2048 expectimax python

The starting move with the highest average end score is chosen as the next move. Here's a screenshot of a perfectly smooth grid. Rest cells are empty. Several linear path could be evaluated at once, the final score will be the maximum score of any path. First, it creates two new variables, new_grid and changed. This file contains all the functions used in this project. (source), Later, in order to play around some more I used @nneonneo highly optimized infrastructure and implemented my version in C++. I am an aspiring developer with experience in building web-based application, have a good understanding of python language and a competitive programmer with passion for learning and solving challenging problems. If no change occurred, then the code simply creates an empty grid. It had no major release in the last 6 months. 10% for a 4 and 90% for a 2). The game contrl part code are used from 2048-ai. But we didn't achieve a good result in deep reinforcement learning method, the max tile we achieved is 512. Sort a list of two-sided items based on the similarity of consecutive items. In ExpectiMax strategy, we tried 4 different heuristic functions and combined them to improve the performance of this method. The while loop runs until the user presses any of the keyboard keys (W, S, A, D). I got very frustrated with Haskell trying to do that, but I'm probably gonna give it a second try! xkcdxkcd Larger tile in the way: Increase the value of a smaller surrounding tile. 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. 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. Use Git or checkout with SVN using the web URL. The code is available at https://github.com/nneonneo/2048-ai. 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. These are impressive and probably the correct way forward, but I wish to contribute another idea. If you recall from earlier in this chapter, these are references to variables that store data about our game board. If there have been no changes, then changed is set to False . These heuristics performed pretty well, frequently achieving 16384 but never getting to 32768. Otherwise, the code keeps checking for moves until either a cell is empty or the game has ended. The tables contain heuristic scores computed on all possible rows/columns, and the resultant score for a board is simply the sum of the table values across each row and column. Next, transpose() is called to interleave rows and column. What is the optimal algorithm for the game 2048? On a 64-bit machine, this enables the entire board to be passed around in a single machine register. A rust implementation of the famous 2048 game. Each function in logic takes two arguments: mat and flag. It just got me nearly to the 2048 playing the game manually. Runs with an AI. This is amazing! endobj The cyclic strategy finished an "average tile score" of. I left the code for these ideas commented out in the C++ code. The changed variable will keep track of whether the cells in the matrix have been modified. It is based on term2048 and it's written in Python. 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 evaluation function tries to keep the rows and columns monotonic (either all decreasing or increasing) while minimizing the number of tiles on the grid. The state-value function uses an n-tuple network, which is basically a weighted linear function of patterns observed on the board. The various heuristics are weighted and combined into a positional score, which determines how "good" a given board position is. Similar to what others have suggested, the evaluation function examines monotonicity . A-143, 9th Floor, Sovereign Corporate Tower, We use cookies to ensure you have the best browsing experience on our website. Do EMC test houses typically accept copper foil in EUT? Learn more. Introduction. 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. According to its author, the game has gone viral and people spent a total time of over 3000 years on playing the game. This is the first article from a 3-part sequence. Scoring is also done using table lookup. Expectimax algorithm helps take advantage of non-optimal opponents. Here I assume you already know how the minimax algorithm works in general and only focus on how to apply it to the 2048 game. mat is the matrix object and flag is either W for moving up or S for moving down. 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. This one will consist of planning our game-playing program at a conceptual level, and in the next 2 articles, we'll see the actual Python implementation. My approach encodes the entire board (16 entries) as a single 64-bit integer (where tiles are the nybbles, i.e. 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. 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. My solution does not aim at keeping biggest numbers in a corner, but to keep it in the top row. 10% for a 4 and 90% for a 2). Answer (1 of 2): > I developed a 2048 AI using expectimax optimization, instead of the minimax search used by @ovolve's algorithm. Source code(Github): https://github.com . This is necessary in order to move right or up. If nothing happens, download GitHub Desktop and try again. If any cells have been modified, then their values will be updated within this function before it returns them back to the caller. just place both the files in the same folder then run 2048.py will work perfectly. The first version in just a draft, the second one use CNN as an architecture, and this method could achieve 1024, but its result actually not very depend on the predict result. Then it calls the reverse() function to reverse the matrix. 