Differential Sensitivity Analysis of Monte Carlo Poker Equity: Jacobian and Hessian Approaches

Published November 15, 2025 | Version v1

Publication Open

We establish a rigorous mathematical framework proving that heads-up play in

poker tournaments yields a strictly higher advancement and win probability

compared to any n-player configuration with n>2. Our analysis combines

(1) combinatorial probability,

(2) Monte Carlo convergence theory,

(3) partial differential sensitivity of the equity estimator,

and (4) regret-minimising dynamics derived from Counterfactual Regret Minimisation.

Using blackboard notation and formal theorem–lemma–corollary structure,

we derive explicit percentage advantages, asymptotic convergence rates,

and structural dominance theorems.

This constitutes an original contribution to incomplete-information game theory.

Files

Name	Size	Download all
main.pdf md5:aa99dbaaa7b40edd5161e163a97f2176	562.8 kB	Preview Download