Mana is one of the fundamental resources of Magic. Without it, you can’t play the game. Every aspect of Magic, from deckbuilding to sideboarding to gameplay, requires a deep understanding of mana.
Looking at a deck or strategy without the context of its mana base can sometimes lead you seriously astray. Building a mana base is an aspect of deckbuilding that’s neglected by players of all formats and levels of experience.
There are no hard and fast rules about what a mana base should look like; any guidelines I can offer might need to be adjusted or completely scrapped under certain circumstances. My hope is to give you some useful starting points, and intuition for when you should deviate from them.
In my opinion, some of our very best offerings here on ChannelFireball.com are Frank Karsten’s math-based articles on a variety of Magic-related topics. Frank can answer all of your questions regarding the probability of mana working out under different conditions.
There’s no need for me to reinvent the wheel. Instead, I’ll link you to a few of Frank’s most relevant articles, and we’ll use them as a baseline for further discussion.