  We consider a random knockout tournament among players $1, \ldots, n$, in
which each match involves two players. The match format is specified by the
number of matches played in each round, where the constitution of the matches
in a round is random. Supposing that there are numbers $v_1, \ldots, v_n$ such
that a match between $i$ and $j$ will be won by $i$ with probability
$\frac{v_i}{v_i+v_j}$, we obtain a lower bound on the tournament win
probability for the best player, as well as upper and lower bounds for all the
players. We also obtain additional bounds by considering the best and worst
formats for player $1$ in the special case $v_1 > v_2 = v_3 = \cdots = v_n.$
