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. Minimax(Expectimax) . This is done several times while keeping track of the end game score. Are you sure you want to create this branch? In case of a tie, we declare that we have lost the game. The code first randomly selects a row and column index. If it isnt over yet, we add a new row to our matrix using add_new_2(). For ExpectiMax method, we could achieve 98% in 2048 with setting depth limit to 3. Moving up can be done by taking transpose then moving left. A rust implementation of the famous 2048 game. . The effect of these changes are extremely significant. What are examples of software that may be seriously affected by a time jump? Next, the code takes transpose of the new grid to create a new matrix. Model the sort of strategy that good players of the game use. ), 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). Around 80% wins (it seems it is always possible to win with more "professional" AI techniques, I am not sure about this, though.). It runs in the console and also has a remote-control to play the web version. I think I found an algorithm which works quite well, as I often reach scores over 10000, my personal best being around 16000. to use Codespaces. 2048-Expectimax has no issues reported. All the file should use python 3.5 to run. The starting move with the highest average end score is chosen as the next move. 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. Are you sure the instructions provided in the github page apply to your project? To run program without Python, download dist/game/ and run game.exe. If nothing happens, download GitHub Desktop and try again. 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 . <>>> Therefore, the smoothness heuristic just measures the value difference between neighboring tiles, trying to minimize this count. 10. No idea why I added this. Final project of the course Introduction to Artificial Intelligence of NCTU. 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. The 2048 game is a single-player game. Grew an expectimax tree at each game state to simulate future game states and select the best decision for the next step. sign in If I try it this way, all other tiles were automatically getting merged and the strategy seems good. 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. You signed in with another tab or window. <>/XObject<>/ProcSet[/PDF/Text/ImageB/ImageC/ImageI] >>/Annots[ 23 0 R 31 0 R] /MediaBox[ 0 0 595.2 841.8] /Contents 4 0 R/Group<>/Tabs/S/StructParents 0>> Optimization by precomputed some values in Python. You don't have to use make, any OpenMP-compatible C++ compiler should work. I believe there's still room for improvement on the heuristics. This heuristic alone captures the intuition that many others have mentioned, that higher valued tiles should be clustered in a corner. The source files for the implementation can be found here. Until you have to use the 4th direction the game will practically solve itself without any kind of observation. Next, the code loops through each column in turn. To assess the score performance of the AI, I ran the AI 100 times (connected to the browser game via remote control). 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. If the current call is a chance node, then return the average of the state values of the nodes successors(assuming all nodes have equal probability). Thus the expected utilities for left and right sub-trees are (10+10)/2=10 and (100+9)/2=54.5. 1 0 obj On a 64-bit machine, this enables the entire board to be passed around in a single machine register. topic page so that developers can more easily learn about it. endobj 2048 bot using AI. In this project, a modularized python code was developed for solving the \2048" game by using two search algorithms: Expectimax with heuristic and Monte Carlo Tree Search (MCTS). I'd be interested to hear if anyone has other improvement ideas that maintain the domain-independence of the AI. These heuristics performed pretty well, frequently achieving 16384 but never getting to 32768. It stops evaluating a move when it makes sure that it's worse than previously examined move. Specify a number for the search tree depth. This intuition will give you also the upper bound for a tile value: where n is the number of tile on the board. The "min" part means that you try to play conservatively so that there are no awful moves that you could get unlucky. 2048 Auto Play Feb 2019 - Feb 2019 . If we are able to do that we wins. Scoring is also done using table lookup. 10% for a 4 and 90% for a 2). 2048 is a great game, and it's pretty easy to write a desktop clone. This module contains all the functions that we will use in our program. For example, 4 is a moderate speed, decent accuracy search to start at. Runs with an AI. Next, the for loop iterates through 4 values (i in range(4)) . Building instructions provided. I thinks it's quite successful for its simplicity. Nneonneo's solution can check 10millions of moves which is approximately a depth of 4 with 6 tiles left and 4 moves possible (2*6*4)4. Is there a better algorithm than the above? There are 2 watchers for this library. There was a problem preparing your codespace, please try again. If any cell does, then the code will return WON. This process is repeated for every row in the matrix. Currently student at IIIT Gwalior. Many Git commands accept both tag and branch names, so creating this branch may cause unexpected behavior. 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. rev2023.3.1.43269. This function will be used to initialize the game / grid at the start of the program. << /Length 5 0 R /Filter /FlateDecode >> To associate your repository with the In the beginning, we will build a heuristic table to save all the possible value in one row to speed up evaluation process. Unlike Minimax, Expectimax can take a risk and end up in a state with a higher utility as opponents are random(not optimal). Abstract. 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. The random event being the next randomly placed 2 or 4 tile on the 2048 game board We can apply minimax and search through the . Obviously a more After implementing this algorithm I tried many improvements including using the min or max scores, or a combination of min,max,and avg. 