Twenty peeks at a checkout test and a suspiciously fast win

To build trust in their A/B tooling, an e-commerce team runs an A/A test: both arms get the exact same checkout flow, so any measured difference is pure noise. They watch the conversion dashboard once a day for 20 days and record whenever the p-value dips below 0.05. To their surprise, it crosses 0.05 on two separate days.

Explain why an A/A test with no real difference still produces "significant" days, and roughly how likely at least one false crossing is over 20 daily looks.