We have 30 competitors and they are throwing a hammer. Let's assume they have equal skill. Let's assume competitors cannot have equal throws. Each one throws only once. If result of a competitor is better then result of previous competitors then he becomes a temporary leader. What is expected value of a numbers of leaders in this competition?
I have issues with expressing this question in framework of probability, I see that the answer is greater than $\frac{3}{2}$ because first competitor always becomes a leader and the second one has $50\%$ chance to become one, but I get confused after that.