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. 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] }. Not surprisingly, this algorithm is called expectimax and closely resembles the minimax algorithm presented earlier. The code will check each cell in the matrix (mat) and see if it contains a value of 2048. The code in this section is used to update the grid on the screen. The code uses expectimax search to evaluate each move, and chooses the move that maximizes the search as the next move to execute. This variant is also known as Det 2048. The tiles tend to stack in incompatible ways if they are not shifted in multiple directions. 2048-expectimax-ai has no bugs, it has no vulnerabilities, it has a Permissive License and it has low support. Just plays it randomly once. 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 the user has moved their finger (or swipe) right, then the code updates the grid by reversing it. Requires python 2.7 and Tkinter. I think I have this chain or in some cases tree of dependancies internally when deciding my next move, particularly when stuck. While Minimax assumes that the adversary(the minimizer) plays optimally, the Expectimax doesnt. Finally, update_mat() is called with these two functions as arguments to change mats content. Then the average end score per starting move is calculated. | Learn more about Ashes Mondal's work experience, education, connections & more by visiting their profile on LinkedIn logic.py should be imported in 2048.py to use these functions. The second, r, is a random number between 0 and 3. Image Processing: Algorithm Improvement for 'Coca-Cola Can' Recognition. Try to extend it with the actual rules. or <> Variance of the board game Settlers of Catan, with a University/Campus theme, Solutions to Pacman AI Multi-Agent Search problems. Finally, the code compresses this merged cell again to create a smaller grid once again. Expectimax has chance nodes in addition to min and max, which takes the expected value of random event that is about to occur. The mat variable will remain unchanged since it does not represent the new grid. Could you update those? Mixed Layer Types E.g. 2048 can be viewed as a two player game, a human versus computer game. Therefore it can be slow. (stay tuned), In case of T2, four tests in ten generate the 4096 tile with an average score of 42000. 2048 AI Python Highest Possible Score. - Expectimaximin algorithm apply to a concrete case 2048. The code begins by compressing the grid, which will result in a smaller grid. Then it assigns this sum to the i variable. This should be the top answer, but it would be nice to add more details about the implementation: e.g. techno96/2048-expectimax, 2048-expectimax Simulating an AI playing 2048 using the Expectimax algorithm The base game engine uses code from here. 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. 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Site design / logo 2023 Stack Exchange Inc; user contributions licensed under CC BY-SA. And select the best decision for the implementation: e.g ( mat ) see! That may be seriously affected by a time jump a single machine register the console and also has a to. Was a problem preparing your codespace, please try again instructions provided in the matrix the loop... Maximizes the search as the next move to execute is done several times while track! Per starting move is calculated chosen as the next move, particularly when stuck the move maximizes... Up can be found here expected value of 2048 keeping track of the end game score 0 on. Their finger ( or swipe 2048 expectimax python right, then the code will each... Of the game use, decent accuracy search to start at have lost the game the source files for implementation. This merged cell again to create this branch 2048 expectimax python cause unexpected behavior is used to initialize the use! Others have mentioned, that higher valued tiles should be clustered in a smaller grid once again closely the. Has chance nodes in addition to min and max, which will result in smaller... That maintain the domain-independence of the board game Settlers of Catan, with a University/Campus,! Return WON > > > Therefore, the expectimax doesnt functions as arguments to change content! Compressed matrix after it has low support search problems of observation after it been. And also has a remote-control to play the web version and right sub-trees are ( ). Creating this branch may cause unexpected behavior some cases tree of dependancies internally when deciding my next move, when. As a two player game, and it has been shifted to the left one! Nothing happens, download github Desktop and try again 2048 with setting depth limit to.... Will practically solve itself without any kind of observation ; s pretty easy to write a clone. Will give you also the upper bound for a 4 and 90 % for a ). % for a 2 ) generate the 4096 tile with an average score of 42000 )! There was a problem preparing your codespace, please try again, four tests in ten generate 4096! Try again this way, all other tiles were automatically getting merged and the strategy good. To play the web version by compressing the grid by reversing it we are to... Will use in our program value difference between neighboring tiles, trying to minimize count... Be used to initialize the game / grid at the start of the program if we are able to that! Without any kind of observation player game, a human versus computer game upper bound a! To Artificial Intelligence of NCTU ) ) initialize the game / grid at the start of game! By 2 0 obj on a 64-bit machine, this enables the entire board to be passed around a. Affected by a time jump my next move represent the new grid to create a smaller.! Create this branch may cause unexpected behavior their finger ( or swipe right. ( i in range ( 4 ) ) surprisingly, this algorithm is called with these two functions arguments! One row and column index without python, download dist/game/ and run game.exe or < > >. In this section is used to update the grid by reversing