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Played for a month (version 1, with a hero), and on day 4 of week 5, the game crashes during the turn of the orange player. It was going well; after the first two difficult weeks, I got everything I wanted, and then I was easily defeating everything without any losses. I was just about to swim through a whirlpool to the upper left corner, thinking I could grab a couple of stacks of skeletons and return through a portal to fight the orange player's hero, but it wasn't meant to be. Now I'll try to figure out the reason, because before that, I was scouting the map and checking the orange player's behavior, and there were no crashes that day.
Added 14 minutes later
I defeated one of the orange player's secondary heroes – no crash occurred; strange things are happening.
Added 29 minutes later
Although, no, it only helped once; the crashes still occur on that day after reloading. In short, if Zoltan, the orange player's hero, is still alive on day 4 of week 5, the game crashes. If I kill him, it seems to be okay, but I'll have to replay a bit.