  Balanced knockout tournaments are ubiquitous in sports competitions and are
also used in decision-making and elections. The traditional computational
question, that asks to compute a draw (optimal draw) that maximizes the winning
probability for a distinguished player, has received a lot of attention.
Previous works consider the problem where the pairwise winning probabilities
are known precisely, while we study how robust is the winning probability with
respect to small errors in the pairwise winning probabilities. First, we
present several illuminating examples to establish: (a)~there exist
deterministic tournaments (where the pairwise winning probabilities are~0 or~1)
where one optimal draw is much more robust than the other; and (b)~in general,
there exist tournaments with slightly suboptimal draws that are more robust
than all the optimal draws. The above examples motivate the study of the
computational problem of robust draws that guarantee a specified winning
probability. Second, we present a polynomial-time algorithm for approximating
the robustness of a draw for sufficiently small errors in pairwise winning
probabilities, and obtain that the stated computational problem is NP-complete.
We also show that two natural cases of deterministic tournaments where the
optimal draw could be computed in polynomial time also admit polynomial-time
algorithms to compute robust optimal draws.
