Spawned from: [URL=http://www.indie-rpgs.com/viewtopic.php?p=130933#13093]This thread on dice

In the context of dice mechanics, I put forward the following definition of "randomness":

A dice mechanic is considered more random if it is less predictable. That is, the more strongly a dice mechanic clusters around a particular result, the less random it is.

"Result" can be the number that the dice are used to generate, or the game event that the dice are used to determine.

"Randomness" and "unpredictability" are virtual synonyms in this context.

I agree. That's exactly the sense I was using it in my post near the end of the parent thread. "More random" therefore means simply less predictable.

While "random" has many different technical meanings in different disciplines including mathematics, information theory, physics, and philosophy, making any statement about relative randomness open to endless argument, statements about relative "predictability" can be backed up with actual cash wagers. :-)

"Clustering around a particular result" might be a bit misleading in some cases, though, because when we're discussing systems we're often looking at how the distribution of results changes across a range of some other variable (such as character skill level or task difficulty or situational modifiers). Consider three systems in which a character's snark-bagging chances are being evaluated:

System A: The average character has a 45% chance of successful snark-bagging; the world's best snark-bagger has a 55% chance.

System B: The average character has no chance of successful snark-bagging; the world's best snark-bagger has a 20% chance.

System C: The average character has no chance of successful snark-bagging, but anyone with a proficiency in snark-bagging has a guaranteed success.

System A is the least predictable. System B is very predictable always, since a prediction of failure is very likely correct in every instance. System C is even more predictable if we know whether the character has the proficiency or not. I'd call system C the most predictable because it trends most strongly toward higher predictability over the relevant range of input conditions. However, in a specific instance it's no more predictable than system A if we don't know whether or not the character has the proficiency.

- Walt

From reaction over on the parent thread, my little post over there was unclear as to my intent. The sum of what I was trying to say is now easier to express under this idea that "more random equals less predictable."

My ideas on this have been developed because I have a half-finished game design which includes a dice mechanic that doesn't quite work, yet...
However, I think it is a good illustration of randomness. Basically, one die is used, plus a constant, per roll. The number of sides on the die and the constant must equal 20. Having a d20+0 is obviously not as good as having a d4 +16 because it (the d20) has potential for more results. (outside the range of the d4, none of which are "as good") Thus, result of the roll is more random...

I think I neglected the concept of having the sides+number being equal over in the parent thread, which added confusion on what I was trying to point out. I used multiple dice and compared it to a single die, which adds all of the other factors mentioned by various posters. However, randomness is dependant, to an extant, on die size and added constants.
Mine is not the only system that is reliant on this idea. Look at the Window...

Hopefully, this clears up my point on the parent thread and adds to the meaningful discussion on this one. Please forgive me if I have been unclear on anything.

(note: the above dice system has some problems with playability that I'm still considering, but I don't think it is a randomness issue...)

Cheers
Jonathan

If more random means less predictable, why not just say 'less predictable'? Game and probability are already both rich in the terminology we need to describe these concepts, why start inventing our own?

We're not inventing a definition of randomness, we're selecting one from the various definitions used by various disciplines.

Vaxalon wrote: We're not inventing a definition of randomness, we're selecting one from the various definitions used by various disciplines.

Originally posted by ErrathofKosh
(note: the above dice system has some problems with playability that I'm still considering, but I don't think it is a randomness issue...)

MarcoBrucale wrote: The characteristics would run on a numeric scale of multiples of four: 4,8,12,16,20,24, etc. When you attempted a task related to one of your characteristic, you had to pick one or more dice, whose maximum possible result had to be equal to the relevant char. If you rolled the maximum (or the minimum) possible result, you could trigger some positive (or negative) 'special effect'.

simon_hibbs wrote: Therefore the only incentive I can see for ever rolling less than the maximum number of dice is laziness.

MarcoBrucale wrote: Your system reminds me in some way of an old italian game called 'LexArcana'.

Jack Aidley wrote:

Vaxalon wrote:
We're not inventing a definition of randomness, we're selecting one from the various definitions used by various disciplines.

Ok. But why? What is this extra terminology getting you, that simply saying 'less predictable', doesn't get you?

Jack, I think you've kinda missed the point. We understand that you view randomness as an either / or binary proposition. But randomness does not have an all or nothing definition. Randomness means many things across many different fields. In this thread, for example, Vaxalon is using the term in exactly the same way that they do in the cryptgraphic field: randomness is a measure of relative predictability. Something that is more easily predicted (say, an algorithmic PRNG) is a lot less random than a "real" RNG, like a white noise generator.

May I suggest a slight modification to the definition of randomness as 'unpredictability'?

Take the following scenarios: D4 roll, and 2d4 roll.

For a D4 roll, your maximum 'predictability' is going to be 25%. For 2D4, it's also going to be 25% (assuming your prediction is "5".)

