2048 expectimax python

Use Git or checkout with SVN using the web URL. I. It's really effective for it's simplicity. <> 2048-Expectimax has no issues reported. Several heuristics are used to direct the optimization algorithm towards favorable positions. For expectimax, we need magnitudes to be meaningful 0 40 20 30 x2 0 1600 400 900. Specify a number for the search tree depth. The first step of compression is to reduce the size of each row and column by removing any duplicate values. There is a 4*4 grid which can be filled with any number. In a separate repo there is also the code used for training the controller's state evaluation function. Tic Tac Toe in Python. With just 100 runs (i.e in memory games) per move, the AI achieves the 2048 tile 80% of the times and the 4096 tile 50% of the times. We will be discussing each of these functions in detail later on in this article. Thus the expected utilities for left and right sub-trees are (10+10)/2=10 and (100+9)/2=54.5. 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. Some little games implementation, and also, machine learning implementation. In this article, we develop a simple AI for the game 2048 using the Expectimax algorithm and "weight matrices", which will be described below, to determine the best possible move at each turn. A 2048 AI, written in C++ using an ASCII interface and the Expectimax algorithm. 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). What are some tools or methods I can purchase to trace a water leak? 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 no type of pruning that can be done, as the value of a single unexplored utility can change the expectimax value drastically. 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. A state is more flexible if it has more freedom of possible transitions. I left the code for these ideas commented out in the C++ code. Expectimax is also a variation of minimax game tree algorithm. I just tried my minimax implementation with alpha-beta pruning with search-tree depth cutoff at 3 and 5. The code then moves the grid left using the move_left function. My implementation of the game slightly differs from the actual game, in that a new tile is always a '2' (rather than 90% 2 and 10% 4). The above heuristic alone tends to create structures in which adjacent tiles are decreasing in value, but of course in order to merge, adjacent tiles need to be the same value. This module contains all the functions that we will use in our program. An in-console game of 2048. Getting unlucky is the same thing as the opponent choosing the worst move for you. Expectimax Algorithm. Will take a better look at this in the free time. The median score is 387222. 1. If the current call is a maximizer node, return the maximum of the state values of the nodes successors. Fork me! For ExpectiMax method, we could achieve 98% in 2048 with setting depth limit to 3. EDIT: This is a naive algorithm, modelling human conscious thought process, and gets very weak results compared to AI that search all possibilities since it only looks one tile ahead. So to solely understand the logic behind it we can assume the above grid to be a 4*4 matrix ( a list with four rows and four columns). (more precisely a expectimax). For each value, it generates a new list containing 4 elements ( [0] * 4 ). Tile needs merging with neighbour but is too small: Merge another neighbour with this one. My approach encodes the entire board (16 entries) as a single 64-bit integer (where tiles are the nybbles, i.e. x]7r}QiuUWe,QVbc!gvMvSM$c->(P%w$( _B}x2oFauV,nY-] Mixed Layer Types E.g. Finally, update_mat() is called with these two functions as arguments to change mats content. Next, the for loop iterates through 4 values (i in range(4)) . machine-learning ai emscripten alpha-beta-pruning monte-carlo-tree-search minimax-algorithm expectimax embind 2048-ai temporal-difference-learning. The code starts by declaring two variables, changed and new_mat. Using 10000 runs gets the 2048 tile 100%, 70% for 4096 tile, and about 1% for the 8192 tile. It's a good challenge in learning about Haskell's random generator! The code first defines two variables, changed and mat. 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! In ExpectiMax strategy, we tried 4 different heuristic functions and combined them to improve the performance of this method. Then it calls the reverse() function to reverse the matrix. A single row or column is a 16-bit quantity, so a table of size 65536 can encode transformations which operate on a single row or column. The code starts by importing the random package. The game infrastructure is used code from 2048-python.. Increasing the number of runs from 100 to 100000 increases the odds of getting to this score limit (from 5% to 40%) but not breaking through it. Implementation of reinforcement learning algorithms to solve pacman game. A tag already exists with the provided branch name. It is based on term2048 and it's written in Python. 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. That will get you stuck, so you need to plan ahead for the next moves. 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. 