I tested Bertrand's 1887 ballot formula on 648 vote splits and the answer was always (p-q)/(p+q).

In 1887 Joseph Bertrand sent a four-page note to the *Comptes Rendus* of the French Academy. The question he asked is one you can pose to a child. Two candidates run for office. A wins with p votes, B loses with q < p. The ballots are pulled from the