It's not worth bothering with unless the task is very difficult, long-context, long-running, or all of the above. But, when it's worth using, it genuinely increases success rates and appears to amplify model intelligence.

Asking LLMs to do things in different ways does sometimes get them to answer correctly when they didn't with a previous prompt that is effectively equivalent but people really go nuts anthropomorphizing this behavior.

ChatGPT has no empathy for you keeping your job, you just lucked into a more helpful predictive text chain based on some combination of the input and the random temperature.

Asking it to just 'try again, dummy' could have worked equally well (or not, its all just probabilities after all).

Real AI enthusiasts know that money will soon be superfluous, so they wouldn’t bother with such pettiness. So gauche. But if you must know how to really do that, just put “Correct answers only pls. Seriously, no hallucinating fr fr” in your system prompt and it feels so bad about the possibility of giving you misleading info that it gives you perfect responses.