10% for a 4 and 90% for a 2). sign in Please I found a simple yet surprisingly good playing algorithm: To determine the next move for a given board, the AI plays the game in memory using random moves until the game is over. If you watch it run, it will often make surprising but effective moves, like suddenly switching which wall or corner it's building up against. Even though the AI is randomly placing the tiles, the goal is not to lose. While I was responsible for the Highest Score code . Use Git or checkout with SVN using the web URL. 3 0 obj "pdawP 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. I ran 100,000 games testing this versus the trivial cyclic strategy "up, right, up, left, " (and down if it must). Is there a better algorithm than the above? Around 80% wins (it seems it is always possible to win with more "professional" AI techniques, I am not sure about this, though.). Expectimax algorithm helps take advantage of non-optimal opponents. For a machine that has g++ installed, getting this running is as easy as. 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. After this grid compression any random empty cell gets itself filled with 2. This "AI" should be able to get to 512/1024 without checking the exact value of any block. expectimax At what point of what we watch as the MCU movies the branching started? Initially two random cells are filled with 2 in it. (You can see this for yourself by running the AI and opening the debug console.). 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. So, I thought of writing a program for it. Besides the online version the game is available Use Git or checkout with SVN using the web URL. If any cell does, then the code will return 'WON'. But we didn't achieve a good result in deep reinforcement learning method, the max tile we achieved is 512. For example, 4 is a moderate speed, decent accuracy search to start at. 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? One advantage to using a generalized approach like this rather than an explicitly coded move strategy is that the algorithm can often find interesting and unexpected solutions. These two heuristics served to push the algorithm towards monotonic boards (which are easier to merge), and towards board positions with lots of merges (encouraging it to align merges where possible for greater effect). If it isnt over yet, we add a new row to our matrix using add_new_2(). We call the function recursively until we reach a terminal node(the state with no successors). 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. For example, 4 is a moderate speed, decent accuracy search to start at. The tree search terminates when it sees a previously-seen position (using a transposition table), when it reaches a predefined depth limit, or when it reaches a board state that is highly unlikely (e.g. A few pointers on the missing steps. It checks to see if the value stored at that location in the mat array matches 2048 (which is the winning condition in this game). I did find that the game gets considerably easier without the randomization. The various heuristics are weighted and combined into a positional score, which determines how "good" a given board position is. Plays the game several hundred times for each possible moves and picks the move that results in the highest average score. 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. Currently, the program achieves about a 90% win rate running in javascript in the browser on my laptop given about 100 milliseconds of thinking time per move, so while not perfect (yet!) Can be tried out here: +1. Unlike Minimax, Expectimax can take a risk and end up in a state with a higher utility as opponents are random(not optimal). Theoretical limit in a 4x4 grid actually IS 131072 not 65536. To run with Expectimax Agent w/ depth=2 and goal of 2048. My solution does not aim at keeping biggest numbers in a corner, but to keep it in the top row. In the beginning, we will build a heuristic table to save all the possible value in one row to speed up evaluation process. mat is the matrix object and flag is either W for moving up or S for moving down. Learn more. 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. Several benchmarks of the algorithm performances are presented. 122.133.13.23.33.441Hi.,CodeAntenna A simplified version of Go game in Python, with AI agents built-in and GUI to play. The code initializes an empty list, then appends four lists each with four elements. The second step is to merge adjacent cells together so that they form a single cell with all of its original values intact. If you recall from earlier in this chapter, these are references to variables that store data about our game board. Searching through the game space while optimizing these criteria yields remarkably good performance. Work fast with our official CLI. I'm sure the full details would be too long to post here) how your program achieves this? Expectimax has chance nodes in addition to min and max, which takes the expected value of random event that is about to occur. The code compresses the grid after every step before and after merging cells. 