Let's say I have two ropes of length $1$ which have each been broken into three pieces with each breaking point being chosen randomly and independently. We know from previous results that the expected value of the largest length in each is $11/18$ and the expected value of the smallest length is $1/9$.
If I however have two ropes how can I determine the expected value of the largest length from the two of them. That is to say I want to pick the longest piece from the two ropes, how does the expected value of the longest piece from two ropes differ from the expected value of the longest with just one.
Thanks.
