alt Hacker NewsServer-authoritative games. Basically the client does stuff, gives the list of moves to the server along with a checksum/end result. Then the server runs the same commands on the same starting state and checks if it got the same result.
If a==b, then everything moves on as normal. If not, the client gets a synchronisation error and has to rewind back to the last known good state.
Completely unfeasible for anything real-time pretty much.
Having done modding for some older shooter games built on the server-authoritative model, it's still possible to create a "pingless" experience, but it requires more calculations and compromises on client/server trust to make it work. For shooters specifically, you want the client to provide instant feedback when the gun fires, and ideally when they hit an enemy. You can achieve this by telling the server "I was at position A and shot my gun at position B and hit enemy Bob." The server will validate all of this before informing the client who fired and the client for "Bob" that Bob was killed. The compromise here is that the server must trust that the client isn't sending forged data, or the server must do additional computations to validate it.