The three-set series containing two wins in a row are \(WWW\), \(WWL\), and \(LWW\) (where \(W\) is a win, and \(L\) is a loss). Let \(p\) be the probability that Elmer beats his father, and let \(q\) be the probability that he beats the champion.
Using the champion-father-champion ordering, the probability of two wins in a row is:
\[qpq + qp(1-q) + (1-q)pq = 2pq-q^2p\]
Using the father-champion-father ordering, the probability of two wins in a row is: \[pqp + pq(1-p) + (1-p)qp = 2pq - p^2q\]
Since, \(p > q\), we know that: \[p > q\] \[pq > q^2\] \[p^2q > q^2p\]
It follows that \(2pq - q^2p > 2pq - p^2q\). Thus, Elmer should choose the champion-father-champion ordering.