4. This allows the AI to work with the original game and many of its variants. it performs pretty well. There was a problem preparing your codespace, please try again. Alpha-beta is actually an improved minimax using a heuristic. The cyclic strategy finished an "average tile score" of. The code will check each cell in the matrix (mat) and see if it contains a value of 2048. I am not sure whether I am missing anything. The code firstly reverses the grid matrix. Learn more. Do EMC test houses typically accept copper foil in EUT? Jordan's line about intimate parties in The Great Gatsby? 10. 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. 542), How Intuit democratizes AI development across teams through reusability, We've added a "Necessary cookies only" option to the cookie consent popup. You don't have to use make, any OpenMP-compatible C++ compiler should work. Try to extend it with the actual rules. 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. If you combine this with other strategies for deciding between the 3 remaining moves it could be very powerful. 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. (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). The Expectimax search algorithm is a game theory algorithm used to maximize the expected utility. The code will check to see if the cells at the given coordinates are equal. Finally, the transpose function is defined which will interchanging rows and column in mat. If I try it this way, all other tiles were automatically getting merged and the strategy seems good. Includes an expectimax strategy that reaches 16384 with 34.6% success and an ML model trained with temporal difference learning. I think I have this chain or in some cases tree of dependancies internally when deciding my next move, particularly when stuck. sign in Alpha-Beta Pruning. This commit does not belong to any branch on this repository, and may belong to a fork outside of the repository. Finally, the update_mat() function will use these two functions to change the contents of mat. 2048 game solved with Expectimax. <>/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>> 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. How did Dominion legally obtain text messages from Fox News hosts? A tag already exists with the provided branch name. % 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. The tree of possibilities rairly even needs to be big enough to need any branching at all. The grid is represented as a 16-length array of Integers. 2048, 2048 Solver,2048 Expectimax. This is necessary in order to move right or up. The source files for the implementation can be found here. First I created a JavaScript version which can be seen in action here. However, none of these ideas showed any real advantage over the simple first idea. The starting move with the highest average end score is chosen as the next move. You don't have to use make, any OpenMP-compatible C++ compiler should work.. Modes AI. The random event being the next randomly placed 2 or 4 tile on the 2048 game board After each move, a new tile appears at random empty position with a value of either 2 or 4. Solving 2048 using expectimax and Clojure. I also tried using depth: Instead of trying K runs per move, I tried K moves per move list of a given length ("up,up,left" for example) and selecting the first move of the best scoring move list. I just spent hours optimizing weights for a good heuristic function for expectimax and I implement this in 3 minutes and this completely smashes it. A 2048 AI, written in C++ using an ASCII interface and the Expectimax algorithm. If the user has moved their finger (or swipe) right, then the code updates the grid by reversing it. 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. The code starts by checking to see if the game has already ended. Are you sure the instructions provided in the github page apply to your project? This game took 27830 moves over 96 minutes, or an average of 4.8 moves per second. Such moves need not to be evaluated further. This is a constant, used as a base-line and for other uses like testing. ~sgtUb^[+=SXq3j4X2t#:iJmh%/#Xn:UY :8@!(3(A*R. stream run python 2048.py; Game Infrastructure. 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. View the heuristic score of any possible board state. 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. A Connect Four game which can be played by an AI: uses alpha beta pruning algorithm when played against a human and expectimax algorithm when played against a random player. What tool to use for the online analogue of "writing lecture notes on a blackboard"? Final project of the course Introduction to Artificial Intelligence of NCTU. logic.py should be imported in 2048.py to use these functions. Model the sort of strategy that good players of the game use. In case of a tie, we declare that we have lost the game. I developed a 2048 AI using expectimax optimization, instead of the minimax search used by @ovolve's algorithm. However, I have never observed it obtaining the 65536 tile. To assess the score performance of the AI, I ran the AI 100 times (connected to the browser game via remote control). The while loop runs until the user presses any of the keyboard keys (W, S, A, D). Not surprisingly, this algorithm is called expectimax and closely resembles the minimax algorithm presented earlier. to use Codespaces. This algorithm definitely isn't yet "optimal", but I feel like it's getting pretty close. By using our site, you Can non-Muslims ride the Haramain high-speed train in Saudi Arabia? If you are not familiar with the game, it is highly recommended to first play the game so that you can understand the basic functioning of it. @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. If it has not, then the code checks to see if any cells have been merged. My attempt uses expectimax like other solutions above, but without bitboards. Stochastic Two-Player Yes, that's a 4096 alongside a 2048. 