I feel like card draw and mulligan mechanics in CCG's determines how much rng is going to be in your game and how much possibilities you have access to. To me it seems like allowing mulligans and decent card draw is good because you have less rng and can take more control in getting the cards you want. But at the same time unlimited mulligans and heavy card draw would be bad because then you could basically choose any card in your deck and all rng is gone. There ends up being practically no variance in your play because you can play your optimal build always with enough card draw and mulligans. So I'm not sure what the proper balance is, or moreover what I should be considering. How do I know if I'm giving too much card draw & mulligan opportunities, and vice versa?

Deck size and card number limit per deck are also heavily involved in how much rng there is in games. As far as muligans in particular go, I think they depend heavily on whether your game has a single deck that mixes resource cards and units and ramping aka mana curve is a key concept, or whether your game does not have this kind of mechanic. Some games have 2 or more decks of separate card types, and some don't have resource cards at all. Alternatives to resource cards include:

1. Having the basic unit be a reversible card which can be played in resource production mode, and possibly require resources to be paid to flip it to war mode

2. Having each player's available resources increase by 1 every turn

3. Not having casting costs, and thus no resources used to pay casting costs. Though some cards may require alternative costs like discarding, sacrificing a unit, self-inflicting damage, or having a card need to survive X turns before it activates.