  We investigate a new tournament format that consists of a series of
individual knockout tournaments; we call this new format a Serial Knockout
Competition (SKC). This format has recently been adopted by the Professional
Darts Corporation. Depending on the seedings of the players used for each of
the knockout tournaments, players can meet in the various rounds (eg first
round, second round, ..., semi-final, final) of the knockout tournaments.
Following a fairness principle of treating all players equal, we identify an
attractive property of an SKC: each pair of players should potentially meet
equally often in each of the rounds of the SKC. If the seedings are such that
this property is indeed present, we call the resulting SKC stable. In this note
we formalize this notion, and we address the question: do there exist seedings
for each of the knockout tournaments such that the resulting SKC is stable? We
show, using a connection to the Fano plane, that the answer is yes for 8
players. We show how to generalize this to any number of players that is a
power of 2, and we provide stable schedules for competitions on 16 and 32
players
