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Message: <blockquote data-quote="Ovinomancer" data-source="post: 7892801" data-attributes="member: 16814">Good, all true.And, as long as you're talking about a single PDF, you're still okay for doing this.  The problem is, of course, that we're not talking about looking at all possible events, but only those that occur in the reality we're using the probabilities to model.  The scale of targets is relevant to the scale of the die rolls.  We don't have half-step target numbers because we can't roll half-step numbers.  I hope that sinks in, because it's important in a bit.It only fixes the mean, and that by way of a kludged system that doesn't address anything but the mean.  When you apply a change to fix the mean that also results in being able to have half-step results, you need to question what it is you've done.Fair enough.I strongly advise you do the same.  All of your above talks about how do deal with a single rolling method, independent of others, and I have no real beef with it (except your patting yourself on the back for your cleverness about the confirmation mechanic, which is still kludge to address the fact that you wanted to compare at a mean of 10.5 and couldn't commit to being unphysical to start with).  The issue is, and has been, in the comparison.  Recall what I said above, as it's now important.We're talking about systems that do not do half-step increments in practice, nor do dice allow for half-step increments.  So, when you compare, you MUST avoid half-step increments or you're not comparing the same things.  When you compare a d20 incremented by 1 per step to 2*3d6 incremented by 2 per step, comparing anything in a half-step of the 2*3d6 isn't meaningful in any way.  You're comparing a real outcome on d20 to an impossible outcome on 2*3d6.  This goes exactly the same for comparing 3d6 to d20/2, no matter how you recenter, because d20/2 steps in .5 increments while 3d6 steps in increments of 1.  If you compare a 6.5 on the d20/2, it doesn't match anything possible on the 3d6.  This is what I mean when I say you toss half the data, you just ignore this because there's an extrapolation and you're assuming it's a valid comparison at that point because you can derive a number.  That you invented a confirmation method just continues to let you confuse yourself that you've created a system that has half-step values when it does not have them.You even missed the boat on the fact that your confirmation mechanic produces minuscule probabilities at the half steps (a fact you glossed in your hurry to point out you know the difference between conditional an  joint probabilities -- I presented the joint probability when I set the first conditional to all, because I actually knew that was an argument to make against what I was saying).   Your method sets the half-steps at half of the probability of the full step above it.  This helps you recenter, but it doesn't create a useful comparison because you've created data where it doesn't exist via a kludge.I posted raw data above.  You cannot compare the probabilities of rolling a 12 on d20 with the probability of rolling a 12 on 2*3d6-10, because a 12 does not exist with the latter.  If you kludge it in with a post-hoc confirmation method that reduces the likelihood of rolling exactly a thirteen by half and gives that to 12, I question if you've thought through what you've done or have you just arrived at a way to make 1+1 look like 2+2 and stopped thinking about it.Maybe it's because I'm an engineer, so I always have to examine my models to see if they do what I assume they do, but the above bits about how data doesn't align is glaringly obvious to me.  You cannot compare data points where one set doesn't exist.  Data is data.  Statistics is often how you lie to yourself with math.  Always check your assumptions against reality and run a test.  Which is why I took the OP example and showed how a skew of 3 on the normal modifiers takes the near match to impossible in one method in one direction and a 10% delta in the other.  That's not the hallmark of a stable system (and it does this because of the half-step problem, a skew of 3 on the 3d6 is a skew of 6 in the scaled d20 version.  A little movement on the 3d6 curve is a lot of movement on the d20 curve, a fact I've been trying to point out to you for many posts and you've just glossed as if there's some fundamental basic I've failed to understand.  I get the basics, I'm actually looking at what the models tell us while you're still looking at lines.[/spoiler]</blockquote>

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