Managing the Entrepreneur's Miracle Budget

Entrepreneurial ventures typically require multiple independent conditions to hold simultaneously for success. This paper develops a formal framework for decision-making under such multiplicative uncertainty. When a venture's success depends on several factors—each of which must resolve favourably—even modestly uncertain factors compound to produce low overall success probabilities. I introduce the concept of a miracle budget: the maximum aggregate uncertainty a venture can carry while remaining viable. The miracle budget increases with a venture's payoff-to-cost ratio but only logarithmically, so even transformative opportunities buy only modest additional slack in aggregate uncertainty. The framework characterises optimal experimentation strategies, including the value of information from different experimental designs, conditions for optimal sequencing of experiments, and the allocation of experimental effort across uncertain factors. A hierarchical model distinguishes real miracles—genuinely uncertain factors that can only be resolved by trying—from apparent miracles—factors that seem uncertain but can be resolved through investigation. The framework yields actionable principles for early-stage entrepreneurs: compute your budget, prioritise low-cost tests with high “kill” probability (and, when experiment costs are similar, start with the most uncertain factors), and focus early-stage work on learning how many miracles you actually face.