Hey!

So mutations are a pretty chance occurrence. Without items, it's pretty unlikely to get one, however, there are some breeding items that can be used to slightly increase your chances. Additionally, some mutations can pass naturally, while others cannot. Those would need items in order to get a chance at passing.
There's no real "benefit" to having mutations, in that they don't affect the lions at all (unless they are lethal, clawless*, eyeless, blind, or toothless. Lions with these mutations cannot hunt, patrol, or be kinged, *clawless exempt. They can patrol and be kinged, but cannot hunt). A mutated lioness isn't any better at hunting / etc than a non-mutated one. The only difference is that mutations are sought after, therefore, you can usually sell mutated lions for more currency, and mutated studs tend to be a little more popular.

Exploring will be your best friend to level up your king. As he levels, his impression will increase, which will give you lionesses in Explore that may already be in heat, be chased lionesses, or even a chance at CRB'd lionesses (lionesses who had a Cotton Root Bark used to terminate a pregnancy, they are slightly more likely to produce a mutated cub). CRB'd lionesses occur after he reaches Dreamboat impression.

Creating a hunting party and hunting your lionesses as often as possible is a great way to get a start on stocking up carcasses. Selling your surplus can help you rack up some SB quickly, which in turn can allow you to enter raffles for items / lions / currency, buy decors or lions, etc. Playing games can also help you stat up your king, gain some items, and stock up on SB as well!

Hope this helped! Welcome to the game :)

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