Nonstandard Rant: Opposed rolls ARE more random, dammit!

[Valamir]

Am I not being clear...or are you just getting all caught up in mathematical minutia...either way we seem to be talking in circles.

So I'll try again.

Given two systems which involve identical die rolls the degree of randomness as perceived by a player in the game may in fact be very different between those systems.

It is largely irrelevant to the perception (and completely 100% irrelevant to my point) that those identical die rolls have the same range, the same mean and the same standard deviation.  They DO NOT necessarily have the same degree of perceived randomness.  Therefor any mathematical analysis that attempts to describe the systems merely in terms of the statistical parameters of the roll is flawed.

How "random" a roll is depends on several factors, IMO the most important of which is how large the random range of the roll is to the final output.  By attempting to reword my premise you are completely missing the entire key to what was being said.  The number rolled is NOT (in most systems) an indicator of anything until it is interprested by some final standard.  Knowing in d20 that you are rolling 1d20+5 tells you absolutely nothing until you know what the target difficulty is.  That target difficulty is a fixed value (once its determined) and the +5 is a fixed value.  The random range comes from the d20 but the degree of randomness as percieved by a player is contingent on the interplay of all three.

[Walt Freitag]

From a pure math standpoint, standard deviation has no relation to randomness. If I lay out a table of the sums of all 36 possible pairs of the integers 1 through 6, that set of numbers, which is not in any way random, will have the same standard deviation as a sufficiently large number of truly random fair d26 rolls. Testing for randomness requires much more sophisticated statistical analysis. I doubt any mathematician would take seriously the notion that a random string of ones and zeros was somehow less random, by virtue of its lower standard deviation, than a random string of integers between 1 and 1 million.

Erm... no. The 'table' has a standard deviation of 0. It's there. It's not random. At all. As for a 'sufficiently large' number of 2d6 rolls, that's also irrelevant. We're talking about rolling once. That's your random variable. (Sometimes, it's easy to confuse the random variable with the distribution of the variable. This may or may not be what you were doing.)

Huh? I didn't refer to the standard deviation of 'the table,' I specifically said the standard deviation of the set of numbers in the table. All sets of numbers have standard deviations, whether they're randomly generated or not. That's the point. Standard deviation has no fixed relation to randomness. It can be used to characterize one particular aspect of the behavior of a random or partially random (or totally non-random) process, function, or system, but it does not measure degree of randomness.

A clue is the fact that you state you "assume a linear scale". Well, any function that includes an added constant is, by definition, not linear.

Really, where do you keep coming up with these whoppers? Are you really saying that f(x) = 5x is a linear function but f(x) = 5x + 2 (note the added constant) is not? (Obviously yes, you're really saying that, your assertion is clear enough, but it's so patently false that perhaps you meant something else.)

It's bad enough that you insist on interpreting perfectly useful common English words (random, linear) according to specialized mathematical definitions, but then your interpretation of those definitions is so bizarre and so contrary to elementary mathematical concepts that I wonder if you might be trolling me here.

Anyhow, Valamir, I think your point is congruent with mine. "How large the random roll is to the [range of the] final output" has a direct bearing on how predictable individual outcomes become when one moves toward the extremes of the range. The standard deviation adjusts that a bit: all other things being equal, a more center-weighted roll with the same overall range (more small dice summed instead of fewer larger ones) will have a smaller randomizing effect in play than a less center-weighted one. (It may or may be felt or perceived as such in play, which adds an interesting and important twist to the issue.) But when you simply add more dice, the resulting increased range of the random roll overwhelms the additional center-weightedness and makes the mechanism less "random."

Another way of saying this is that re-interpreting the scale of the stats has just as much of an effect on the perceived (and actual, by my definition) randomness of the mechanism as changing the range of the die roll. If a strength of 3 is considered "average strength" and a strength of 5 is considered "extraordinary superhuman strength," then a resolution mechanism in which the strength is added to a roll of d10 and compared against a target is either going to feel very random (if the average target is close to 10) or very one-sided (if the average target is less than about 7 or greater than about 13).

