This is a list of important strategies which can save large amounts of time, in order of approximately decreasing importance:

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1. Flee strats

• Fleeing an island will always unlock the connected island that's furthest ahead of the mist, even if you flee as soon as possible. Doing this is risky since you don't get the gold, but it can save relatively massive amounts of time. Once you're sure enough that you can beat the Last Stand, you can flee islands until then. You may want to still do flat islands though, since they have a better gold/time ratio.
• However, small boats can only hold 7 people, not a full squad of 9. To flee sooner, you can use warhammer, mines, and bombs to kill your own troops. Bombs are most effective for this, since they can hit many squads at once if you get them all in the same tile at the right time. Be careful though: the now commanders will be knocked down for several seconds. Your troops can also be shot at while in the boats. If any of your commanders die, just restart the island and try again.

2. Slow motion reduction

• Try not to spend too long in slow-motion.
• Squads can be selected with hotkeys, which can be changed in the settings. By default, the squads are bound to 1, 2, 3, and 4. They can be rearranged at the start of each island.
• You can move squads without any real amount of slow motion by moving the cursor to the tile, selecting the squad with the hotkey, and clicking immediately. Similar things can be done with abilities.
• My hotkeys for squads are q, w, e, and r, and abilities are a, s, d, and f.

3. Upgrade planning

• Ironically, in-between islands is the most difficult part of the game to speedrun optimally, since there's nothing to wait for. While you're waiting for vikings to land, try to think about how much gold you have and what you plan to spend it on.

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Final minor tips:

• Pikes can actually set up next to viking archers and even brute archers, meaning they can actually be used to kill them in tight circumstances.
• You can finish islands sooner by using archers to kill the last vikings before they land. This could be done slightly faster by fleeing with archers from a boat next to where the last boat is going to land. This also probably means it makes sense to have two archer squads, so you can do this more often.
• There's no reason to turn level restarts off. This also allows you to play riskier with flee strats.

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Good luck! Though all this seems pretty hard, you definitely don't need to do all this perfectly to get a good time or even a world record, at least not yet.