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A turquoise player showed up when I captured my second town. It took some effort to defeat him – the difficulty was medium. I rebuilt the towns as much as possible and headed towards the sea.
Then, two purple players appeared – both with medium difficulty as well. I thought, "Oops," and started running away from them – luckily, my Sextant and Logistics skills were maxed out, and I also had a Beacon.
They started chasing me. And that's exactly what I wanted – while this pair was circling around me, I calmly cleared the waters of gems, wood, and artifacts. The resources I obtained were used to rebuild the towns, and after a couple of weeks, I returned to land. By the time the purple players caught up, I had already managed to visit a Castle, upgrade my "toys," and gather troops. After that, defeating the purple players wasn't a problem – I had four dozen Blood-Eyed creatures and the rest in proportion.
I captured the remaining castles in just a couple of weeks. The entire mission took 4 months.