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The point of buying a large number of heroes is to speed up map exploration.
Usually, this looks like this: 3-4 heroes spread out in different directions, scouting for resources and other valuable locations. Another 2-3 heroes defend valuable resources located off the main paths, which are too far for the main hero to reach efficiently. Meanwhile, the main hero travels along the main paths, defeating the guards and occasionally venturing off-road to conquer particularly valuable resources.
Also, someone needs to boost the main hero at the end of each turn. And to collect what he has conquered (spending the main hero's movement points on this should only be done as a last resort).
When the free resources on the starting area run out, the scouts usually return to the main path and form a chain to transport/return troops, while the main hero usually leaves the starting area by this time.
The number of heroes for the first day is calculated based on the layout. Usually, it's something like "the number of scouting directions (including promising ones) + 2 (the main hero and the apprentice)." If a chain is needed to defend a valuable off-road resource, you can buy more heroes.
There's no point in buying the maximum number of heroes; they can be bought later and used to transport newly built troops to the main hero. I usually end up with about 5-6 heroes on the first day and then buy one hero every day or two, bringing their number to 7-8.
Hero management is calculated approximately like this: you identify the objects that need to be captured, then calculate the army's trajectory, which it will follow as it moves between these objects. Then, you adjust the available heroes to fit this trajectory.
On many maps, 8 heroes are not enough; there is so much work to be done that 15-20 would be useful.