Gemini vs Grok: Playing Towers of Annoy

LLMs were asked to write a Python 3.10 client that plays a two-player adversarial variant of the Towers of Hanoi. Rules: Hero moves a disk; Villain must immediately move that same disk to an adjacent tower (or pass if no legal move). Hero's budget is 2^m + 1 moves — barely more than the 2^m - 1 solo optimum, so almost any wasted move loses. Round-robin tournament with penalty-shootout matchups: up to 5 rounds (+ sudden death), 2 simultaneous games per round with hero/villain roles swapped. Rou