The naive estimator is biased. If there are $N$ trials and $i$ success, a Rao-Blackwellisation of the naive estimator gives the unbiased estimator $\frac{2l}{d}\left(\frac{n}{i}+\frac{1}{i}\right)$ (to be fair this hides an assumption for a uniform prior for the probability of crossing, which induces a weird prior on $\pi$).
One can look at the variance of the estimator conditional on obtaining one success. The strategy is then to set $l=d$. Intuitively this makes sense, we want the term in $1/i$ to be as small as possible. Though for $n$ small enough, the prior dominates and the optimum is actually achieved for a small value of $2l/(d\pi)$.