Probability of Assembling Urza's Tron by Turn 3 — A Case Study in Magic: The Gathering
Abstract
We present a rigorous probabilistic analysis of assembling Urza's Tron opening hands in Magic: The Gathering. Using multivariate hypergeometric distributions and inclusion-exclusion principles, we derive exact expressions for Natural Tron, Assisted Tron via Expedition Map, and Turn-3 Tron probabilities in seven-card opening hands, extending these results through comprehensive mulligan analysis. All theoretical predictions are validated through Monte Carlo simulations with one million iterations, confirming the analytical framework's accuracy.
Fields of Study & Subjects
Probability and Statistical Research
Artificial Intelligence in Games
Advanced Combinatorial Mathematics
Publication details
- Journal / source
- Zenodo (CERN European Organization for Nuclear Research)
- Publication date
- 27 February 2026
- Language
- EN
- Document type
- Preprint