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What does flipping a coin actually buy you?

You want to test a new onboarding flow. One engineer suggests giving it to everyone who signs up on odd-numbered days and using even-day sign-ups as the control, since that is easy to implement. Another insists on assigning each user by a coin flip.

Explain what randomization buys you that a rule like "odd versus even days" cannot, especially regarding things you never measured.

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