Seeding for Success: Skill and Stochasticity in Tabletop Games

TL;DR

This work proposes a quantitative framework to measure and decompose randomness in tabletop games and to study how randomness interacts with player skill. By running large-scale simulations with controlled random seeds and varied agent budgets, the authors demonstrate that randomness can be disentangled into controllable sources and that skill often drives determinism as seed effects become more exploitable. The study provides robust metrics (Span, Trimmed Span, Outliers, Entropy) and practical guidance for design iterations, showing how targeted seed control and heuristics can shape perceived fairness and excitement. The approach offers a general tool for designers and researchers to evaluate whether a game's randomness aligns with its intended player experience and experimental analyses.

Abstract

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 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.

Figures (6)

• Figure 1: Plot of variance ($p(1-p)$) shows the variance peaks at $p=0.5$, and is zero for $p \in \{0, 1\}$. Any change in the distribution of $p$ from a constant $p=0.5$ will therefore reduce the variance from this peak.
• Figure 2: Random Seed plot for all 4 example games. The green shading is the 99% confidence interval for the win rate assuming that the random seed has no effect. The x-axis is first player win rate, and the win rates for the 100 seeds are plotted as a histogram with buckets of width 2%.
• Figure 3: Impact of randomness with skill of players. Trimmed Span is reported for each of the five agent budgets. All games are played between agents using the same budget. There is a general trend for higher budget (more skilled) agents to better exploit any benefit from different random seeds.
• Figure 4: Individual seed results. The central green line is the average win rate of the first player (P1) as agent budget changes. The grey lines show the same lines for 10 randomly selected seeds.
• Figure 5: Comparison of the impact of initial Character, Round and Train shuffles for Colt Express. Of these three factors, only the Character randomisation has a major impact on game outcome.