Pascal's formulation of expected value was revolutionary: multiply each possible outcome by its probability, then sum. This single operation transforms uncertain choices into comparable quantities. Before Pascal, decisions under uncertainty were guided by intuition or superstition. After Pascal, they became arithmetic.
The triangular array of binomial coefficients that bears Pascal's name provides the combinatorial backbone for probability distributions. Each row gives the number of ways to achieve k successes in n trials — the foundation of the binomial distribution and, by extension, of statistical testing.
Pascal's famous wager was an early application of decision theory under uncertainty: when the probability of an outcome is unknown but the payoff is asymmetric, act on the side of the larger expected value. This reasoning pervades modern portfolio construction and risk management.
Every position we take is an expected-value calculation. Pascal's framework — weighting outcomes by their probability and comparing alternatives on a common scale — is the operating logic of systematic capital allocation.