This is one of the rare cases where you can outperform the mean by a large margin.
The standard deviation of the mean-based estimator, which measures its accuracy, will go down like 1/sqrt(n) where n is the number of samples in the finite set. This is the rate standardly seen in lots of estimation problems.
But the standard deviation of the max-based estimator will go down like 1/n, a much faster rate. That's one manifestation of the "weirdness" of this problem. It means you can get surprisingly good estimates of the number of tanks considering the small numbers of observations.
EDIT : So there's about a fifty fifty chance that the second observation will be bigger than the first. After the second observation the range of possible future observations will be divided into 3 zones, 1 below the lowest of the previous 2 observations 1 above the higher and 1 between the two previous observations, so there is now only a 1/3 possibility of the next observation being above the higher of the 2 previous observations. Next time that drops to 1/4 then 1/5, so that's how the standard deviation decreases proportional to 1/n