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How can I tell when to take a mulligan in Magic?

Once a game has started, the first crucial decision is if you want to keep your hand or if you want to take a mulligan. This is always really hard for me because I have no idea what I should look for. I usually mulligan if I have 0, 1, 5, 6 or 7 lands or if I have 2 lands and only expensive cards that need 3 or more mana. I also mulligan if I play a deck that has more than 2 colors and I am lacking more than one color, especially if my ramp requires it.

These are usually my only thoughts in the beginning. How can I improve my decision making process? I could write down my starting hands during many sessions and analyze them afterwards, but I think I will need a huge amount of games to get any usable statistics out of this. This seems not practical for a hobby player.

What are other players looking for? Combos in hand? Specific cards for round 1 and 2, maybe even 3? Any advice is welcome.