They would not have different distributions of results on their first die roll.

They would have different distributions of results on their reported die roll.

If I am looking at their first die roll, the fact that they would have different reported die rolls doesn't matter!

Say you have a lazy researcher. They flip a coin, and if it comes up heads, they do the experiment. If it comes up tails, they just write down a random number.

If you _only get access_ to the final number, then you should discount what they wrote down – it’s 50% likely to be fake.

If you do 1,000,000 simulations of this, it’s useless 50% of the time.

But if you know the result of the coin flip, it doesn’t matter whether they would have generated a nonsense number in a different timeline, or that they’re not reliably accurate. _You know_ they’re reliably accurate in _this case_, so you can trust their data.

However, one could just move the argument up a level and manufacture a case of different intentions leading to the same distributions and then ask the same question.