On the other hand, if average strength is 50 and "somewhat stronger than average" is 100, then the roll of d10 will add hardly any unpredictability at all. It's practically a Karma system, because the random component can result in only a tiny advantage or disadvantage relative to the stats.

The importance of stat scales relative to the range (and, yes, the standard deviation) produced by the random component applies just as much to opposed rolls as well.

- Walt

[Valamir]

Walt...yup, I think we're saying the exact same thing.  Your examples at the end are 100% in line with how I view it.  I was about to make a comment about the length as well as the fatness of the tails in the bell curve, but you already addressed that as well.

[JMendes]

Hey, :)

I'm just gonna post some considerations, without quoting anything:

1 - I have a tendency for formal mathematics. Sometimes, this is not the most useful of attitudes, especially when the discussion migrates from the actual underlying phenomena to points of perception. Nevertheless, throughout life, I have become convinced that formalisms help to expose unconscious underlying assumptions, and that's exactly what I have been aiming for.

2 - I'm not entirely familiar with the expression 'trolling'. Some newsgroups I read often refer to 'the resident troll' and 'don't feed the troll'. In the past, I assumed this to mean disruptive or otherwise obnoxious posting. From context of this discussion, I presume this may also mean any sort of ironic leading-on, disguised as serious posting. If my interpretation is correct, then let me assure everyone that I meant everything I wrote and that I was not 'trolling'.

3 - Upon careful rereading of the threads, I have become convinced that our understanding of the underlying phenomena of fortune-based mechanisms are completely congruent. However, the language we use to describe them is much too different for this to become immediately apparent. Not only that, our methods to 'measure' randomness are highly non-intuitive to each other, furthering this miscommunication.

Well, that's it. I hope I made some sense at last. :)

Cheers,

J.

[Valamir]

For the record, while most folks on gaming forums associate Trolling with the fantasy / mythological creature of troll (where the don't feed the troll thing comes in), the actual origin of the word comes from fishing.  Trolling is the (to keep it simple) the act of throwing out lines behind the boat and then sailing around hoping some thing bites.

In reference to internet communication its precise use refers to the act of intentionally (but often surreptitiously) throwing out controversal (even inflamatory) statements (the hook) hoping someone bites on them.  Often this is done just for the carnage (i.e. fun for some people) it causes but a more sophisticated use (often seen done with some skill in political debates and interviews) is to throw people off the scent (hows that for mixing metaphors) by giving them some obvious bait to bite on.

Unfortuneatly many folks just use the term as a label for all disruptive types, which IMO diminishes its usefulness as a word.

At any rate, for the record, I did not think your comments were trolling at all but as you conclude entirely miscommunication (which is why I tried several different ways to explain what I meant hoping to find one we could connect on).  Walt was correct in pointing out how incorrect your comment on Linear was, but I expect that was a simple mistake and certainly not an effort to bait a hook (although if it had been it would be a perfect example of the sophisticated use of the trolling tactic I mentioned above...an attempt to divert the discussion into one on mathematical formulae).

This and Vincent's credibility thread are two of the most enjoyable theoretical discussions we've had recently.

[Walt Freitag]

I agree with everything Ralph said, and I apologize for the "trolling" comment. I realized soon (but not soon enough) after I posted it that what I had meant to say was "I'd think you were trolling me if I didn't know better." Because I did, in fact, know better.

But having posted the comment and it having been out there for several hours already, I thought it might be unfair to go back and edit it. A way of weaseling out of doing the right thing, which is to apoloize.

This has been an interesting discussion, and I hope it might be useful to present and future system designers. Even if only to convey the invaluable message (after Mike Holmes) that these sorts of design decisions are a lot trickier than they look, and deserve the most careful thought you can put into them.

- Walt