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. Such moves need not to be evaluated further. The result: sheer impossibleness. It may fail due to simple bad luck close to the end (you are forced to move down, which you should never do, and a tile appears where your highest should be. There was a problem preparing your codespace, please try again. At what point of what we watch as the MCU movies the branching started? techno96/2048-expectimax, 2048-expectimax Simulating an AI playing 2048 using the Expectimax algorithm The base game engine uses code from here. The code inside this loop will be executed until user presses any other key or the game is over. 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. 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. If it does not, then the code declares victory for the player and ends the program execution. And that's it! 1500 moves/s): 511759 (1000 games average). sign in It will typically prevent smaller valued tiles from getting orphaned and will keep the board very organized, with smaller tiles cascading in and filling up into the larger tiles. What tool to use for the online analogue of "writing lecture notes on a blackboard"? In theory it's alternating 2s and 4s. However that requires getting a 4 in the right moment (i.e. Congratulations ! The 2048 game is a single-player game. The precise choice of heuristic has a huge effect on the performance of the algorithm. Connect and share knowledge within a single location that is structured and easy to search. A multi-agent implementation of the game Connect-4 using MCTS, Minimax and Exptimax algorithms. If two cells have been merged, then the game is over and the code returns GAME NOT OVER.. There seems to be a limit to this strategy at around 80000 points with the 4096 tile and all the smaller ones, very close to the achieving the 8192 tile. That will get you stuck, so you need to plan ahead for the next moves. << /Length 5 0 R /Filter /FlateDecode >> Final project of the course Introduction to Artificial Intelligence of NCTU. Searching later I found this algorithm might be classified as a Pure Monte Carlo Tree Search algorithm. to use Codespaces. Thanks. <> 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 first thing that this function does is declare an empty list called mat . (PSO) algorithm in Python which includes a basic model along with few advanced features such as updating inertia weight, cognitive, social learning coefficients and . Initially two random cells are filled with 2 in it. Watching this playing is calling for an enlightenment. I became interested in the idea of an AI for this game containing no hard-coded intelligence (i.e no heuristics, scoring functions etc). (stay tuned), In case of T2, four tests in ten generate the 4096 tile with an average score of 42000. Optimization by precomputed some values in Python. The code then moves the grid left using the move_left function. Also, I tried to increase the search depth cut-off from 3 to 5 (I can't increase it more since searching that space exceeds allowed time even with pruning) and added one more heuristic that looks at the values of adjacent tiles and gives more points if they are merge-able, but still I am not able to get 2048. If any cell does, then the code will return WON. If nothing happens, download Xcode and try again. Finally, an Expectimax strategy with pruned trees outperformed others and get a winning tile two times as high as the original winning target. Not surprisingly, this algorithm is called expectimax and closely resembles the minimax algorithm presented earlier. One, I need to follow a well-defined strategy to reach the goal. Around 80% wins (it seems it is always possible to win with more "professional" AI techniques, I am not sure about this, though.). By using our site, you 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). Just try to keep the top row filled, so moving left does not break the pattern), but basically you end up having a fixed part and a mobile part to play with. How can I figure out which tiles move and merge in my implementation of 2048? Expectimax is not optimal. game.exe -a Expectimax. The grid is represented as a 16-length array of Integers. The first, mat, is an array of four integers. This algorithm is a variation of the minmax. These lists represent the cells on the game / grid. Expectimax is also a variation of minimax game tree algorithm. If it has not, then the code checks to see if any cells have been merged. Use ExpectiMax and Deep Reinforcement Learning to play 2048 with Python. The second heuristic counted the number of potential merges (adjacent equal values) in addition to open spaces. The code begins by compressing the grid, which will result in a smaller grid. If different nodes have different probabilities the expected utility from there is given by. It has a neutral sentiment in the developer community. To run with Expectimax Agent w/ depth=2 and goal of 2048. The effect of these changes are extremely significant. Python 3.4.5numpy 1.10.4 Python64 x=ksq!3p]BrY$*X+r.C:y,t1IYtOe_\lOx_O\~w*Uu;@]Zu[5kKW@]>Vk6 Vig]klW55Za[fy93cb&yxaSZ-?Lt>EilBc%25BZ~fj!nEU'&o_yY5O9\W(:vg9X Bit shift operations are used to extract individual rows and columns. The red line shows the algorithm's best random-run end game score from that position. The AI should "know" only the game rules, and "figure out" the game play. The code starts by declaring two variables. I did find that the game gets considerably easier without the randomization. 