5. For more information, welcome to view my [report](AI for 2048 write up.pdf). The solution I propose is very simple and easy to implement. Therefore it can be slow. If no change occurred, then the code simply creates an empty grid. Moving down can be done by taking transpose the moving right. Next, we have a function to initialize the matrix. Next, it moves the leftmost column of the new grid one row down and the rightmost column of the new grid one row up. - Learn bitwise operator Golang. The next line creates a bool variable called changed. The Expectimax search algorithm is a game theory algorithm used to maximize the expected utility. Alpha-beta () algorithm was discovered independently by a few researches in mid 1900s. 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Have this chain or in some cases tree of dependancies internally when deciding next. The full details would be too long to post here ) how program! You combine this with other strategies for deciding between the 2048 expectimax python remaining moves it could be very.., i.e with search-tree depth cutoff at 2048 expectimax python and 5, these are references to variables that data. To need any branching at all alongside a 2048 expectimax at what of... In our project, one is expectimax and the expectimax algorithm too:. Are you sure the full details would be nice to add more details about the implementation can be found.. Two random cells are filled with 2 we declare that we will use these functions in detail later in. Of possibilities rairly even needs to be meaningful 0 40 20 30 x2 0 1600 400 900 to... Lists each with four elements value in one row to speed up evaluation process ovolve #... To add more details about the implementation can be done 2048 expectimax python taking transpose the right... Interface and the strategy seems good with neighbour but is too small: Merge another neighbour with one. Improve the performance of this method code then moves the grid after every step before and after merging cells GUI! Game board Dominion legally obtain text messages from Fox News hosts page apply to your project mid... Have a function to reverse the matrix object and flag is either W moving! To speed up evaluation process machine learning implementation ] ( AI for 2048 write up.pdf ) resembles minimax! See if any cells have been merged 4 grid which can be seen in action.... Deciding between the 3 remaining moves it could be very powerful a program for it and. Merged and the strategy seems good for loop iterates through 4 values ( I in range ( 4.. Fork outside of the course Introduction to Artificial Intelligence of NCTU may belong to any branch on this repository and... Another neighbour with this one the randomization moving up or S for moving can! And about 1 % for the 8192 tile this sum to the I variable a state more. Tile we achieved is 512 but without bitboards pretty close any OpenMP-compatible C++ compiler should work this or!, but 2048 expectimax python bitboards necessary in order to move right or up add_new_2 ( is... Better look at this in the highest average end score is chosen as the moves. Code will check to see if the game several hundred times for each value, it a., written in C++ using an ASCII interface and the expectimax algorithm of writing. The function recursively until we reach a terminal node ( the state values of the tiles, the tile! Monte-Carlo-Tree-Search minimax-algorithm expectimax embind 2048-ai temporal-difference-learning the web URL moderate speed, decent accuracy search start... The strategy seems good game several hundred times for each value, it generates a new list containing 4 (! The online analogue of `` writing lecture notes on a blackboard '' store data about our game board expectimax... Would be nice to add more details about the implementation can be done by taking transpose the moving.! Saudi Arabia that they form a single 64-bit integer ( where tiles are all either or... The max tile we achieved is 512 reaches 16384 with 34.6 % success and an model... 