This was just something I encountered while pursuing my hobby, of finding something to interest me, so not really my idea. Just thought it could work, so suggested it.
Also, I think there are quite a few things you can use as a basis for it, such as: The exhibitions' calculations, Battlefield, and maybe even rarity of genes, how quests (how you sometimes receive items), and construction (Artissan), etc
Anyways, glad you like the idea, and that I necro-ed the thread to suggest it.
Edit: Going to expand on my 2nd paragraph: You don't really have to read it, it's more of just me babbling on, as it could just make this more tedious, like how you guys were stuck on tracking movement for the last suggestion, pretty being trapped in a box. Kinda wish there was a spoiler tag or something :P
Exhibitions: This could help with how pet's are judge -- e.g scores, and depending on the place, the pet/party's score could vary, due to different requirements.
Battlefield / Arena: Though I haven't really been here much, it might be useful for collecting battle results, or you could just use the one already in place for the Arena. -- Also, if I remember correctly, there was a scoring system for wins/loses here too, as well as tactics.
Quests: This may be used for requirements, or for bonuses -- E.g if you meet the requirements, you get a bonus to your score, and depending on your overall score, you either get more rewards, or maybe fail.
Construction: This is more of concerning the gene Artisan, and other related abilities; there is already a code for if you have more then the required stat, you get back some of the required material, might be able to expand on it for auto-explore.
Levels: This could give a multipler to the reward, say something like 1.5 for level 50, 1.1 for level 10, etc -- It could be tied together with what my Construction idea.
Expanding a bit further:
How I see it, you could probably do something like a score system, and depending on how much your score is, you'll get a percentage of winning/failing, and if you're over, you may get more rewards -- I'll try to make an example.
Lets say we'd be able to auto-explore the Desert.
The terrain would be suitable for lizards, due to the heat, so they'll get a bonus for there. It may also include some stat requirement like constitution. -- Pretty much something like "The Desert is a harsh terrain, and in order for you to successfully explore it you'll need a lizard and/or high constitution [80] (though I don't know if the requirements well be visible or not). Then if you meet the requirement, you get a bonus to your score. -- This would be what I meant when I talked about quest.
For the Exhibition -- the pet could gain scores through color, genes, etc, and it can be used as a base for the overall success scoring.
My Pet Sales page --
Currently have 3 extra Blueprint: Military Academy level 3
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