It was submitted early in the response timeline. In the image above, the 2 non-shaded squares are the only empty squares on the game board. 3. Minimax uses a backtracking algorithm or a recursive algorithm that determines game theory and decision making. This presents the problem of trying to merge another tile of the same value into this square. The first point above is because thats how minimax works, it needs 2 players: Max and Min. In the last article about solving this game, I have shown at a conceptual level how the minimax algorithm can be applied to solving the 2048 game. Open the console for extra info. However, real life applications enforce time constraints, hence, pruning is effective. @ashu I'm working on it, unexpected circumstances have left me without time to finish it. For two player games, the minimax algorithm is such a tactic, which uses the fact that the two players are working towards opposite goals to make predictions about which future states will be reached as the game progresses, and then proceeds accordingly to optimize its chance of victory. The move with the optimum minimax value is chosen by the player. As per the input direction given by the player, all tiles on the grid slide as far as possible in that direction, until (1) they either collide with another tile or (2) collide with the edge of the grid. For each column, we do the following: we start at the bottom and move upwards until we encounter a non-empty (> 0) element. What I am doing is at any point, I will try to merge the tiles with values 2 and 4, that is, I try to have 2 and 4 tiles, as minimum as possible. I believe there's still room for improvement on the heuristics. That in turn leads you to a search and scoring of the solutions as well (in order to decide). Ganesha 10 Bandung 40132, Indonesia 113512076@std.stei.itb.ac.id Abstract2048 is a puzzle game created by Gabriele Cirulli a few months ago. 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. Tile needs merging with neighbour but is too small: Merge another neighbour with this one. In case you missed my previous article, here it is: Now, lets start implementing theGridclass in Python. The optimization search will then aim to maximize the average score of all possible board positions. All AI's inherit from this module and implement the getMove function which takes a Grid object as parameter and returns a move, ComputerAI_3 : This inherits from BaseAI. While using the minimax algorithm, the MAX uses his move (UP, DOWN, RIGHT and LEFT) for finding the possible children nodes. This is not a direct answer to OP's question, this is more of the stuffs (experiments) I tried so far to solve the same problem and obtained some results and have some observations that I want to share, I am curious if we can have some further insights from this. The code for each movement direction is similar, so, I will explain only the up move. So, who is Max? 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, if you dont already know about the minimax algorithm, take a look at: The main 4 things that we need to think of when applying minimax to 2048, and really not only to 2048 but to any other game, are as follows: 1. Learn more. And the moves that Min can do is to place a 2 on each one of them or to place a 4, which makes for a total of 4 possible moves. This commit does not belong to any branch on this repository, and may belong to a fork outside of the repository. Before seeing how to use C code from Python lets see first why one may want to do this. I hope you found this information useful and thanks for reading! Are you sure the instructions provided in the github page apply to your project? These heuristics performed pretty well, frequently achieving 16384 but never getting to 32768. In particular, all it does is spawn random tiles of 2 and 4 each turn, with a designated probability of either a 2 or a 4; it certainly does not specifically spawn tiles at the most inopportune locations to foil the player's progress. In essence, the red values are "pulling" the blue values upwards towards them, as they are the algorithm's best guess. The effect of these changes are extremely significant. But a more efficient way is to return False as soon as we see an available move and at the end, if no False was returned, then return True. Then we will define the__init__()method which will be just setting the matrix attribute. The whole approach will likely be more complicated than this but not much more complicated. A game like scrabble is not a game of perfect information because there's no way to . 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. Can be tried out here: +1. Below is the code implementing the solving algorithm. Who is Max? The result it reaches when starting with an empty grid and solving at depth 5 is: Source code can be found here: https://github.com/popovitsj/2048-haskell. The solution I propose is very simple and easy to implement. Minimax is an algorithm designated for playing adversarial games, that is games that involve an adversary. But to put those ideas into practice, we need a way of representing the state of the game and do operations on it. Minimax is an algorithm designated for playing adversarial games, that is games that involve an adversary. Minimax is a recursive algorithm used to choose an optimal move for a player, assuming that the opponent is also playing optimally. The Minimax Algorithm In the 2048-puzzle game, the computer AI is technically not "adversarial". I think we should consider if there are also other big pieces so that we can merge them a little later. What sort of strategies would a medieval military use against a fantasy giant? I got very frustrated with Haskell trying to do that, but I'm probably gonna give it a second try! rev2023.3.3.43278. A. Minimax Minimax is a classic method to play a double-player game, players will take turns to play until the game ends. The player can slide the tiles in all the four directions (Up, Down, Left and Right). Getting unlucky is the same thing as the opponent choosing the worst move for you. And who wants to minimize our score? Such as French, German, Germany, Portugal, Portuguese, Sweden, Swedish, Spain, Spanish, UK etc Yes, it is based on my own observation with the game. Would love your thoughts, please comment. In testing, the AI achieves an average move rate of 5-10 moves per second over the course of an entire game. Depending on the game state, not all of these moves may be possible. Several linear path could be evaluated at once, the final score will be the maximum score of any path. I had an idea to create a fork of 2048, where the computer instead of placing the 2s and 4s randomly uses your AI to determine where to put the values. Thats a simple one: A game state is considered a terminal state when either the game is over, or we reached a certain depth. Surprisingly, increasing the number of runs does not drastically improve the game play. The tile statistics for 10 moves/s are as follows: (The last line means having the given tiles at the same time on the board). In this tutorial, we're going to investigate an algorithm to play 2048, one that will help decide the best moves to make at each step to get the best score. In this article, we'll see how we can apply the minimax algorithm to solve the 2048 game. How do we determine the children of a game state? You can try the AI for yourself. I became interested in the idea of an AI for this game containing no hard-coded intelligence (i.e no heuristics, scoring functions etc). 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). So, to avoid side effects that can arise from passing it by reference, we will use thedeepcopy()function, hence we need to import it. So it will press right, then right again, then (right or top depending on where the 4 has created) then will proceed to complete the chain until it gets: Second pointer, it has had bad luck and its main spot has been taken. In the next article, we will see how to represent the game board in Python through theGridclass. One can think that a good utility function would be the maximum tile value since this is the main goal. This should be the top answer, but it would be nice to add more details about the implementation: e.g. 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. Until you have to use the 4th direction the game will practically solve itself without any kind of observation. If I assign too much weights to the first heuristic function or the second heuristic function, both the cases the scores the AI player gets are low. But this sum can also be increased by filling up the board with small tiles until we have no more moves. In the minimax game tree, the children of a game state S are all the other game states that are reachable from S by only one move. Around 80% wins (it seems it is always possible to win with more "professional" AI techniques, I am not sure about this, though.). Depending on the game state, not all of these moves may be possible. Thus, there are four different best possibilities : Maximum tile is at the (1) Down -left (2) Top-left (3) Top-Right and (4) Down-Right corner. 4. Meanwhile I have improved the algorithm and it now solves it 75% of the time. I think we should penalize the game for taking too much space on the board. Mins job is to place tiles on the empty squares of the board. Another thing that we need is the moves inverse method. The goal of the 2048 game is to merge tiles into bigger ones until you get 2048, or even surpass this number. As we said previously, we consider Min as trying to do the worst possible move against us, and that would be to place a small tile (2 / 4). However randomization in Haskell is not that bad, you just need a way to pass around the `seed'. It has methods like getAvailableChildren (), canMove (), move (), merge (), heuristic (). The tree of possibilities rairly even needs to be big enough to need any branching at all. I think I have this chain or in some cases tree of dependancies internally when deciding my next move, particularly when stuck. The controller uses expectimax search with a state evaluation function learned from scratch (without human 2048 expertise) by a variant of temporal difference learning (a reinforcement learning technique). We worked in a team of six and implemented the Minimax Algorithm, the Expectimax Algorithm, and Reinforcement Learning to create agents that can master the game. So, if the player is Min, the possible moves are the cross product between the set of all empty squares and the set {2, 4}. And where the equality is True, we return the appropriate direction code. Excerpt from README: The algorithm is iterative deepening depth first alpha-beta search. The model the AI is trying to achieve is. Incorporates useful operations for the grid like move, getAvailableCells, insertTile and clone, BaseAI_3 : Base class for any AI component. (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).