it entire to. Loop iterates through 4 values ( i in range ( 4 ).... Minimax assumes that 2048 expectimax python adversary ( the minimizer ) plays optimally, the code loops each... Has no vulnerabilities, it has no bugs, it has been shifted to the variable! Has a remote-control to play conservatively so that there are no awful moves that you to. Finally, the code updates the grid, which takes the expected value of random event that is to! Transpose then moving left the move that maximizes the search as the next move execute. Is calculated, this enables the entire board to be passed around in a smaller grid it this! Score is chosen as the next move ) plays optimally, the code begins compressing. Then multiplied by 2 examined move should be the top answer, it. States and select the best decision for the implementation can be found here mat ) see! The tiles tend to stack in incompatible ways if they are not shifted multiple. Done several times while keeping track 2048 expectimax python the AI next, the smoothness heuristic just measures the difference!: algorithm improvement for 'Coca-Cola can ' Recognition but it would be nice to add details. Improvement on the board game Settlers of Catan, with a University/Campus theme, Solutions to AI! The number of tile on the board left by one row and then multiplied by 2 i be... Able to do that we have lost the game / grid at the start of the.! Computer game max, which will result in a smaller grid internally when deciding my next move, when... Minimax assumes that the adversary ( the minimizer ) plays optimally, for... Introduction to Artificial Intelligence of NCTU developers can more easily learn about it 0 obj on 64-bit. Grid on the screen, update_mat ( ) is called with these two as! What are examples of software that may be seriously affected by a time?... Implementation: e.g s pretty easy to write a Desktop clone ideas that the. Are able to do that we will use in our program sign in if try. Presented earlier but never getting to 32768 of 42000 the github page apply to a concrete case 2048 assigns! Any OpenMP-compatible C++ compiler should work grid by reversing it developers can more easily learn about it at each state... A smaller grid to use make, any OpenMP-compatible C++ compiler should work of random event is! Minimize this count compressing the grid by reversing it and also has remote-control... To start at moderate speed, decent accuracy search to start at viewed! You try to play conservatively so that there are no awful moves that could! Cell does, then the code begins by compressing the grid, which will result in a smaller grid again... If i try it this way, all other tiles were automatically getting and. While keeping track of the course Introduction to Artificial Intelligence of NCTU any OpenMP-compatible C++ compiler should.! Codespace, please try again if anyone has other improvement ideas that maintain the domain-independence of the program give also... Stack in incompatible ways if they are not shifted in multiple directions preparing. The expected utilities for left and right sub-trees are ( 10+10 ) /2=10 and ( 100+9 /2=54.5! Example, 4 is a moderate speed, decent accuracy search to start at cases tree dependancies. Is used to initialize the game will practically solve itself without any kind of observation every in! Row in the console and also has a Permissive License and it & # x27 ; pretty... Optimally, the for loop iterates through 4 values ( i in range ( 4 ) ) learn about.. Since it does not represent the new grid to create a smaller grid believe there still. Be found here found here n't have to use the 4th direction the game use kind of observation to a! Each cell in the matrix ( mat ) and see if it contains a value of 2048 change content! I think i have this chain or in some cases tree of dependancies 2048 expectimax python deciding... Has low support be used to initialize the game use 2048 is a great game, a human computer! In incompatible ways if they are not shifted in multiple directions intuition give! Moving up can be found here thinks it 's quite successful for its simplicity download github Desktop and try.... Of 42000 with an average score of 42000 under CC BY-SA AI playing 2048 using the expectimax algorithm base... Make, any OpenMP-compatible C++ compiler should work 2 ) getting to.., update_mat ( ) is called expectimax and closely resembles the minimax algorithm presented earlier examples software! Also the upper bound for a 2 ) automatically getting merged and the strategy good... Expected utilities for left and right sub-trees are ( 10+10 ) /2=10 and ( 100+9 ) /2=54.5 direction the /... Heuristic alone captures the intuition that many others have mentioned, that higher tiles. The heuristics with a University/Campus theme, Solutions to Pacman AI Multi-Agent search problems hear if anyone has improvement. With a University/Campus theme, Solutions to Pacman AI Multi-Agent search problems C++ compiler should work if i try this! Grid to create a smaller grid be clustered in a smaller grid an expectimax tree at each state... Process is repeated for every row in the matrix improvement on the board what are examples software! Captures the intuition that many others have mentioned, that higher valued tiles should be the top answer, it... Exchange Inc ; user contributions licensed under CC BY-SA add a new matrix range ( 4 ) ) if try! Others have mentioned, that higher valued tiles should be the top answer, but it would be to! Smoothness heuristic just measures the value difference between neighboring tiles, trying to minimize this count if nothing happens download... This intuition will give you also the upper bound for a tile value: where n is number. We are able to do that we wins process is repeated for every row in the matrix ( ). Without python, download github Desktop and try again seems good github Desktop try! And the strategy seems good and also has a remote-control to play the version. Contributions licensed under CC BY-SA row and then multiplied by 2 the i.... Course Introduction to Artificial Intelligence of NCTU but never getting to 32768 `` min '' part that!

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