Parthenon wrote:PhoneLobster thinks two is the same as a whole lot. Dumbass.
Those were sample graphs of normal distribution they appear in the article on mean deviation due to their significant relevance to the term standard deviation which is largely used to determine how steep a normal distribution graph will look.
If you were capable of clicking on that little
linky on the pretty picture you would have discovered that actually the bell curve graph is very common.
...the normal distribution or Gaussian distribution is a continuous probability distribution that often gives a good description of data that cluster around the mean. The graph of the associated probability density function is bell-shaped, with a peak at the mean, and is known as the Gaussian function or bell curve...
And importantly the curves being discussed by Murtak and frank... are indeed bell curves that adhere to this exact definition.
And indeed do it better than most since effectively the RNG involved is nothing BUT a normal distribution generator.
Don't try and bluff me with your brief skim of the wikipedia article I linked you (brief enough to apparently neither understand it or even read the associated links). I did this and a hell of a lot more at a university level.
The standard deviation is a measure of spread that can be calculated for any group of data, not just bell curves.
Yes and no.
In that ANY set of data
has a standard deviation you are, in a rather trifling manner.
But rather specifically Frank and co were describing LOW standard deviation normal distribution curves (3d6, etc...). If you intend to actually use the term to describe data including a 1d20 then you are going to such a HIGH standard deviation that you are not only rendering the term meaningless for this discussion you are effectively revealing that you and Frank
have used the wrong term.
Talking about bell curves is MORE correct than discussing standard deviation as if it was a fixed term meaning LOW standard deviation, and indeed a rather specific and arbitrarily mapped curve at that, which is what Frank tried to do and what you now inexplicably defend.
Of course all this is still stupid because we have already at length discussed the actual odds of results occurring and the impact of all that
on this thread.
Frank introduced the term "Standard Deviation" and waved it around like a distraction, and I responded with the term "Bell Curve" while talking to him about it.
Because talking about how many times you can add a term that merely
gives you an idea of how lumpy the middle of a graph of probability distribution looks to the mean of that distribution before you exceed the maximum distribution... is
fucking mathematical gibberish.
I am pretty confident it isn't even what Frank MEANT to talk about.
But it really doesn't matter because the DATA has already been discussed, the fact that it HAS a Standard Deviation and that it FORMS a Bell Curve is really fucking irrelevant. The numbers are there the behavior is there we already spent 4 pages discussing
exactly that behavior
This is nothing more than a (poorly executed) attempt to bury the actual numbers and what they actually do in official sounding terminology that actually doesn't do anything other than describe the numbers we have already discussed.
It isn't even telling us anything NEW about the numbers already discussed. We already knew that they did that (well at least
I certainly did, apparently it was news to Frank).
Zeezy wrote:**: Depth, in this case, is defined as how many full standard deviations from the mean you can go before you leave the boundaries of the sample -- one with 1d20 (σ~5.766), versus two with 3d6 (σ~2.958); thus, 3d6 is twice as deep as 1d20. But Parthenon beat me to that, apparently!
Interestingly depth is NOT a term that you will find anywhere in those now rapidly more infamous wikipedia articles on Standard Deviation OR Normal Distribution. Indeed good luck finding the word "Depth" anywhere in the linked articles on various terms at all.
Not surprising really because it is not an especially valuable term to know, it is certainly not actually a valuable term here since it
A) Tells us nothing we didn't know already.
B) Is essentially an term invented on this very thread to describe a behavior that someone then declared beneficial. At no point has it been described WHY this behavior is beneficial.
C) Your invented depth term is especially interesting because by your own definition a Standard Deviation does not HAVE a "Depth" but a Bell Curve or Normal Distribution DOES have a "Depth".
But you know you apparently don't want to talk about bell curves and normal distributions, only standard deviations. So how the fuck we can start talking about this Depth invention of yours I have NO idea.
Parthenon wrote:For the coin flip it is easy: add another coin flip and if both are heads you succeed
You are mixing your math in bad ways here. Using binary 0-1 number generators and an "And" condition really isn't a nice thing to add at this point. So even if the numbers involved are small and aspects of combinational logic and probability theory MIGHT
sorta kinda brush on each other a bit... lets keep the combinational logic out of it for everyone's sanity.
And really if it's easy for you to "And" a coin flip to a coin flip why can't you "And" a coin flip to a 1d20 or even a 3d6? I mean. That actually IS what the d20 system does in some cases after all.
But that departs from telling us importantly what is DIFFERENT about 1d20 and 3d6 rolls. Adding an additional layer of obfuscation for no specific benefit. So again, lets not do that.
And so you describe a scenario where you
once again equate a +3 bonus at several points in a 3d6 range to a +5 bonus in a 1d20 range.
1) This is nothing new to this thread. People have been doing that since page one. It is incorrect because a +3 bonus is NOT equal to a +5 bonus over the range you are discussing. It is NOT a fair
or accurate comparison of bonus values over the discussed ranges.
2) You know that because you actually TALK about how the value changes. You even describe, for a change, why you apparently think that is a good thing.
So, this is better since you can have different sized bonuses, there is still an actual chance of success with two penalties and it is closer to what we'd expect to happen.
Lets see what you expected to happen...
with a single penalty of about 50% miss chance, or blindness in D&D. If you have two such penalties your chance of success should be around 12.5%, so I'm going to compare each action resolution method to the hoped for chance to see if they work at all.
(aside from the fact that you arbitrarily decided upon multiplicative rather than additional factoring of modifiers, which remember is bad in RPGs because
players don't like multiplying and dividing things in their heads lets just carry on with your declared goal/"expected outcome"...)
a penalty of 2.96 changes it to an 80% chance of failure rather than 75% (a 60% penalty rather than 50%) so the penalty of -3 is actually slightly too large.
So lets see. is it what was "expected"/desired from the FIRST increment of the "50%" modifier?
No.
So lets take a little note of that. "3d6 mechanic did not perform as desired on first application of modifier due to weird and shitty numbers involved in its increments of percentage chance of success".
So lets check how it performs on the SECOND bonus application.
you can have two such penalties and still be on the RNG, admittedly with a 2% chance of success rather than a 12.5% chance of success.
So lets see. is it what was "expected"/desired from the SECOND increment of the "50%" modifier?
No.
So lets take a note of THAT down. "3d6 mechanic did not perform as desired on SECOND application of modifier due to weird and shitty numbers".
But wait you have a tiny explanatory note...
Interestingly, given that a -3 penalty gives a 60% chance of failure we are actually looking at an expected 8% chance of success, which is a lot closer to the actual 2%.
Oh a revised expectation. Somewhat out of left field since we are arbitrarily declaring we must never ever revise expectations bonuses on a 1d20 mechanic in any way, but lets run with it and...
...oh no!
Even the REVISED expectation is not met and instead encounters a chance of success one QUARTER of the desired goal!
So lets take THAT down as a note "Even when cheating by revising expectations the 3d6 mechanic STILL did not perform as desired".
I
wonder why that is. Could it be because as an approximation to a
Bell Curve[/i] the results of the 3d6 behave like a Bell Curve and instead of producing the results you declared (entirely arbitrarily) as desirable over those produced by a simple transparent 1d20 mechanic just so happened to be... oh yes... that's right... the results that I expect to be generated by...
A BELL CURVE.
Now do you want to have a discussion about how a basic mechanic that has only a 2% chance of success is a generally either bad or insignificant thing to build your RPG system around including?
Or how 1d100 would be a much nicer way of doing that? (should the need to do it inexplicably arise)
Or do you want to pretend you know something about maths again so I can rip you apart in public again?