Every depth from 0 to 10 hunts the same set of starting positions. Pick the settings and run.
See the numbers
Start with ten predators of every depth. Each generation, every predator hunts once and the well-fed leave more offspring. Depth is inherited, with the odd mutation.
The world
A 20 by 20 field with walls. One predator, one prey, both moving one cell per tick, or holding still. The prey forages: it picks a spot and walks there, then picks another. The predator wants to eat it within 200 ticks.
Seeing and being seen
The prey notices any predator that moves within four cells of it, and then runs from that spot for four ticks before it forgets. A predator holding still is invisible, even next door. Since both move at the same speed, a prey that has seen you cannot be run down. The only way to eat is to be where the prey is going before it gets there, and to be still when it arrives.
Foresight
A predator with depth k can play the next k ticks forward in its head. It knows the prey's rule and where the prey is heading, so it can imagine, for each thing it might do, what the prey would do in reply. It considers chasing, holding still, and going to wait at any cell on the prey's expected path, and takes the plan that eats soonest. If none eats within k ticks, it takes the plan that ends closest, counting the prey's remaining alarm as distance it will still put between them. It re-thinks every tick. Depth 0 is a plain chase.
The predator's imagination has limits that are not noise. It cannot know where the prey will head next once the prey reaches its current spot, so its picture of the future ends there. And the prey's fickleness dial makes the prey change its mind with some probability per step, which no model can see coming. A forecast t steps ahead is right only if the prey has not changed its mind in the meantime.
What foresight costs
Every tick costs one unit of energy, plus the cost dial times depth. A capture is worth 150. The hunt's result is what is left. With the dial at zero, deeper is never worse; with it above zero, there is a depth past which seeing further costs more than it earns.
The cost never changes what the predator does, only the bill. So one batch answers the question at every price: the "where the energy goes" chart splits each depth's result into what it earned, what it spent hunting and what it paid for seeing, and the chart below it shows which depth earns most as the price of seeing rises. With a predictable prey the answer is a cliff: ten moves of foresight wins until seeing costs about 0.3 per tick per unit of depth, then one move wins outright. The depths in between are always beaten by one side or the other. That is worth dwelling on: a middling foresight pays the price of seeing without buying the ambush.
What you will see
A plain chaser starves. Shallow foresight, one to three moves, produces a patient stalker that waits when the prey wanders near and eats in fifty ticks or so. Around four to five moves there is an awkward middle: the predator can see the prey take fright but not calm down again, so it sometimes chases an alarmed prey that it cannot catch. From six moves up the predator plans real ambushes and eats in about twenty ticks.
Turn the fickleness up and the picture inverts. Long plans are built on a path the prey abandons; patient, shallow predators do about as well as before, since a wandering prey blunders into a still one just as readily. Turn the cost up and evolution settles on a middling depth. That inversion is the point of the game: foresight is an adaptation to a world regular enough to be worth forecasting.
A whole field
The field mode puts two predators of every depth on a larger board with a standing population of prey. Each predator hunts the prey nearest to it and imagines only its own effect on that prey; each prey fears the nearest predator it saw move. A meal pays 150 energy and the prey is replaced elsewhere, so the prey never run out. A predator that reaches zero energy dies; one that reaches 250 divides into two, the child inheriting its depth with the odd mutation. What you see is which depths can pay their way in that world, and how quickly the others starve. The crowd changes the answer: a prey alarmed by one predator's movement spoils another predator's ambush, so the long plans that win the solo hunt are often wrecked, and the patient shallow stalkers do better than they did alone. That, too, is a lesson about foresight: its value depends on how many other actors are stirring the same future.
Reproducibility
Every hunt is a pure function of its settings and a seed. In the batch runs, every depth hunts the same seeds, so all eleven predators start from the same positions and face the same fickle prey. A difference between depths is a difference in foresight, not in luck.