However, I think that we would consider the 2D4 roll to be more random.

Therefore: consider randomness as a combination of unpredictability and degrees of freedom.

The 2D4 roll has a similar predictability for certain guesses, but the extra degrees of freedom (ie potential different results) makes it more random.

I guess this may be a bit of a subjective or 'perceptual' definition, but it feels (to me at least) closer to what we're aiming for here.

- Tetsuki

I don't think that's as useful a definition, Tetsuki.

For a 1d4 roll, any prediction is as good as another; on a 2d4 roll, a prediction of 5 is the best prediction because it has the highest chance of coming up. Randomness isn't MAXIMUM predictability, it's the TOTAL predictability.

Hmmm, maybe. I guess it means what you mean by 'total predictability'. A definition woud be useful, but I'm guessing (for now, and because it's fun) that you mean the average chance of predicting any outcome from all of the possibles.

If so, there may be a problem:

For example, a 2D6 roll has 11 different outcomes, the average 'predictability' of the outcomes is 1 in 11.

A D11 roll (D12, re-roll any 12s) also has 11 different outcomes, and an average 'predictability' of 1 in 11.

But D11 'feels' more random, doesn't it?

I suppose what I'm trying (very poorly, sorry) to say is that randomness isn't just about 'clustering' - there's something else going on here.

Regards,

Tetsuki

As most of us know, a single die (1dx) has a flat distribution (equal probabilities for each outcome) while multiple dice (2+dx) have a bell-shaped or "normal" distribution (highest probability for the mean roll, decreasing probabilities as one moves further away from the mean).

The concept that measures how likely it is that an individual result is close to or far away from the mean result (the "average roll") is in statistics called "variance" (closely related is "standard deviation").

So 1d11 feels "more random" even though it has the same range as 2d6-1 because it has higher variance; any result is equally likely to be close to or far away from the mean (that is, a roll of 6). The results for 2d6-1 will cluster around 6, with 1 and 11 equally unlikely rolls (a 1 in 36 chance for each, as we all know).

The implication is that any concept of "randomness" should include (a) range, (b) variance, and (c, borrowing from an earlier post) degrees of freedom, which here is used to indicate how many different possible rules conditions there are that affect the resolution. So, for example, a system described as "Have the skill, roll 2d6 plus your skill; don't have it, automatically fail" would have (1) range 11, variance 6 (standard deviation about 2.5), (2) range 0, variance 0, and 2 degrees of freedom.

Note that this use of degrees of freedom is slightly different than I've seen it used in statistics. But I'm not a statistician, so I may be in error.

I'm not sure how helpful this is, but if the goal is to be able to compare the degree of randomness in different game mechanics, I think these are some of the things that need to be taken into account.

Bill

Let's say that you have a system where you roll 1d100+skill against "difficulty ratings" that run from 10 to 150, and skill ratings run from 0 to 100.

Also, you have a system where you roll 1d20+skill against "difficulty ratings" that run from 2 to 30, and skill ratings run from 0 to 20.

Is the first system "more random" than the second? I would argue that even though the first system has more individual values that can be rolled, it's no more random than the second; in practice they're nearly identical.

Bill_White wrote: The implication is that any concept of "randomness" should include (a) range, (b) variance, and (c, borrowing from an earlier post) degrees of freedom, which here is used to indicate how many different possible rules conditions there are that affect the resolution. So, for example, a system described as "Have the skill, roll 2d6 plus your skill; don't have it, automatically fail" would have (1) range 11, variance 6 (standard deviation about 2.5), (2) range 0, variance 0, and 2 degrees of freedom.

Note that this use of degrees of freedom is slightly different than I've seen it used in statistics. But I'm not a statistician, so I may be in error.

Vaxalon wrote: Let's say that you have a system where you roll 1d100+skill against "difficulty ratings" that run from 10 to 150, and skill ratings run from 0 to 100.

Also, you have a system where you roll 1d20+skill against "difficulty ratings" that run from 2 to 30, and skill ratings run from 0 to 20.

Is the first system "more random" than the second? I would argue that even though the first system has more individual values that can be rolled, it's no more random than the second; in practice they're nearly identical.

Bill,

I used 'degrees of freedom' to describe what you refer to as 'range' - but I think your terms are much better, so I'll change!

And thanks for the reminder about std. deviation... that exactly explains why 1d11 'feels' more random to me than 2d6-1.

I agree that range & variance both affect randomness. But does the existence of a separate mechanic (such as automatically failing if you don't have the skill) affect randomness? Or does it simply increase the number of possible resolution methods, each of which may have a different randomness?

- Tetsuki

I agree that range & variance both affect randomness. But does the existence of a separate mechanic (such as automatically failing if you don't have the skill) affect randomness? Or does it simply increase the number of possible resolution methods, each of which may have a different randomness?

Take a look at the dice mechanic in Skein to see how I use randomness directly in the game.