The "Sultan's Dowry" problem

A sultan has granted a commoner a chance to marry one of his hundred daughters. The commoner will be presented the daughters one at a time. When a daughter is presented, the commoner will be told the daughter's dowry. The commoner has only one chance to accept or reject each daughter; he cannot return to a previously rejected daughter. The sultan's catch is that the commoner may only marry if he chooses the daughter with the highest dowry. What is the commoner's best strategy assuming that he knows nothing about the distribution of dowries?

The answer

The answer (without all of the probabilistic math) is that the commoner should wait until he has seen 37 of the daughters, and then choose the first one with a dowry bigger than any so far. With this strategy, the odds of choosing the daughter with the highest dowry are about 37%.