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We investigate parking in a one-dimensional lot, where cars enter at a rate$\lambda$ and each attempts to park close to a target at the origin. Parkedcars also depart at rate 1. An entering driver cannot see beyond the parkedcars for more desirable open spots. We analyze a class of strategies in which adriver ignores open spots beyond $\tau L$, where $\tau$ is a risk threshold and$L$ is the location of the most distant parked car, and attempts to park at thefirst available spot encountered closer than $\tau L$. When all drivers usethis strategy, the probability to park at the best available spot is maximalwhen $\tau=\frac{1}{2}$, and parking at the best available spot occurs withprobability $\frac{1}{4}$.

Where Should You Park Your Car? The $\frac{1}{2}$ Rule