How many sources of a colour your deck needs to cast a spell on time, and how often the sources you have will get you there.
How this is worked out
It’s the same exact maths as Opening Hands: the chance that your opening seven, plus a draw a turn, include enough sources of the colour. The approach follows Frank Karsten’s work on mana bases, in his article “How Many Sources Do You Need to Consistently Cast Your Spells? A 2022 Update”, worked out here for Commander’s 99 cards and a draw on everyone’s first turn.
The switch for games where you hit your mana answers a narrower question: of the games where you have as many mana sources as your turn number, how often is the colour there too. That’s how Karsten frames his own tables, so expect a higher figure with it on.
Your opening hand is 7 cards and each turn you draw one more. In a pod of three or more players nobody skips their first draw, so by your turn 3 you’ve seen 10 cards. In a duel, the player going first skips it. Your commander starts in the command zone, so it isn’t in your library: that’s 99 cards, or 98 with partners or a background.