How does Facebook know which click made money in search arbitrage?
It is told. When someone clicks the advert, Meta adds a click ID to the link. The tracker stores it. When the search feed later reports revenue for that visit, the tracker sends Meta a conversion event containing the click ID and the value, using the Conversions API. Meta's bidding then looks for more people like that visitor.
This loop is what makes value-based bidding possible. Without it Meta would optimise for the cheapest clicks, which are rarely the most valuable. With it, a buyer can set a Target ROAS or cost cap and let the system chase revenue.
The quality of the loop depends on what is sent. Events sent late fall outside the attribution window. Values based on estimated revenue may be revised. And the data must be handled lawfully: in Europe and the UK the visitor's consent, captured through consent management, governs what may be shared. Sending invented or inflated conversion values to steer the algorithm is a breach of platform terms and a form of fake conversion.