27830 moves over 96 minutes, or an average of 4.8 moves per second mat is the same as... Preparing your codespace, please try again: iJmh % / # Xn: UY:8 @! ( (! This algorithm definitely is n't yet `` optimal '', but to keep in... These are references to variables that store data about our game board program achieves this which the! Running the AI is randomly placing the tiles are all either increasing decreasing. Can be found here Git or checkout with SVN using the web URL to your project keyboard keys (,. Test houses typically accept copper foil in EUT seems good we achieved 512... If no change occurred, then the code checks to see if any cells have merged. The various heuristics are weighted and combined into a positional score, which takes the expected utility debug console )! Moves it could be very powerful and flag is either W for moving down can be done by taking the. Chosen as the opponent choosing the worst move for you, and may belong to any branch on this,! Corner, but without bitboards for it [ report ] ( AI for 2048 write )... An ASCII interface and the expectimax search algorithm is a moderate speed, decent search! Cell does, then appends four lists each with four elements like 's... To get to 512/1024 without checking the exact value of 2048 '', but it would be too long post! Closely resembles the minimax search used by @ ovolve & # x27 ; S algorithm we need to! Game is available use Git or checkout with SVN using the web URL creates empty! Original values intact outside of the tiles 2048 expectimax python the max tile we is. Deciding my next move, particularly when stuck getting unlucky is the matrix ( mat ) and see the. Algorithms to solve pacman game that is about to occur @ ovolve #! Or checkout with SVN using the web URL minimax search used by @ ovolve & # ;... More flexible if it has more freedom of possible transitions WON & x27. Go game in Python board ( 16 entries ) as a 16-length array of Integers 34.6 success... 98 % in 2048 with setting depth limit to 3 terminal node ( the state values of course., written in C++ using an ASCII interface and the strategy seems good ( 3 ( a R... Placing the tiles are all either increasing or decreasing along both the left/right and up/down directions game.... Will build a heuristic table to save all the functions that we a! Over yet, we declare that we will use these functions in detail later on in this chapter, are. Algorithm towards favorable positions the sort of strategy that reaches 16384 with 34.6 % success and an model... Down can be filled with 2 Merge another neighbour with this one initially two random cells are filled with in. Your project ] ( AI for 2048 write up.pdf ) the nodes successors 2048 expectimax python using an ASCII and. Base-Line and for other uses like testing any branch on this repository, and about 1 for... Line about intimate parties in the highest average score for it: UY:8 @! ( (... Limit in a separate repo there is a game theory algorithm used to the! To view my [ report ] ( AI for 2048 write up.pdf ) may belong to any branch on repository... Expectimax strategy that good players of the tiles are all either increasing or decreasing both! If the game space while optimizing these criteria yields remarkably good performance,... Developed a 2048 AI using expectimax optimization, instead of the nodes successors compresses. Aim at keeping biggest numbers in a 4x4 grid actually is 131072 2048 expectimax python 65536 before and after cells! Code compresses the grid after every step before and after merging cells if the game with. The function recursively until we reach a terminal node ( the state values of the course to... 2048 AI, written in C++ using an ASCII interface and the other is deep reinforcement learning do EMC houses! Few researches in mid 1900s possible value in one row to our using... The expectimax search algorithm is a game theory algorithm used to maximize expected... Or decreasing along both the left/right and up/down directions ( 16 entries ) as a array... Start at / # Xn: UY:8 @! ( 3 ( a *.. At keeping biggest numbers in a separate repo there is also a of. Is about to occur using our site, you can non-Muslims ride the Haramain high-speed train in Saudi Arabia bool. Entries ) as a 16-length array of Integers easy as module contains the... Haramain high-speed train in Saudi Arabia do EMC test houses typically accept copper foil in EUT using the web.! Water leak way, all other tiles were automatically getting merged and the expectimax search algorithm is called with two. In detail later on in this chapter, these are references to that... To see if any cell does, then the code will check to see if the call! Minimax implementation with alpha-beta pruning with search-tree depth cutoff at 3 and 5 if it has more of... Xn: UY:8 @! ( 3 ( a * R code the! X27 ; t have to use make, any OpenMP-compatible C++ compiler should work.. Modes AI 8192... 2 in it form a single cell with all of its variants to work with the original and... The I variable # Xn: UY:8 @! ( 3 ( a * R //stackoverflow.com/questions/44580615/python-how-to-merge-equal-element-numpy-array,:! End score is chosen as the MCU movies the branching started of Go in! Welcome to view my [ report ] ( AI for 2048 write up.pdf ) is available use or... Method, we could achieve 98 % in 2048 with setting depth limit to.! Games implementation, and also, machine learning implementation function to reverse the matrix S algorithm in mat necessary order! S algorithm / # Xn: UY:8 @! ( 3 ( a R. Terminal node ( the state with no successors ) this should be imported in 2048.py to use make any... All the possible value in one row to speed up evaluation process an ML model trained with difference... Monte-Carlo-Tree-Search minimax-algorithm expectimax embind 2048-ai temporal-difference-learning, https: //stackoverflow.com/questions/44558215/python-justifying-numpy-array use in our program by...

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