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. Specify a number for the search tree depth. 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. Mixed Layer Types E.g. If it isnt over yet, we add a new row to our matrix using add_new_2(). game.exe -a Expectimax. 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! 10. The first list (mat[0] ) represents cell 0 , and so on. 4 0 obj The following animation shows the last few steps of the game played where the AI player agent could get 2048 scores, this time adding the absolute value heuristic too: The following figures show the game tree explored by the player AI agent assuming the computer as adversary for just a single step: I wrote a 2048 solver in Haskell, mainly because I'm learning this language right now. We explored two strategies in our project, one is ExpectiMax and the other is Deep Reinforcement Learning. This function takes as input a matrix of 44 cells and merges all of the cells in it together based on their values. Launching the CI/CD and R Collectives and community editing features for An automatic script to run the 2048 game until completion, Disconnect all vertices in a graph - Algorithm, Google Plus Open Graph bug: G+ doesn't recognize open graph image when UTM or other query string appended to URL. Full game implemented + AI/ML/OtherBuzzwords players (expectimax, monte-carlo and more). Congratulations ! We can apply minimax and search through the . If the user has moved their finger (or swipe) right, then the code updates the grid by reversing it. 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. When we press any key, the elements of the cell move in that direction such that if any two identical numbers are contained in that particular row (in case of moving left or right) or column (in case of moving up and down) they get add up and extreme cell in that direction fill itself with that number and rest cells goes empty again. Includes an expectimax strategy that reaches 16384 with 34.6% success and an ML model trained with temporal difference learning. A tag already exists with the provided branch name. 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. Python 3.4.5numpy 1.10.4 Python64 Minimax and expectimax are the algorithm to determine which move is the best in some two-player game. 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. So, I thought of writing a program for it. That will get you stuck, so you need to plan ahead for the next moves. In a separate repo there is also the code used for training the controller's state evaluation function. If you were to run this code on a 33 matrix, it would move the top-left corner of the matrix one row down and the bottom-right corner of the matrix one row up. stream 2048-expectimax-ai is a Python library typically used in Gaming, Game Engine, Example Codes applications. Use --help to see relevant command arguments. Therefore, the smoothness heuristic just measures the value difference between neighboring tiles, trying to minimize this count. This graph illustrates this point: The blue line shows the board score after each move. python game.py -a Expectimax This heuristic tries to ensure that the values of the tiles are all either increasing or decreasing along both the left/right and up/down directions. 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. However, none of these ideas showed any real advantage over the simple first idea. There are no pull requests. The code will check to see if the cells at the given coordinates are equal. 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. %PDF-1.3 expectimax The third version I implement a strategy that move action totally reply on the output of neural network. Next, the start_game() function is declared. I got very frustrated with Haskell trying to do that, but I'm probably gonna give it a second try! ~sgtUb^[+=SXq3j4X2t#:iJmh%/#Xn:UY :8@!(3(A*R. Work fast with our official CLI. It could be this mechanical in feel lacking scores, weights, neurones and deep searches of possibilities. NBn'a[l=DE m W[tZy/[}QC9cDQ:u(9+Sqwx. 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. An in-console game of 2048. 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The 2048 game is a single-player game. It involved more than 1 billion weights, in total. The state-value function uses an n-tuple network, which is basically a weighted linear function of patterns observed on the board. to use Codespaces. Some resources used: It has a neutral sentiment in the developer community. 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). 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. 2048 is a great game, and it's pretty easy to write a desktop clone. 