The Molecular Decision

The Monty Hall problem: a contestant picks one of three doors, the host opens an empty door, and the contestant decides whether to switch. Switching wins 2/3 of the time. The correct strategy is counterintuitive but mathematically elementary.

The paper encodes the problem in mass-action kinetics. Each element — the player’s choice, the host’s reveal, the final decision — becomes a molecular species. The rules become reactions: the initial choice creates a molecular state; the reveal step converts it; the final decision step resolves it. The stoichiometry enforces the problem’s logic.

Under pseudo-first-order conditions, a single rate constant controls the strategy. At one extreme, the system always stays (1/3 success). At the other, it always switches (2/3 success). Between them, the rate constant tunes the strategy continuously. The authors derive closed-form solutions for the time-dependent success kinetics — explicit functions describing how the probability of winning evolves as the reactions proceed.

The encoding is not a metaphor. The molecular system literally computes the correct decision. The concentrations at equilibrium correspond to the probability of winning under a given strategy. The chemistry executes the logic.

The structural point: mass-action kinetics is computationally rich enough to instantiate probabilistic reasoning. A chemical reaction network with the right stoichiometry does not merely model a decision problem — it solves it, with the solution encoded in equilibrium concentrations. The computation is not performed on the chemistry; the chemistry is the computation. A single rate constant is the degree of rationality.