Optimal Single-Choice Prophet Inequalities from Samples

We study the single-choice Prophet Inequality problem when the gambler is given access to samples. We show that the optimal competitive ratio of \(1/2\) can be achieved with a single sample from each distribution. When the distributions are identical, we show that for any constant \(\varepsilon > 0\), \(O(n)\) samples from the distribution suffice to achieve the optimal competitive ratio (\(\approx 0.745\)) within \((1+\varepsilon)\), resolving an open problem of Correa, D\"utting, Fischer, and Schewior.