Wednesday 26 March 2014

An Artificial Intelligence for the 2048 game

Lately the 2048 game reached a good notoriety on the internet.


A discussion about possible algorithms which solve the 2048 game arose on StackOverflow.

The main discussed algorithms are:

The solution I propose is very simple and easy to implement. Although, it has reached the score of 131040. Several benchmarks of the algorithm performances are presented.


Algorithm

Heuristic scoring algorithm

The assumption on which my algorithm is based is rather simple: if you want to achieve higher score, the board must be kept as tidy as possible. In particular, the optimal setup is given by a linear and monotonic decreasing order of the tile values.

This intuition will give you also the upper bound for a tile value: $2^{n} \rightarrow 2^{16} = 65536$ where $n$ is the number of tile on the board. (There's a possibility to reach the 131072 tile if the 4-tile is randomly generated instead of the 2-tile when needed)

Two possible ways of organizing the board are shown in the following images



To enforce the ordination of the tiles in a monotonic decreasing order, the score si computed as the sum of the linearized values on the board multiplied by the values of a geometric sequence with common ratio $r<1$ .

$p_n \in Path_{0 \cdots N-1}$

$score = \sum_{n=0}^{N-1} value(p_n) * r^n$

Several linear path could be evaluated at once, the final score will be the maximum score of any path.

Decision rule

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. Obviously a more
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. (stay tuned)

Benchmark


  • 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 - $r = 0.5$



In case of T2, four tests in ten generate the 4096 tile with an average score of $\sim 42000$

Code

The code can be found on GiHub at the following link: https://github.com/Nicola17/term2048-AI
It is based on term2048 and it's written in Python. I will implement a more efficient version in C++ as soon as possible.

StackOverflow

You can upvote my answer on StackOverflow here :)

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  123. My approach is built on a basic assumption: if you want to get a better score, keep the board as neat as possible.
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  126. Your approach to implementing an AI algorithm for the 2048 game is both insightful and practical. The emphasis on maintaining a tidy board and the benchmark results showcase the effectiveness of your strategy. Looking forward to seeing the future developments and a more efficient version in C++. Well done!
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  131. One of the strengths of this blog is its clear and structured approach to explaining the AI algorithms and techniques employed in solving the game. The blog breaks down the problem into manageable components, discussing concepts such as search algorithms, heuristics, and decision-making processes. The inclusion of code snippets and visual representations helps readers better understand the implementation details.
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  132. I must say, this is quite an innovative approach to improving the gameplay experience of the 2048 game. The concept of creating an artificial intelligence to assist players in making strategic moves is truly genius.
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  134. Your innovative approach to solving the 2048 game by prioritizing a tidy board and implementing a heuristic scoring algorithm is commendable. The benchmarks and results you presented demonstrate the effectiveness of your solution. I'm excited to see how your future implementations, such as the minimax approach, will further enhance the algorithm. Well done!
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  135. The article on building an artificial intelligence for the 2048 game was fascinating. It provided valuable insights into the algorithms and strategies used to create an AI that can play the game efficiently. Online learning portals in India the need of the hour

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  143. Fantastic job on creating an artificial intelligence algorithm for the 2048 game! Your simple yet effective approach of organizing the board and implementing a heuristic scoring algorithm is impressive. Keep up the great work!
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  144. Great job on developing an AI for the 2048 game! Your simple heuristic scoring algorithm is impressive, and the benchmarks demonstrate its effectiveness. Looking forward to seeing your future updates and improvements. Well done!
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  149. Hello Blogger!
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  150. Impressive AI solution for the 2048 game! Your heuristic scoring algorithm and decision rule are well thought out and show great potential. Looking forward to seeing further improvements. Keep up the excellent work!
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  151. Thank you for providing us with such valuable insights. The article was truly engaging and informative, and I thoroughly enjoyed reading it. For those interested in exploring the future of full stack development, I highly recommend checking out the blog: [The Future of Full-Stack Developers: Job Market Trends and Insights]. It offers a comprehensive perspective on the evolving landscape of full stack development and is definitely worth a read!

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  154. Hi, It's fascinating to see the diverse approaches taken to tackle the challenge of creating an AI for the 2048 game. Your heuristic-based algorithm stands out due to its simplicity and effectiveness, reaching an impressive score. Good job.
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  159. Hi,
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  160. The article discusses algorithms for solving the 2048 game, including heuristic-based approaches, presenting a simple solution based on maintaining a linear and decreasing order of tile values to achieve high scores.
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  161. Interesting details on 2048 algorithms! It's interesting how you used a heuristic. I look forward to your C++ release and future improvements. On StackOverflow, voted up!

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  162. Hello,
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  164. "An intriguing approach to mastering the 2048 game using heuristic scoring and board organization. Simple yet effective!
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  165. This article likely discusses the development or implementation of artificial intelligence (AI) for playing the popular 2048 game, showcasing the capabilities of AI in mastering and potentially optimizing gameplay in complex scenarios.

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  166. Appreciate the author for presenting a simple yet effective algorithm for the 2048 game. The focus on maintaining a tidy board and heuristic scoring is impressive. The commitment to further improvements showcases dedication to the gaming community. Looking forward to more of such informative articles in coming days.
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  167. Creating an artificial intelligence to play the 2048 game is a fascinating project! It's impressive to see how AI techniques can be applied to solve puzzles and games. Your blog post provides valuable insights into the development process. Great work!
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  168. The step-by-step approach and insights into the game's mechanics are incredibly valuable for players looking to improve their skills. Thanks for sharing your expertise—I'll be using your tips and strategies, Keep up the fantastic work!
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