  Fictitious play is a natural dynamic for equilibrium play in zero-sum games,
proposed by [Brown 1949], and shown to converge by [Robinson 1951]. Samuel
Karlin conjectured in 1959 that fictitious play converges at rate
$O(1/\sqrt{t})$ with the number of steps $t$. We disprove this conjecture
showing that, when the payoff matrix of the row player is the $n \times n$
identity matrix, fictitious play may converge with rate as slow as
$\Omega(t^{-1/n})$.
