benlehman

We had this debate last night, neh? I agree, that many of the people on the theory board don't grok probability. But, to be fair, it's really not simple stuff. Complex enough that I'll say you're WRONG. But I think we actually agreed on this last night. I also think, though, it should be made clear.

From the perspective of a single event, you are correct: they are indistinguishable, in that their probability distributions are identical. However, you're making a big assumption, that there is no prior knowledge and no knowledge contained in the event. Let's take D20 as an example, as it is fairly simple probabilistically (flat distribution).

Let's assume that you have no prior knowledge on the difficulty of the task, no indications from the GM such as "this looks hard." It is a complete black box. If the GM rolls hidden, then you gain one bit of information: success or failure. With enough such events (under controlled conditions, no changing modifiers, etc.) you can estimate your success probability to reasonable accuracy. This is a simple Bernoullli trial.

Take, in contrast, when you roll openly: you can gain a *lot* more information. If you roll a 10, for example, depending on success or failure you have defined the probability -- with certainty -- as greater than or less than fifty percent.

This is important when you make series of rolls; if the underlying mechanisms are changing so quickly that each action is functionally independent of the others, then sure. But this is rarely the case.

To be specific, much more important than raw probabilities is conditional probabilities: p(A) | B, etc.