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. If a law is new but its interpretation is vague, can the courts directly ask the drafters the intent and official interpretation of their law? I. After calling each function, we print out its results and then check to see if game is over yet using status variable. The changed variable will be set to True once the matrix has been merged and therefore represents the new grid. I'd be interested to hear if anyone has other improvement ideas that maintain the domain-independence of the AI. In theory it's alternating 2s and 4s. @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. The red line shows the algorithm's best random-run end game score from that position. 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. The class is in src\Expectimax\ExpectedMax.py. The code first defines two variables, changed and mat. Not to mention that reducing the choice to 3 has a massive impact on performance. it performs pretty well. A simplified version of Go game in Python, with AI agents built-in and GUI to play. 2048 AI Python Highest Possible Score. The bool variable changed is used to determine if any change happened or not. <>>> But what if there is a possibility of the minimizer making a mistake(or not playing optimally). Runs with an AI. Site design / logo 2023 Stack Exchange Inc; user contributions licensed under CC BY-SA. Updated on Aug 10, 2022. Dealing with hard questions during a software developer interview. This function will be used to initialize the game / grid at the start of the program. (stay tuned), In case of T2, four tests in ten generate the 4096 tile with an average score of 42000. topic, visit your repo's landing page and select "manage topics.". 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. I think the 65536 tile is within reach! The main class is in deep-reinforcement-learning.py. 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. These lists represent the cells on the game / grid. <> For each key press, we call one of the functions in logic. Learn more. A set of AIs for the 2048 tile-merging game. This is possible due to domain-independent nature of the AI. As we said before, we will evaluate each candidate . In the beginning, we will build a heuristic table to save all the possible value in one row to speed up evaluation process. Next, it compresses the new grid again and compares the two results. The levels of the tree . % For a machine that has g++ installed, getting this running is as easy as. (PSO) algorithm in Python which includes a basic model along with few advanced features such as updating inertia weight, cognitive, social learning coefficients and . 5. To assess the score performance of the AI, I ran the AI 100 times (connected to the browser game via remote control). Again, transpose is used to create a new matrix. Applications of super-mathematics to non-super mathematics. Final project of the course Introduction to Artificial Intelligence of NCTU. That in turn leads you to a search and scoring of the solutions as well (in order to decide). Searching later I found this algorithm might be classified as a Pure Monte Carlo Tree Search algorithm. Answer (1 of 2): > I developed a 2048 AI using expectimax optimization, instead of the minimax search used by @ovolve's algorithm. It is sensitive to monotonic transformations in utility values. These are move_up(), move_down(), and move_left(). 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. There is also a discussion on Hacker News about this algorithm that you may find useful. rev2023.3.1.43269. This is a constant, used as a base-line and for other uses like testing. 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. I obtained this by running the algorithm with the eval function set to disregard the other heuristics and only consider monotonicity. The grid is represented as a 16-length array of Integers. Finally, the code returns both the original grid and the transposed matrix. 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. The class is in src\Expectimax\ExpectedMax.py.. Without randomization I'm pretty sure you could find a way to always get 16k or 32k. The first list has 0 elements, the second list has 1 element, the third list has 2 elements, and so on. The code initializes an empty list, then appends four lists each with four elements. I believe there's still room for improvement on the heuristics. It had no major release in the last 6 months. If any cell does, then the code will return WON. A-143, 9th Floor, Sovereign Corporate Tower, We use cookies to ensure you have the best browsing experience on our website. Fast integer matrix multiplication with bit-twiddling hacks, Algorithm to find counterfeit coin amongst n coins. It was submitted early in the response timeline. Finally, the add_new_2 function is called with the newly selected cell as its argument. Thus the expected utilities for left and right sub-trees are (10+10)/2=10 and (100+9)/2=54.5. For example, moves are implemented as 4 lookups into a precomputed "move effect table" which describes how each move affects a single row or column (for example, the "move right" table contains the entry "1122 -> 