Editing Openai/6924d898-a68c-8009-beac-944d19ca0daf (section)

==== Just to sanity check: ====

z50=50−μσ≈50−78.825.2≈−1.14z_{50} = \frac{50 - \mu}{\sigma} \approx \frac{50 - 78.8}{25.2} \approx -1.14z50=σ50−μ≈25.250−78.8≈−1.14
PL(50)=Φ(z50)≈0.126P_L(50) = \Phi(z_{50}) \approx 0.126PL(50)=Φ(z50)≈0.126
PN(50)≈0.874P_N(50) \approx 0.874PN(50)≈0.874
So under a normal-distribution flip with:
* Fight 1 ≈ “essentially 0” for Luffy
* Fight 100 = 0.8 for Luffy

you get:
* Fight 50: Naruto still wins ~87% of the time
* Fight ~79: the matchup hits 50/50

Which lines up with your intuition:
the curve stays flat (Naruto-dominated) for a long time and only really drops off late.

So:

>