>If You asked me to pick a random number between one and six and ignore all previous attempts, I would roll a die and you would get a uniform distribution

I believe what GP is getting at is that if you didn't have a die, and you truly ignored all your previous attempts to the point of genuinely forgetting that the question had been asked, then your answer would likely be the same every time. Imagine asking a person with severe Alzheimer's to pick a number, then asking again a few minutes later. You'd probably get the same answer.