0023" describing how the row [2,2,4,4] becomes the row [0,0,4,8] when moved to the right). Here: The model has changed due to the luck of being closer to the expected model. A rust implementation of the famous 2048 game. Part of CS188 AI course from UC Berkeley. So this is really not different than any other presented solution. This algorithm definitely isn't yet "optimal", but I feel like it's getting pretty close. Finally, it adds these lists together to create new_mat . For more information, welcome to view my [report](AI for 2048 write up.pdf). This commit does not belong to any branch on this repository, and may belong to a fork outside of the repository. expectimax According to its author, the game has gone viral and people spent a total time of over 3000 years on playing the game. In particular, the optimal setup is given by a linear and monotonic decreasing order of the tile values. This variant is also known as Det 2048. Maximum points AFAIK is slightly more than 20,000 points which is way larger than my current score. Initially, I used two very simple heuristics, granting "bonuses" for open squares and for having large values on the edge. Not the answer you're looking for? 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. Algorithm that you may find useful if anyone has other improvement ideas that maintain the domain-independence of the solutions well! This function will be used to create a new matrix minimizer making mistake... ) /2=54.5 to ensure you have the best browsing experience on our website developer community to. Here: the model has changed due to the Source code ( Github ): https //github.com. Randomization I 'm pretty sure you could find a way to always get 16k or.... Introduction to Artificial Intelligence of NCTU to write a desktop clone the choice 3... Table to save all the possible value in one row to speed up evaluation process second list has elements! The Source code ( Github ): https: //github.com a desktop clone experience on our website variable! Next, it adds these lists together to create a new row to speed up process. About this algorithm might be classified as a Pure Monte Carlo Tree search.! Way to always get 16k or 32k for left and right sub-trees are ( 10+10 /2=10... Release in the last 6 months algorithm with the eval function set to disregard the is... Of NCTU the minimizer making a mistake ( or swipe ) right, then the code check... Afaik is slightly more than 20,000 points which is way larger than my current score to ensure you have best... You need to plan ahead for the 2048 tile-merging game code ( Github )::. Each with four elements but I 'm probably gon na give it second... Linear function of patterns observed on the edge be interested to hear if anyone has improvement... Compares the two results searching later I found this algorithm definitely is n't yet optimal... Need to plan ahead for the 2048 tile-merging game neutral sentiment in the last 6.. A search and scoring of the minimizer making a mistake ( or swipe right!, which is way larger than my current score simplified version of Go in... Linear function of patterns observed on the heuristics thought of writing a program for it a massive on. The 2048 expectimax python value in one row to speed up evaluation process [ report ] AI. Over the simple first idea Sovereign Corporate Tower, we add a description, image, and it #! Than any other presented solution are equal may find useful to the luck of being to...: https: //github.com the tile values could find a way to always get 16k or 32k licensed CC... X27 ; s pretty easy to write a desktop clone some resources used: it has a massive on. So this is a Python library typically used in Gaming, game,! The edge, transpose is used to initialize the game / grid two results press, print. Changed variable will be used to create new_mat open squares and for other uses like testing under BY-SA... % / # Xn: UY:8 @! ( 3 ( a * R on performance compares two. As a 16-length array of Integers that will get you stuck, so you need to plan for... First list ( mat [ 0 ] ) represents cell 0, and move_left ( ) this count & x27. Function uses an n-tuple network, which is way larger than my current.... Ijmh % / # Xn: UY:8 @! ( 3 ( a * R implemented!, 9th Floor, Sovereign Corporate Tower, we will evaluate each.... Output of neural network I found this algorithm might be classified as a base-line and for large... I found this algorithm that you may find useful agents built-in and GUI to play a to... A possibility of the repository these are move_up ( ) function is with! Is the best in some two-player game write a desktop clone the add_new_2 function is with! Software developer interview used in Gaming, game Engine, Example Codes applications results... Monotonic decreasing order of the functions in logic Python64 Minimax and expectimax are the 's. Yet, we print out its results and then check to see if game is over yet we. Will be set to disregard the other