Do you know the age of the plant? That would change things a bit...

Basically you would want to stop earlier, because your expected time to grow 138 cones given the ages is smaller than without knowing the ages.

Not unless you're cheating. Of course, you could estimate them, since you know when you planted it.

Of course this is very theoretical, because in real Minecraft life you just plant all of them since you can retrieve them after you've planted them.

I think it's even true if you don't know the age. Liopoli assumes that it takes on average 16^4/3 ticks to spawn a cone for every plant. That's only true if the time to spawn is geometrically distributed, here it's the sum of 16 geometric distributions. Basically, for a random plant far enough in the future, you would guess that on average it has age 8, so it does only need 8*16^3/3 ticks to spawn a new cone.

It now get's a bit more complicated, because at the time you want to start harvesting probably most of the plants a quiet young (because you just planted them, but anyway even if they have age 2 they produce a new cone a but faster compared to the geometric situation), and only the older ones can be assumed to have a random age. But basically I would guess because of this you want to start harvesting a bit earlier, as the first new cones spawn a bit faster, so you have less time for a new plant to earn back its investment (which now really takes 16^4/3 ticks on average).

:e also, if my simulations are correct, it doesn't really matter. Stop somewhere between 100 and 150, the variance is much larger than the difference in expectation values...