Comment by kstenerud

My first guess would be that polite requests cause some agents to trust their initial approach to the problem more, as the caller has indicated that the agent is more capable, and agents tend to take the implications of what you say at face value since they are trained to be accommodating.

It would be interesting to see this experiment run using prompts leading with "You'll probably get this wrong, but I'm asking anyway in case you get it right: ..."