This month, I will talk about a number of mostly unrelated things, each of which weren't big enough on its own to make a complete installment. These are scale, non-dice randomizers and some personal opinions about dice-roll methods.

Scale

If you want to handle powers of vastly different scales in the same game, some mechanisms break down or become unmanageable. For example, if the number of dice rolled is equal to your ability, what do you do if the ability is a thousand times higher than human average? And if you compare a roll against ability, all abilities higher than what the dice can show are effectively equal.

The first thing to do is consider how in-game values translate to real-world values. If this translation is linear (e.g., each extra point of strength allows you to lift 10kg more), you get very large in-game numbers. If you, instead, use a logarithmic scale (e.g., every point of strength doubles the weight you can lift), you can have very large differences in real-world numbers with modest differences in in-game numbers.

Doubling the real-world values for every step is rather coarse-grained, so you may want a few steps between each doubling. A scale that has been used by several designers is to double for every three steps. This means that every increase multiplies the real-world value by the cube root of two (1.25992). This is sufficiently close to 1.25 that you can say that every step increases the real-world value by 25%. Another thing that makes this scale easy to use is that 10 steps multiply the real-world value by almost exactly 10 (10.0794, to be more precise), so you can say that 10 steps in a factor of 10 with no practical loss of precision. Some adjust the scale slightly, so 10 steps is exactly a factor of 10, which makes three steps slightly less than a doubling, but close enough for practical use. This scale (both variants) have many steps that are very close to integer multiplas, which is not common in logarithmic scales, so this scale is often used outside RPGs. The decibel scale for sound, for example, has each increase of 10dB multiply the energy of the sound by 10.

Even with a logarithmic scale, you may get numbers that are too large to be practically manageable (e.g., in dice pools or when you use dice-types to represent abilities), so you can add a scaling mechanism that say that for every increase of $ in ability, you are at one higher scale.

When resolving an action between two entities, you reduce (or increase) both scales such that the weakest of the two entities is at scale 0. For example, if =10$ (i.e., every increase of 10 increases scale by 1) and a struggle between one entity of ability 56 and another of ability 64, you reduce it to a battle between abilities of 6 and 14. You can add an additional rule that if the difference in scale is more than, say, 2, then you don't roll: The higher scale automatically wins. So if you get into a boxing match with Galactus, he doesn't need to roll to wipe the floor with you.

Issaries' HeroQuest game integrates a scale system directly: A unit of scale (or "Mastery") is a difference of 20, and you denote an ability as a number between 1 and 20 plus a number of Masteries. You must roll under your ability number on a d20 to succeed, but each Mastery increases the degree of success by one (or reduces that of the opponent by one). Effectively, this means that if you have sufficient more masteries than your opponent, you can never lose.

One thing to note, though, is that not all abilities have quantifiable real-world measures: How do you measure beauty numerically? Or agility, leadership or intelligence? The latter does have a numeric measure (IQ), but this is an artificial construction, defined to average to 100 and be normally distributed around this with a predefined spread. So saying that someone with an IQ of 160 is twice as intelligent as one with IQ 80 is meaningless. When games assign numbers to unquantifiable properties and abilities like these, the numbers are as much a construction as IQ numbers are, and can really only be used to determine which of two characters are better (or how well they do against equally abstract difficulty numbers).

Other randomizers

Here I will briefly look at other ways of bringing randomness into games.

Cards

Next to dice, cards seem to be the most common randomizer in RPGs. Some games (like R. Talsorian's Castle Falkenstein) use standard playing cards, others (like WoTC's SAGA system) invent their own.

Drawings of cards from the same deck are, unlike die rolls, not independent events, so analysing probabilities becomes more complex. Some argue that this makes cards superior - "luck" would tend to even out, as you will get all numbers equally often (if all cards in a deck are drawn before it is reshuffled). But this assumes that all draws are equally important, which I find questionable.

The main advantages of using cards over dice are:

• Players can keep hands of cards and choose which to play.
• You can use the suit or colour of the card as well as its value to affect the outcome in different ways.
• With special-made cards, you can have text on the cards that provide for special effects (such as critical results).

