Traditional Wisdom and Monte Carlo Tree Search Face-to-Face in the Card Game Scopone

We present the design of a competitive artificial intelligence for Scopone, a popular Italian card game. We compare rule-based players using the most established strategies (one for beginners and two for advanced players) against players using Monte Carlo Tree Search (MCTS) and Information Set Monte Carlo Tree Search (ISMCTS) with different reward functions and simulation strategies. MCTS requires complete information about the game state and thus implements a cheating player while ISMCTS can deal with incomplete information and thus implements a fair player. Our results show that, as expected, the cheating MCTS outperforms all the other strategies; ISMCTS is stronger than all the rule-based players implementing well-known and most advanced strategies and it also turns out to be a challenging opponent for human players.Comment: Preprint. Accepted for publication in the IEEE Transaction on Game

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Making Change in 2048

The 2048 game involves tiles labeled with powers of two that can be merged to form bigger powers of two; variants of the same puzzle involve similar merges of other tile values. We analyze the maximum score achievable in these games by proving a min-max theorem equating this maximum score (in an abstract generalized variation of 2048 that allows all the moves of the original game) with the minimum value that causes a greedy change-making algorithm to use a given number of coins. A widely-followed strategy in 2048 maintains tiles that represent the move number in binary notation, and a similar strategy in the Fibonacci number variant of the game (987) maintains the Zeckendorf representation of the move number as a sum of the fewest possible Fibonacci numbers; our analysis shows that the ability to follow these strategies is intimately connected with the fact that greedy change-making is optimal for binary and Fibonacci coinage. For variants of 2048 using tile values for which greedy change-making is suboptimal, it is the greedy strategy, not the optimal representation as sums of tile values, that controls the length of the game. In particular, the game will always terminate whenever the sequence of allowable tile values has arbitrarily large gaps between consecutive values

Procedural Content Generation for Real-Time Strategy Games

Videogames are one of the most important and profitable sectors in the industry of entertainment. Nowadays, the creation of a videogame is often a large-scale endeavor and bears many similarities with, e.g., movie production. On the central tasks in the development of a videogame is content generation, namely the definition of maps, terrains, non-player characters (NPCs) and other graphical, musical and AI-related components of the game. Such generation is costly due to its complexity, the great amount of work required and the need of specialized manpower. Hence the relevance of optimizing the process and alleviating costs. In this sense, procedural content generation (PCG) comes in handy as a means of reducing costs by using algorithmic techniques to automatically generate some game contents. PCG also provides advantages in terms of player experience since the contents generated are typically not fixed but can vary in different playing sessions, and can even adapt to the player herself. For this purpose, the underlying algorithmic technique used for PCG must be also flexible and adaptable. This is the case of computational intelligence in general and evolutionary algorithms in particular. In this work we shall provide an overview of the use of evolutionary intelligence for PCG, with special emphasis on its use within the context of real-time strategy games. We shall show how these techniques can address both playability and aesthetics, as well as improving the game AI

Volcano: An interactive sword generator

In this work, we introduce Volcano, a tool for the procedural generation of 3D models of swords. Unlike common procedural content generation tools, it exploits interactive evolution to reduce as much as possible the effort of the users during the generation process. Indeed, Volcano allows to forge the desired type of swords through a rather simple visual exploration of the design space. The 3D models generated with the tool can be directly used as game assets or further developed with a standard modeling software. A prototype of Volcano was tested by 30 users, including both students and game developers. The feedbacks received are very positive: tools like Volcano might be useful both for players, to create user contents, and for developers, to speed-up the design of game contents