There are two kinds of random on these sites: the kind you can audit later, and the kind you are asked to trust. Only one of them survives a bad night.
Three things. A seed history, so yesterday's rounds still have their commitments on record. A nonce log, so every round sits in sequence with none missing. And a verifier you can run yourself, ideally a formula you can check with your own tools rather than a button on the same site. With those, any round can be replayed months later, by anyone.
No history means old rounds cannot be re-checked, only believed. A verifier that only exists on the operator's own page can say whatever the page wants. Seeds that rotate without a record break the chain between what was committed and what was revealed. Each gap turns an audit into a favour you are asking from the house.
If you would like to learn more about the technical workings of provably fair algorithms, you can download the whitepaper.