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Flax has a somewhat atypical starting battle tactic.
Air should be upgraded in about 10% of cases—when the situation is very difficult, with many tough medium-slow contact units, etc. Usually, battles are fought with non-upgraded air.
The peculiarity of Flax's starting army is that combat power is spread across 3 slots: pixies, air, and water. In TE they are roughly equal in strength; in SoD the water stack is weaker since it comes less frequently with heroes.
Typical formation against contact units: 1p-1p-1p-1p-water-air-pixies. If the contact units are slow, single pixies use wait to absorb the retaliation while other slots wipe them out. If the striking power of air and pixies is insufficient, retaliation is absorbed until the wait, after which water can also be used to attack.
If the contact units are fast, a combat formation is set on the very first turn: pixies in the bottom left corner, air to their right, water above them, all surrounded by a layer of single pixies.
Against shooters, the formation is usually 1p-air-1p-1p-water-air-1p. That is, the air is split in half. One air slot can be replaced with fire. However, it's better to put fire in the 3rd slot and keep the air split. Though this depends on the strength of the shooters. In the first round, pixies fly forward immediately; in 90% of cases, shooters hit them specifically. Then, using wait, the elementals reach and block them in the 2nd round.
Formation for crypts: 1p-air-1p-water-1p-1p-pixies. The tactic is simple—since both air and pixies are faster than all other stacks, they wipe them out one by one, with water helping as needed.
With the appearance of fens, the shooter problem becomes irrelevant, and overall problems decrease sharply. You just need to make sure the fens don't burn their own units, especially in Dragon Utopia.
The hero, by the way, isn't particularly relevant. Grinya is a cheat, yes, but other elementalists are also good; the main thing is to have a shooter in the guild from the start. That is, you fight with the hero, spend mana—then give the troops to someone else who has mana, while this one either goes home/to the well, or on scouting/resource gathering.
Monya starts becoming useful around the 2nd week when a decent amount of power has accumulated. On the 1st week, his breakthrough strength is significantly inferior to that of the elementalists.