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Lucky Rats Survival.

Glad to hear you managed to win. As I said, it is beatable, just requires player do right moves and decisions.

I tried the map with all four underlords on one team, and amazingly won. I would still like to be able to get further on my own, but will keep trying

Initially, the idea of the map was to survive and indeed be the last man standing. It's quite tricky to do if Empire will decide to go for you, so there's a factor of luck involved. Apparently if Empire doesn't go for you then you will be the last one, but if it will - you probably won't be. Do note that game doesn't support special victory conditions, so I had to improvise here.

If you play 4v1, you can assist each other by dropping own units at AI ally's core or casting spells on their territory. This way, map turns into CO-OP survival, where your role is not only to survive, but make sure your AI allies don't die and together you manage to outpush and maybe even beat the Empire AI. It can be played 2v2, where it is competition of 2 teams trying to survive and help each other. If it is FFA, then it's survival mostly, though you can go further and try to beat Empire as well. Beating Empire in FFA may indeed be way too hard, so I recommend playing this map either as FFA survival ( russian roulete type ) or as 4p CO-OP ( Underlords vs Empire ).

The reason I gave Empire a core and thus AI is because otherwise I would have to put lots of units instead in order to offer any form of competition. Empire units when not managed by AI don't offer much resistance and can be lured and slaughtered one by one, unless there's an insane pack of high level Empire units sitting in one spot. I didn't want this kind of challenge so instead, I made it so players have to play smart and avoid angering Empire too early and getting killed. It's the same reason why I didn't make all rooms neutral - it would be an easy challenge for all players, while also would destroy the very idea of the map itself.

Off to bed for me for now

I have not played the level at all with any of the AI players on the same team, since there would seem to be no reason to do so, with the way the map is laid out, there is no way one player can actually assist another, unless I am missing something.
I really do appreciate that you've taken the time to look at this and make some changes.

P.S All Empire Bosses and units given to Empire AI from start begin with level1. They simply gain XP by killing your imps and your beasts if you claim beast den and don't manage your beasts correctly.

I gave Empire 4 mana shrines in the corner for specific reason - they will use spells to slow player's progress with lighting and heal their troops because they have to deal with all 4 players at the same time. Additionally, this is the acceptable form of Empire AI's aggression, another form ( using rally flags from start ) would simply result into player being crushed from minute 1.

Do note that 4 shrines reduce mana price by very high amount - 100 lightning spell will cost 6 mana ( 100 > 50 > 25 > 12 > 6 ), so if you provoke Empire AI too much, you might end up zapped to death. I suggest you try to learn the way Empire AI works and make sure you don't give them reason to go full force on you. This map is basically out-smarting Empire AI, as I said, don't try to beat them by sheer force of units.

Something else just came to mind. Why are all the rooms owned by the Empire anyway? Wny not have them neutral, so that both the players and the Empire have to fight to claim them? Just a thought. The other thing about being last one standing- if the goal is mainly to just survive, why does the Empire have a dungeon core that needs to be destroyed?
As to your note about game not ending-I was not referring to my core being destroyed, but, once again, if the goal is to be last one standing, and the other three underlord cores are destroyed, shouldn't that end the level?--But again, since even with the AI set on Master Level for the other three, they still do not last as long as I do, so if it did work that way, the game would be over very quickly