We study the prophet inequality when the gambler has an access only to a single sample from each distribution. Rubinstein, Wang and Weinberg showed that an optimal guarantee of 1/2 can be achieved when the underlying matroid has rank 1, i.e. in the case of a single choice. We show that this guarantee can be achieved also in the case of a uniform matroid of rank 2 by a deterministic mechanism, and we show that this is best possible among deterministic mechanisms. We also conjecture that a straightforward generalization of our policy achieves the guarantee of 1/2 for all uniform matroids.

翻译：我们研究了当赌徒只能从每个分布中获得一个样本时的先知不等式问题。Rubinstein、Wang和Weinberg已经证明，当底层拟阵的秩为1时（即单次选择的情况），可以实现1/2的最优保证。我们证明，在秩为2的均匀拟阵情况下，通过确定性机制同样可以实现这一保证，并且这是确定性机制所能达到的最优结果。此外，我们猜想，通过直接推广我们的策略，可以在所有均匀拟阵中实现1/2的保证。