  We consider the problem of correctly identifying the \textit{mode} of a
discrete distribution $\mathcal{P}$ with sufficiently high probability by
observing a sequence of i.i.d. samples drawn from $\mathcal{P}$. This problem
reduces to the estimation of a single parameter when $\mathcal{P}$ has a
support set of size $K = 2$. After noting that this special case is tackled
very well by prior-posterior-ratio (PPR) martingale confidence sequences
\citep{waudby-ramdas-ppr}, we propose a generalisation to mode estimation, in
which $\mathcal{P}$ may take $K \geq 2$ values. To begin, we show that the
"one-versus-one" principle to generalise from $K = 2$ to $K \geq 2$ classes is
more efficient than the "one-versus-rest" alternative. We then prove that our
resulting stopping rule, denoted PPR-1v1, is asymptotically optimal (as the
mistake probability is taken to $0$). PPR-1v1 is parameter-free and
computationally light, and incurs significantly fewer samples than competitors
even in the non-asymptotic regime. We demonstrate its gains in two practical
applications of sampling: election forecasting and verification of smart
contracts in blockchains.
