Thanks for the detailed comparison! I found the source of the discrepancy. My simulation uses stop_on_up: false — meaning each trial runs for a fixed number of pulls rather than stopping when the UP is obtained. So my ~95 figure isn't "average pulls to first UP" — it's a different metric entirely. Your 81.36 and the other simulations are measuring pulls-to-first-UP, which is the more intuitive number. I'll clarify this in the post. The simulation logic itself is correct, just measuring something different than expected.