"Ouch?!" - improved crit or +2 damage?

[orsal]

First - most people when they respond include most of the post so that readers can see the context

When I respond to a long post, I quote only the specific points to which I am responding. It makes it easier to identify the issues under contention. When I want more context than is included in a quote, I scroll up. I can read the entire thread if I want the context; it is unnecessary to see every little bit repeated in the responses.

#1 I state that you would effectively roll the dice 16 times before making a critical (eluding to rolls 17-20 being crits)

#2 You reply that that is irrelevant - " A single die has uniform distribution"

That line was responding to your mention of a bell curve. Are you still maintaining that attack rolls have a bell curve? Or did I misinterpret

#3 I state that I was talking about effectively rolling the dice 16 times before making a critical (eluding to rolls 17-20 being crits)

#4 You reply "What does that have to with the difference between a uniform distribution and a bell curve?"

Who is talking about a uniform distribution and/versus a bell curve? I did not.

You referred to 20 rolls of your die having a bell curve distribution. I contradicted you. You then wrote:

Oh, and "bell curve"? A single die has uniform distribution... nowhere near a bell curve

Read the post again - I said 16 rolls directly and implied 20 rolls.

If that line of yours was not intended as a reply to my contradiction of your assertion about the distribution, I don't understand why you quoted that line (and only that line!)

The advantage to probability theory is that it can identify some parameters that capture the key aspects of a distribution. I know enough probability theory to use them.

And is this actually incorporated into your numbers or not? If it is my apologies; if not?

I thought the whole basis for this subthread is a disagreement about which particular features of the distribution of random damage variable to focus on. I focus on expected value (aka mean average). Since I expect to take many attacks to finish off a challenging monster, I can justify this choice the following way: By the Central Limit Theorem, when many independent identically distributed random variables are combined, their average will almost certainly be close to the expected value of each one. In this case, the damage from each individual attack is a random variable, and I am concerned with their sum -- after all, the monster dies when that sum reaches a particular total. Since sum is (average)*(number of terms added), I maximize the sum by maximizing the average. This is why I think it is important to recognize that multiple attacks are typically involved.

No matter how you do it the numbers will, in the long run, represent a bell curve.

Which numbers do you have in mind? When you first mentioned a bell curve, I understood you were talking about attack rolls, and as I noted above, they have a uniform, not bell-shaped, distribution. It is completely unclear from the context which random variable you are referring to here. Please clarify if you wish me to decide whether I agree that the distribution is bell-shaped.

Please explain here why that is even important?

You made a statement which, if I understood correctly, demonstrated an appalling misunderstanding of probability. I wished to correct this mistake. However, I recongized that I might have misunderstood you, so I asked you to clarify. What random variable is it that you keep asserting has a bell-shaped distribution?

So lets see here - in English that would mean the context was to state, simply, over time random events create a bell curve…hmmm a tough concept to pull out of there.

That depends on how those random events are combined. If lots of independent random variables are added together, or averaged, then you will indeed get a bell curve. But your first reference to a bell curve was in the context of attack rolls or critical confirmation rolls, and I can't see why you'd want to add or average them. If you had made the same remark in the context of damage (which is a random variable), I would have let it go by uncontested.