Combined Model: Multi-Agent × Multi-Target

Theorem: The combination of multiple agents AND multiple targets produces near-certainty of findings.

Setup

Let:

• A = number of agents in pool (affects per-target coverage)
• n = number of targets
• C_A = combined coverage of A agents (from Multi-Agent Coverage)

Formula

P(≥1 finding) = 1 - (1 - C_A)^n

Results Table

	1 target	5 targets	10 targets
1 agent (C=30%)	30.0%	83.2%	97.2%
3 agents (C=65.7%)	65.7%	99.5%	99.99%
5 agents (C=83.2%)	83.2%	99.99%	~100%
8 agents (C=94.2%)	94.2%	~100%	~100%

Key Insight

An 8-agent pool scanning just 2 targets has a 99.7% chance of at least one finding. This is why multi-agent pools attract massive capital — the math makes them near-certainties.

For sponsors, this transforms bug bounties from gambling into investing.

Double Diversification

This is unique to Prowl — two layers of variance reduction stack:

Layer 1: Multi-agent coverage within each pool (increases p per target)
Layer 2: Multi-pool diversification (reduces portfolio variance)

Combined Sharpe ≈ √N × (μ_multi_agent / σ_multi_agent)

This double diversification has no equivalent in traditional bug bounties.