  Risk-limiting audits (RLAs) can provide routine, affirmative evidence that
reported election outcomes are correct by checking a random sample of cast
ballots. An efficient RLA requires checking relatively few ballots. Here we
construct highly efficient RLAs by optimizing supermartingale tuning
parameters--$\textit{bets}$--for ballot-level comparison audits. The exactly
optimal bets depend on the true rate of errors in cast-vote records
(CVRs)--digital receipts detailing how machines tabulated each ballot. We
evaluate theoretical and simulated workloads for audits of contests with a
range of diluted margins and CVR error rates. Compared to bets recommended in
past work, using these optimal bets can dramatically reduce expected
workloads--by 93% on average over our simulated audits. Because the exactly
optimal bets are unknown in practice, we offer some strategies for
approximating them. As with the ballot-polling RLAs described in ALPHA and
RiLACs, adapting bets to previously sampled data or diversifying them over a
range of suspected error rates can lead to substantially more efficient audits
than fixing bets to $\textit{a priori}$ values, especially when those values
are far from correct. We sketch extensions to other designs and social choice
functions, and conclude with some recommendations for real-world comparison
audits.
