Meanwhile if you let the person actually continue, you may actually get 'Left..... Left Right Left Left... etc'.

If you are saying that this thing can't generate random numbers on the first try then it can't generate random numbers. Which makes sense. Computers have a really hard time with random, and that's why every computer science course makes it clear that we're doing pseudo random most of the time.

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.

The die is an analogy for our decision making. They are implicitly claiming that randomness must come in an order and that simply isn't how randomness works or even halfway decent pseudo randomness.

Any system whether it be a die, a person, or an llm doesn't have to know about its previous random choices to make random choices that follow some distribution going forward presuming it's actually capable of randomness.