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Analysis of Uncertainty in Procedural Maps in Slay the Spire

Mahsa Bazzaz, Seth Cooper

TL;DR

This work introduces an information-theoretic framework to quantify uncertainty in Slay the Spire's procedurally generated maps by computing the entropy of possible play paths and relating it to run outcomes and player skill. It reconstructs full maps from seeds, enumerates all possible paths, and evaluates location- and path-level uncertainties across monsters, elites, bosses, treasures, shops, rests, and unknown locations for 20,000 ascension-mode Iron Clad runs. The key findings show that victorious runs exhibit higher normalized path entropy, indicating advantageous risk-taking, while higher ascension levels modulate risk-taking patterns in later game stages. The results offer insight into how randomness shapes play in roguelike deck-builders and suggest design considerations for adaptive difficulty in procedurally generated games.

Abstract

This work investigates the role of uncertainty in Slay the Spire using an information-theoretic framework. Focusing on the entropy of game paths (which are based on procedurally-generated maps) we analyze how randomness influences player decision-making and success. By examining a dataset of 20,000 game runs, we quantify the entropy of paths taken by players and relate it with their outcomes and skill levels. The results show that victorious runs are associated with higher normalized entropy, suggesting more risk-taking. Additionally, higher-skill players tend to exhibit distinct patterns of risk-taking behavior in later game stages.

Analysis of Uncertainty in Procedural Maps in Slay the Spire

TL;DR

This work introduces an information-theoretic framework to quantify uncertainty in Slay the Spire's procedurally generated maps by computing the entropy of possible play paths and relating it to run outcomes and player skill. It reconstructs full maps from seeds, enumerates all possible paths, and evaluates location- and path-level uncertainties across monsters, elites, bosses, treasures, shops, rests, and unknown locations for 20,000 ascension-mode Iron Clad runs. The key findings show that victorious runs exhibit higher normalized path entropy, indicating advantageous risk-taking, while higher ascension levels modulate risk-taking patterns in later game stages. The results offer insight into how randomness shapes play in roguelike deck-builders and suggest design considerations for adaptive difficulty in procedurally generated games.

Abstract

This work investigates the role of uncertainty in Slay the Spire using an information-theoretic framework. Focusing on the entropy of game paths (which are based on procedurally-generated maps) we analyze how randomness influences player decision-making and success. By examining a dataset of 20,000 game runs, we quantify the entropy of paths taken by players and relate it with their outcomes and skill levels. The results show that victorious runs are associated with higher normalized entropy, suggesting more risk-taking. Additionally, higher-skill players tend to exhibit distinct patterns of risk-taking behavior in later game stages.

Paper Structure

This paper contains 35 sections, 22 equations, 3 figures, 10 tables.

Table of Contents

  1. Introduction
  2. Related Work
  3. Information Theory
  4. Slay the Spire
  5. Terminology
  6. Dataset
  7. Methodology
  8. Experiments
  9. Parsing the Data
  10. Generating the Full Maps
  11. Generating All the Possible Paths
  12. Uncertainty of Monster (Enemy) Rooms
  13. Act 1: First Three Encounters
  14. Act 1: Rest of Encounters
  15. Act 2: First Two Encounters
  16. ...and 20 more sections

Figures (3)

  • Figure 1: Screenshot of the game showcasing the path selection in Slay the Spire.
  • Figure 2: Relationship between Normalized Entropy and End Result of the Run
  • Figure 3: Relationship between Average Normalized Entropy in each step and Player Level