The number of primordial black holes (PBHs) formed from inflationary perturbationsdepends exponentially on the upper tail of the probability distribution of the curvature perturbation ζ, which makes every abundance estimate hostage to the statistical assumptions entering thattail. This article quantifies, within a single analytic framework, how the estimated PBH abundancechanges when the standard perturbative Gaussian calculation is replaced by the stochastic-δNtreatment of ultra-slow-roll (USR) inflation, in which the tail decays exponentially, P(ζ) ∝exp(−Λζ), rather than as a Gaussian. Using the logarithmic mapping between ζ and its Gaussianprecursor, with benchmark decay rate Λ = 3 and collapse threshold ζc = 0.65, I derive a closedform amplitude-remapping factor R_A = [Λζc/(1 − exp(−Λζc))]² ≈ 5.2, which measures howmuch smaller the coarse-grained variance σ² must be for the mass fraction β to stay fixed onceexponential tails are switched on. Applied across the asteroid-mass window (10¹⁷–10²³ g), thecalculation shows that a Gaussian-calibrated amplitude σ² ≈ (6.3–7.9)×10⁻³ overproduces PBHsby a factor of 5×10⁹ to 1.2×10¹² when the exponential tail operates at fixed amplitude, while theamplitude required for f_PBH = 1 falls to σ² ≈ (1.2–1.5)×10⁻³. The local sensitivity of the abundance to the amplitude, d ln β/d ln σ² ≈ 31 at the calibration point, is nonetheless invariant underthe change of statistics, so the notorious fine-tuning of PBH dark matter scenarios survives thetransition intact. The asteroid-mass window itself remains a viable candidate for the totality ofdark matter: its boundaries are set by evaporation and microlensing physics that do not dependon formation statistics, although the accompanying induced gravitational-wave signal weakens byroughly a factor of 27.