Rules reconstructed for historic games need to be compatible with the literary and archaeological evidence. The simulation of games with computer agents provides a third filter, to check that the rules are consistent with standard understandings of what makes a reasonable game, such as guaranteeing an end state, and the capacity to make interesting decisions. We look at two rulesets proposed in the literature for the ancient game known as Pente Grammai through this filter, and suggest that one is not fully workable.

Games often incorporate random elements in the form of dice or shuffled card decks. This randomness is a key contributor to the player experience and the variety of game situations encountered. There is a tension between a level of randomness that makes the game interesting and contributes to the player's enjoyment of a game, and a level at which the outcome itself is effectively random and the game becomes dull. The optimal level for a game will depend on the design goals and target audience. We introduce a new technique to quantify the level of randomness in game outcome and use it to compare 15 tabletop games and disentangle the different contributions to the overall randomness from specific parts of some games. We further explore the interaction between game randomness and player skill, and how this innate randomness can affect error analysis in common game experiments.

There are well-established methods for rating the relative skill of players such as Elo or TrueSkill ratings. This is not the case for rating games by their relative difficulty, or the level of ‘skill’ required to play them well. Previous work has proposed skill-traces as an answer to this question, which use data from games played between agents with progressively higher computational budgets to estimate the difficulty of the game (or skill-depth). We try to improve on previous work by expanding the algorithmic space considered and that this can radically change the ratings of some games. We then propose a new parameterised model for the level of skill a game requires and test this on a suite of multiplayer tabletop board games, concluding that the parameters can be usefully interpreted and provide a slightly better fit to human-estimates.

Tabletop games often incorporate random elements in the form of dice or shuffled card decks. This randomness is a key contributor to the player experience and the variety of game situations encountered. There is often a tension between a level of randomness that makes the game interesting, and a level at which the outcome itself is effectively random and the game becomes dull. The sweet-spot for any given game will depend on the design goals and target audience. We introduce a new technique to quantify the level of randomness in game outcome due to these elements. We use this to compare 15 different tabletop games, and then to disentangle the different contributions to the overall randomness from specific parts of the game. We show the utility of this approach by using it with a game publisher as a tool in the development phase of a new commercial board game.

Modern Tabletop Games present various interesting challenges for Multi-agent Reinforcement Learning. In this paper, we introduce PyTAG, a new framework that supports interacting with a large collection of games implemented in the Tabletop Games framework. In this work we highlight the challenges tabletop games provide, from a game-playing agent perspective, along with the opportunities they provide for future research. Additionally, we highlight the technical challenges that involve training Reinforcement Learning agents on these games. To explore the Multi-agent setting provided by PyTAG we train the popular Proximal Policy Optimisation Reinforcement Learning algorithm using self-play on a subset of games and evaluate the trained policies against some simple agents and Monte-Carlo Tree Search implemented in the Tabletop Games framework.

In recent years, Game AI research has made important breakthroughs using Reinforcement Learning (RL). Despite this, RL for modern tabletop games has gained little to no attention, even when they offer a range of unique challenges compared to video games. To bridge this gap, we introduce PyTAG, a Python API for interacting with the Tabletop Games framework (TAG). TAG contains a growing set of more than 20 modern tabletop games, with a common API for AI agents. We present techniques for training RL agents in these games and introduce baseline results after training Proximal Policy Optimisation algorithms on a subset of games. Finally, we discuss the unique challenges complex modern tabletop games provide, now open to RL research through PyTAG.

We use AI agents to play successive design iterations of an analogue board game to understand the sorts of question a designer asks of a game, and how AI play-testing approaches can help answer these questions and reduce the need for time-consuming human play-testing. Our case study supports the view that AI play-testing can complement human testing, but can certainly not replace it. A core issue to be addressed is the extent to which the designer trusts the results of AI play-testing as sufficiently human-like. The majority of design changes are inspired from human play-testing, but AI play-testing helpfully complements these and often gave the designer the confidence to make changes faster where AI and humans ‘agreed’.

In a two-player zero-sum game, players classically want to maximise their chance of winning. When a game has more than two players, using the binary win rate as an objective is no longer such an obvious choice. A player might instead have the objective of doing as well as possible in terms of ranked order, or in maximising their score. We investigate the impact of different game-agnostic objectives in several popular tabletop games, and whether it can be better to use the game score as a proxy for winning. We find that the games considered largely fall into two groups. In one it is helpful to focus just on one’s own score during the game, and then shift to beating opponents only in the end-game. In the other, larger, group it is better to ‘Follow the Leader’ and constantly track one’s relative position to the opponents throughout the game.

We introduce MultiTree Monte Carlo Tree Search (MT-MCTS), in which a tree is constructed independently for each player. This permits deeper search for the acting agent’s own move, at the cost of a poorer opponent model and the loss of conditioning a move on the specific action of another player.We test MT-MCTS in eleven different tabletop board and card games, with varying numbers of players. The main benefit occurs in simultaneous-move games, where independent trees better model the information structure. We find that in other games MT-MCTS can outperform vanilla MCTS, which incorporates all players in a single tree, but that this advantage usually decreases as the computational budget increases, and the cost of poor opponent modelling outweighs the gain from deeper search.

In this article, we compare four different “game spaces” in terms of their usefulness in characterizing multiplayer tabletop games, with a particular interest in any underlying change to a game’s characteristics as the number of players changes. In each case, we take a 16-D feature space and reduce it to a 2-D visualizable landscape. We find that a space obtained from optimization of parameters in Monte Carlo tree search is most directly interpretable to characterize our set of games in terms of the relative importance of imperfect information, adversarial opponents, and reward sparsity. These results do not correlate with a space defined using attributes of the game tree. This dimensionality reduction does not show any general effect as the number of players changes. Therefore, we consider the question using the original features to classify the games into two sets: 1) those for which the characteristics of the game change significantly as the number of players changes and 2) those for which there is no such effect.

We present some initial work on characterizing games using a visual ‘fingerprint’ generated from several independent optimisation runs over the parameters used in Monte Carlo Tree Search (MCTS). This ‘fingerprint’ provides a useful tool to compare games, as well as highlighting the relative sensitivity of a specific game to algorithmic variants of MCTS. The exploratory work presented here shows that in some games there is a major change in the optimal MCTS parameters when we move from 2-players to 3 or 4-players.

Opponent Modelling tries to predict the future actions of opponents, and is required to perform well in multiplayer games. There is a deep literature on learning an opponent model, but much less on how accurate such models must be to be useful. We investigate the sensitivity of Monte Carlo Tree Search (MCTS) and a Rolling Horizon Evolutionary Algorithm (RHEA) to the accuracy of their modelling of the opponent in a simple Real-Time Strategy game. We find that in this domain RHEA is much more sensitive to the accuracy of an opponent model than MCTS. MCTS generally does better even with an inaccurate model, while this will degrade RHEA's performance. We show that faced with an unknown opponent and a low computational budget it is better not to use any explicit model with RHEA, and to model the opponent's actions within the tree as part of the MCTS algorithm.

Automated game balancing has often focused on single-agent scenarios. In this paper we present a tool for balancing multi-player games during game design. Our approach requires a designer to construct an intuitive graphical representation of their meta-game target, representing the relative scores that high-level strategies (or decks, or character types) should experience. This permits more sophisticated balance targets to be defined beyond a simple requirement of equal win chances. We then find a parameterization of the game that meets this target using simulation-based optimization to minimize the distance to the target graph. We show the capabilities of this tool on examples inheriting from Rock-Paper-Scissors, and on a more complex asymmetric fighting game.