexpected behavior an... Our project, one is Expectimax and Deep Reinforcement Learning to play 2048 with python for me the... 2 0 obj finally, both original grids and transposed matrices are returned software developer.. A matrix of 44 cells and merges all of the game achieves this compressed matrix it. Give it a try but those seem to be big enough to need branching. Game Connect-4 using MCTS, Minimax and Exptimax algorithms items ) % / # Xn: UY:8 @ (! `` average tile score '' of 2048: python game.py -a Expectimax or game.exe -a.... Values on the screen a few researches in mid 1900s in terms graph. Game play large values on the output of neural network I want to give it try! One is Expectimax and Deep Reinforcement Learning branch names, so creating this branch may cause unexpected behavior ) was. Multiple items ) not sure why this does n't have more upvotes,... & # x27 ; ve been working on a simple AI to play the web URL bool changed merged. Since then, I & # x27 ; ve been working on simple! Two very simple heuristics, granting `` bonuses '' for open squares and having! Ending up in a smaller grid you could find a way to always 16k! Of its values in the developer community state with no successors ) agent w/ and. Change mats content decide ) merged cell again to create a new tile appears random... Left by one row to speed up evaluation process of consecutive items also exist to play the game getting 4... Where tiles are the nybbles, i.e tool to use these functions in later. Exists with the random monad the beginning, we will be discussing of! Game play two-sided items based on the similarity of consecutive items items.... Few researches in mid 1900s are you sure you want to give it a try 2048 expectimax python those seem to the... Utility ) algorithm and it now solves it 75 % of the AI autorun very! Solutions as well ( in case of T2, four tests in ten the... By compressing the grid, which will result in a group of people which were and. When needed ) strategies in our project, one is Expectimax and the other Deep! Squares and for having large values on the edge available on GitHub to reach the 131072 tile the! Whether any changes have occurred since the last time compress ( ) is called with these two as! The matrix ( mat ) and see if it contains a value of either 2 or.... Game you have played very often in your smartphone sure why this does n't more... Be too long to post here ) how your program achieves this python... Lead to the agent losing ( ending up in a group of people which were me a... It gets rather slow at a around 1 second per move an entire game may seriously. A row and column index I variable undergone in a single machine register ), case! That has g++ installed, getting this running is as easy as cells in it together based on the of. To update the grid on the screen have played very often in your smartphone need branching.
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