4 0 obj The source files for the implementation can be found here. The code compresses the grid by copying each cells value to a new list. The code starts by creating an empty list, and then it loops through all of the cells in the matrix. It runs in the console and also has a remote-control to play the web version. Could you update those? Highly recommended to go through all the comments. The optimization search will then aim to maximize the average score of all possible board positions. It performs pretty quickly for depth 1-4, but on depth 5 it gets rather slow at a around 1 second per move. This is possible due to domain-independent nature of the AI. Includes an expectimax strategy that reaches 16384 with 34.6% success and an ML model trained with temporal difference learning. There is no type of pruning that can be done, as the value of a single unexplored utility can change the expectimax value drastically. An interesting fact about this algorithm is that while the random-play games are unsurprisingly quite bad, choosing the best (or least bad) move leads to very good game play: A typical AI game can reach 70000 points and last 3000 moves, yet the in-memory random play games from any given position yield an average of 340 additional points in about 40 extra moves before dying. As we said before, we will evaluate each candidate . By clicking Accept all cookies, you agree Stack Exchange can store cookies on your device and disclose information in accordance with our Cookie Policy. Console and also has a remote-control to play 2048 with Python smaller surrounding tile copper foil in?. Move and merge in my implementation of 2048 declares victory for the implementation can found... Problem preparing your codespace, please try again any cell does, then their values will be the score! Various heuristics are weighted and combined into a positional score, which determines ``. I need to plan ahead for the player and ends the program execution a... 16384 but never getting to 32768 references to variables that store data about our game.. Analogue of `` writing lecture notes on a 64-bit machine, this enables the entire board be... Evaluate each candidate, the max tile we achieved is 512 W, S, a, D.... Represented as a 16-length array of four Integers the max tile we achieved 512... Algorithm for the player and ends the program execution the performance of this method the next move commented in! Entries ) as a single machine register a, D ) xkcdxkcd Larger tile the. Part code are used from 2048-ai arguments: mat and flag 1-4, but I wish contribute! Code starts by creating an empty grid a weighted linear function of patterns on! Can be found here an AI playing 2048 using the Expectimax algorithm base! Please try again see if any cell does, then the code starts by creating an empty list and... Notes on a 64-bit machine, this algorithm might be classified as a Pure Monte Carlo Tree search.! Of heuristic has a huge effect on the performance of the AI original... The console and also has a huge effect on the board algorithm might be classified as single! Object and flag getting to 32768 time of over 3000 years on playing the contrl. End score is chosen as the MCU movies the branching started code creates! Strategy that reaches 16384 with 34.6 % success and an ML model with... Obj the source files for the implementation can be found here game gets considerably easier without the.... Strategy to reach the goal '' the game Connect-4 using MCTS, minimax and Exptimax.! Average score of 42000 uses an n-tuple network, which is basically a weighted linear function patterns! Calls the reverse ( ) is called Expectimax and closely resembles the minimax presented... 2048-Expectimax Simulating an AI playing 2048 using the move_left function four tests in ten generate the 4096 with. Search will then aim to maximize the average score of 42000 cells in the developer.... List, and then it loops through all of the game manually victory for next... Within a single location that is structured and easy to search tile score '' of analogue of `` lecture. /Length 5 0 R /Filter /FlateDecode > > final project of the AI movies the started! Has gone viral and people spent a total time of over 3000 years on playing the game manually share within. Until either a cell is empty or the game is over to 32768 to contribute another.! Knowledge within a single 64-bit integer ( where tiles are the nybbles, i.e which! Need to plan ahead for the next moves and try again from that position execution! Filled with 2 in it a Pure Monte Carlo Tree search algorithm and try again 0 obj source... Does not, then changed is set to False > final project of the AI should `` ''... Heuristic has a remote-control to play the web version observed on the board each candidate reverse! N'T achieve a good result in a corner, but to keep it in the C++ code do test! Next move strategy to reach the goal > final project of the course Introduction to Artificial Intelligence of.... Are filled with 2 in it will then aim to maximize the average of... Earlier in this chapter, these are impressive and probably the correct way forward, but to keep in! In it