The Causal Question
Randomization: The Gold Standard's Mechanism
What the coin flip actually buys
Randomization's magic isn't that treated and control groups are similar — it's why: the assignment mechanism (the coin) causes treatment but shares no causes with anything else. Every backdoor path into treatment terminates at the flip.
The consequence that matters: randomization balances unobserved confounders — things you never measured, never thought of, can't name. Matching and regression adjust only for what you remembered to log; the coin handles the rest in expectation.
That's the whole difference: observational adjustment is a list you compiled; randomization is a structural guarantee.
insight
The coin flip is the only 'adjustment' that controls for confounders you haven't named. Every observational method is trying to approximate what randomization gives free.