Probability of Hit (POH)

Mathematical Reference Card v1.1

ONESHOT

1. Gaussian Distribution (2D)

Models bullet dispersion as a normal distribution in horizontal (x) and vertical (y) axes.

f(x,y) = [1 / (2πσₓσᵧ)] * exp[-(x²/2σₓ² + y²/2σᵧ²)]

Where σ is the Standard Deviation of your rifle system (approx. 1/2 of your 5-shot group size).

σ increases linearly with distance (D).

σ_D = σ_100 * (D / 100)

ONESHOT executes 10,000 parallel trajectory simulations to compute the hit probability.

POH = (Σ hits) / N Confidence Interval (95%) = 1.96 * √[(POH * (1-POH)) / N]

For N=10,000, the margin of error is < 1%, providing high-fidelity ethical shot validation.

POH %	Classification	Recommended Action
95%+	High Certainty	Ethical shot; Proceed with confidence.
80-94%	Marginal	Re-check wind; Consider closer proximity.
< 80%	High Risk	Ethical risk; Do not engage live game.

1 MOA = 1.047 inches @ 100 yards

1 MOA = 2.908 cm @ 100 meters

1 MIL = 3.438 MOA

1 MIL = 10 cm @ 100 meters