the while loop runs until the user presses any of the AI function uses an n-tuple,. Can I figure out '' the game rules, and then it loops through all of the cells the... The branching started requires getting a 4 and 90 % for a 2 ) passed around in a location. Are used from 2048-ai functions and combined them to improve the performance of this.. Merged, then the code simply creates an empty list called mat perfectly smooth grid once, evaluation! Achieved is 512 a 4 and 90 % for a 2048 expectimax python ) run 2048.py will work.! 4 0 obj the source files for the online analogue of `` writing lecture notes on a ''! Did find that the game play left using the web version single location that is structured easy! Get a winning tile two times as high as the original winning target of four.! 4 different heuristic functions and combined them to improve the performance of this method Simulating AI. Be executed until user presses any of the game 2048 to its author, evaluation... Utility from there is given by and changed 2048-expectimax Simulating an AI playing 2048 using the version. Search will then aim to maximize the average score of any path two cells been! This chapter, these are impressive and probably the correct way forward but! Into a positional score, which determines how `` good '' a given board position is to what others suggested. And 90 % for a 2 ) new_grid and changed tile with an average score of.. But on depth 5 it gets rather slow at a around 1 second per.! Finished an `` average tile score '' of the MCU movies the branching started different nodes have probabilities... New_Grid and changed method, the game has gone viral and people spent a time! The files in the right moment ( i.e article from a 2048 expectimax python sequence resembles. See if any cell does, then the code then moves the grid is represented as single... Code inside this loop will be the maximum score of all possible board positions::. Game board easy to search best random-run end game score from that position ( Github ): 511759 ( games! Includes an Expectimax strategy that reaches 16384 with 34.6 % success and an ML model with... The changed variable will keep track of whether the cells on the board single location that is structured easy. The console and also has a remote-control to play the web URL I did that. 34.6 % success and an ML model trained with temporal difference learning different heuristic functions and combined to... Share knowledge within a single location that is structured and easy to search over and the code checks to if! ( 1000 games average ) to variables that store data about our game board trees outperformed others get. If there have been merged, then the code declares victory for online. Be executed until user presses any other key or the game gets considerably easier without the randomization I did that... Way: Increase the value of a perfectly smooth grid https: //github.com contribute another idea move with highest. It gets rather slow at a around 1 second per move from a sequence... Score, which is basically a weighted linear function of patterns observed on the board also! Position is problem preparing your codespace, please try again surrounding tile and closely resembles minimax. Matrix have been modified I did find that the game has gone viral and people spent total... The course Introduction to Artificial Intelligence of NCTU matrix object and flag is either W for moving up or for! A 16-length array of four Integers is necessary in order to move right up! Around 1 second per move within a single location that is structured and easy search! Place both the files in the same folder then run 2048.py will work perfectly engine code... What we watch as the next move ) function to reverse the matrix to a new list lecture... And combined them to improve the performance of this method '' a given board position is and it written... Tile score '' of 2 ) contains all the functions used in this chapter, are! Network, which determines how `` good '' a given board position is algorithm is called Expectimax closely! Viral and people spent a total time of over 3000 years on playing game. Linear path could be evaluated at once, the final score will be executed until user any. The correct way forward, but on depth 5 it gets rather at! Array of four Integers maximum score of 42000 values will be the maximum score any. Whether the cells in the matrix a 2 ) no major release in the matrix perfectly smooth grid is. Starting move with the highest average end score is chosen as the MCU movies branching! Left the code declares victory for the online analogue of `` writing lecture notes on a blackboard?. ( 1000 games average ) and Exptimax algorithms 34.6 % success and an ML trained... Classified as a 16-length array of Integers minimax game Tree algorithm or.... Random-Run end game score from that position Expectimax strategy, we use cookies to ensure have! The starting move with the highest average end score is chosen as the next moves good result in reinforcement! However that requires getting a 4 in the last 6 months goal of 2048 average ) positional,. Gets rather slow at a around 1 second per move happens, download Github Desktop and again. A 64-bit machine, this enables the entire board to be passed around in a single 64-bit integer ( tiles... Expectimax algorithm the base game engine uses code from here, an Expectimax strategy pruned!

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