Not all of these issues will be relevant to all games, though, and some may dislike having the players choose their "luck" from a hand of cards, as this brings meta-game decisions into the game world. Additionally, you can have players doing unimportant tasks simply to get rid of bad cards in a safe way.

Spinners

Spinners are really just dice of a different shape - you get (usually) equal probabilities of a finite number of outcomes. The main advantage of spinners is that you can make them in sizes (number of outcomes) that you don't find on dice (such as 7 or 11) or get unequal probabilities of different results, (depending on the sizes of the corresponding pie slices). Additionally, spinners can be cheaper to make than specialized dice, such as Fudge dice.

Rock-paper-scissors

While this strictly speaking isn't random, it is unpredictable enough that it can be used as a randomizer. Its sole advantage is that it doesn't require any equipment or playing surface, which makes it popular in live role-playing.

There are really only three outcomes: Win, lose and draw, each of which have equal probabilities (assuming random or unpredictable choices for both players), but you can add in special cases, such as special types of characters winning draws on certain gestures. For example, warriors could win when both hands are "rock", magicians when both are "paper" and thieves when both are "scissors". While this would tend to make these types choose those gestures more often, doing this will also make them more predictable, so the advantage is somewhat dubious.

Also, rock-paper-scissors only works with two players, as you otherwise can get circular results (A beats B, who beats C who beats A), which can be hard to interpret. There are generalisations of rock-paper-scissors to five or seven different values that avoid cycles with three or four players, but these tend to be harder to remember.

Some personal opinions

Here, I will discuss a few personal preferences and pet peeves. Rampant subjectivity will abound. So you are warned.

Rerolls

I don't like rerolls. They take extra time that you can't decrease much by experience - the physical action of rolling again can't really be sped up. This is in contrast to time used for calculations based on a single roll, such as adding up the dice or counting successes, which you can decrease almost arbitrarily with training. I have, for example, seen experienced players add up a dozen dice in a few seconds.

Additionally, repeated rerolls remove upper limits on rolls - anyone can conceivably achieve fantastical results, just not very often. It can spoil any game if a street kid kills the dragon that menaces the town by throwing a stone at it, just like it will spoil the game if that same brat downs a high-level PC. Also, the absence of an upper limit will make players insist on rolling even when they are hugely overpowered, on the off chance that they will reroll a dozen times. Sure, the GM can forbid such silliness, but then why have rerolls at all?

Some argue that heroic fiction abounds with cases where the hero wins over a vastly more powerful foe (such as Bard the bowman in The Hobbit killing Smaug with a single arrow), but this is usually due to outrageous skill rather than outrageous luck.

A third problem I see with rerolls is that they make the probability distribution uneven: You can get holes in the distribution (i.e., impossible results) or places where the probability drops sharply but then stays nearly constant for a while. For example, if you roll a d20 and reroll on each 10 or 20, adding the new results to the original (as in Torg), you can never get results that divide evenly by 10, but all other results are possible. Also, every result from 1 to 9 are equally likely at 5% and results between 11 and 19 are all at 5.25%, but then there is a sharp drop to 0.5125% for results between 21 and 29.

Methods that are different just to be different

Many games, especially Indie or homebrew, feature "innovative" dice-roll mechanisms that seem to be different just for the sake of being new. Like haut couture fashion, these are often overly complex and don't seem to add anything other than change and strangeness to what they replace. Such can serve one legitimate purpose - it can get your game noticed where yet another d20 game won't. But it is better to combine innovation with purpose - make the new system do something that can't (as easily) be achieved with existing systems, without sacrificing the good properties of tried-and-tested methods.

Though I may get flak for this, I find Godlike's mechanism (as described in an earlier column to be an example of haut couture dice mechanisms - it is quite complex, the probabilities are weird and it doesn't seem to do much that you couldn't achieve by simpler means.

Until next month

I haven't covered all resolution mechanisms that use dice - partly because of space, partly because of defective memory and just not knowing them all. And I'm sure many new dice-roll mechanisms will be invented, some to be deservedly forgotten again and others to be copied over and over with minor variations.

Whether you plan to use an existing method or invent your own, I hope this column series has given you something to think about when doing so. And stay tuned - I will return next month to discuss the physical shape of dice.