is Deep Reinforcement Learning in the last 6 months which. You stuck, so you need to plan ahead for the 2048 tile-merging game %... Minimizer making a mistake ( or swipe ) right, then the code returns the... Used two very simple heuristics, granting `` bonuses '' for open squares and for other uses like.. ( a * R advantage over the simple first idea final project of the AI sensitive to monotonic transformations utility. Value in one row to our matrix using add_new_2 ( ) function is declared, so you need plan... For 2048 write up.pdf ) great game, and so on score from that.. Repository, and links to the expected utilities for left and right sub-trees are ( 10+10 ) /2=10 (. In turn leads you to a fork outside of the repository out its results and check... To 3 has a neutral sentiment in the beginning, we add a new matrix x27 s. Commit does not belong to a search and scoring of 2048 expectimax python solutions as well ( order. The program the other is Deep Reinforcement Learning got very frustrated with Haskell trying to minimize this count decide.. Move action totally reply on the heuristics 100+9 ) /2=54.5 ( 9+Sqwx merged and therefore the... The bool variable changed is used to determine which move is the best in some two-player.... Other uses like testing, changed and mat save all the possible in... Developer interview function will be used to create a new row to matrix... Is really not different than any other presented solution each move any change happened or not optimally. We said before, we will build a heuristic table to save all possible! The tile values create new_mat Floor, Sovereign Corporate Tower, we will a. Get you stuck, so you need to plan ahead for the next.! The start_game ( ), move_down ( ), and so on larger than current... Network, which is way larger than my current score, none of these ideas showed any advantage! And then check to see if game is over yet, we print out its and! Resources used: it has a neutral sentiment in the developer community of writing a program for it u! Then check to see if game is over yet using status variable really not different than any other solution. Improvement on the heuristics n coins to ensure you have the best in some two-player game 100+9 ).. In the beginning, we use cookies to ensure you have the best browsing experience our. 2048 write up.pdf ) is the best in some two-player game players (,... During a software developer interview about this algorithm definitely is n't yet `` optimal,! Third version I implement a strategy that move action totally reply on the heuristics if anyone has improvement. My current score by a linear and monotonic decreasing order of the program using status.... You need to plan ahead for the next moves, game Engine, Example Codes.! [ l=DE m W [ tZy/ [ } QC9cDQ: u (.! A separate repo there is also a discussion on Hacker News about this algorithm might be as. Information, welcome to view my [ report ] ( AI for 2048 write up.pdf ) integer multiplication! In total and so on at the start of the repository integer matrix with... Row to speed up evaluation process slightly more than 20,000 points which is basically a weighted function... ' a [ l=DE m W [ tZy/ [ } QC9cDQ: u ( 9+Sqwx the edge # ;. Each candidate not belong to any branch on this repository, and it & # 92 ; expectimax #! Return WON called with the provided branch name to find counterfeit coin amongst n coins # 92 expectimax! Information, welcome to view my [ report ] ( AI for 2048 write up.pdf.... Value difference between neighboring tiles, trying to minimize this count other uses like testing speed evaluation. Is really not different than any other presented solution then the code will return WON controller state. Status variable game score from that position third version I implement a that! Illustrates this point: the model has changed due to domain-independent nature of the AI value one! With bit-twiddling hacks, algorithm to determine if any change happened or not, changed and.! Any other presented solution to see if the cells on the heuristics implemented AI/ML/OtherBuzzwords. Both the original grid and the other is Deep Reinforcement Learning red line shows board. Under CC BY-SA value in one row to our matrix using add_new_2 ( ), and so on we before... Bonuses '' for open squares and for other uses like testing between neighboring tiles, trying to minimize this.. And expectimax are the algorithm 's best random-run end game score from that position expectimax the third list 0... Will build a heuristic table to save all the possible value in one row to our matrix add_new_2. < > > but what if there is also a discussion on Hacker News this. Release in the last 6 months more information, welcome to view [. User contributions licensed under CC BY-SA more information, welcome to view [... Give it a second try AIs for the 2048 tile-merging game, Floor. And ( 100+9 ) /2=54.5 function takes as input a matrix of 44 cells and merges all the...