Sandy's Soapbox

A quick note on dice notation: a die is defined by its number of sides, so a 6-sider is a d6, a twenty sider is a d20, a 100-sider (they exist) is d100. For multiple dice, just list how many you throw: "two 6-sided dice" is 2d6, aka number-d-dicetype. So 1 twenty-sider is 1d20 since you're rolling one 'd20', and so it goes.

The classic for board games and some RPGs is the flat distribution of a d6 or d20, where each number has an even probability. Games with spinners or catchy devices usually are simply substituting a mechanical gimmick for a d6 and not changing the probabilities. An even probability is just a flat line, each number has equal odds.

From a game point of view, you can quickly decide what your odds are. Need a 4 on a d6, that's a 1/6th chance. Need above a 3, that's a 50%/50% chance. Need to roll 18+ on a d20, that's 3/20th or a 15% chance. Flat systems are easy to compute.

Countering this is the bell curve of multiple dice, such as 2d6 and 3d6, where the middle numbers are more likely and getting very high or very low is unlikely.

We don't have as intuitive a grasp on bell curves, other than a general sense that 'high is hard and low is unlikely'. This added complexity is a good thing, as it encourages most players to think less on probability and more on the kind of really bad number behavior we're psychologically wired for.

After a series of bad rolls, we'll think we're "due" for a good roll. We'll hope we have lucky dice. We will overestimate our chances of getting a high roll, and underestimate our chance of a low roll. We'll mix up flat and bell curve systems and think the odds of a 16+ on 3d6 (4.61%) is very similar to that on a d20 (25%), even though they are very different.

This makes the game more fun. Instead of worrying about math, we're treating oru dice as frustrating totemistic objects. They are part of the game experience, not just a mechanical system.

Other mechanics include the White Wolf system where you roll a number of ten-sided dice equal to your expertise-- the higher the expertise, the more dice. Any roll 7 or greater is a success, and you simply count successes. Different tasks difficulties require a different number of successes. Oh, and tens count as two successes.

Since each die has a 2/5th chance of being a success (and a 1/10th chance of counting double), you on average will tend to get a success for any 3+ die roll, but of course you'll need more than 1 success for most tricky things. The end result: you get to roll lots and lots of dice and feverishly sort and count and hope for success.

Some systems, both flat and curve, add variety by varying your die choice. Old-school D&D, for example, had different weapons cause different damage based on the die. A dagger or dart might do just 1d4, for example, while a heavier weapon might cause 1d10 or even 2d8.

In such a system, you want to choose the larger dice because they have the greatest potential for a large result, but all share the potential for a low number as well. Your choice is pre-determined: more and/or bigger is better.

Games allowing decisions on which die size to roll usually balance the fact that more is better by adding limitations for larger-dice weapons, such as giving them lower speeds or a higher cost or higher rarity or class-based restrictions on who can use them.

In some senses, this gets too complicated. Rolling lots of dice is fun, but in several game sessions, I've seen people switch to smartphone die rolling apps because the tallying of dice and success is seen as tedious to some. There's always a balance in the 'fun' of dice rolling:

Rolling lots of dice = Fun!
Doing lots of math or counting = Not fun

The "Fudge" and "Fate" systems simplify the math component by using special dice marked with "+", "0" or "-". You simply add plusses and minusses to get your staging. This figure shows your odds of sucess when rolling 4dF.

There are more dice systems than I wish to write about, but fortunately the fine contributors at RPGSystems.wikidot.org have this awesome partial list:

1. Basic Roleplaying: 1D100 under modified skill.
2. Burning Wheel: 1D6 where 1-3 fail & 5-6 succeess but this varies with shades. Roll dice equal to skill and need successes equal to the obstacle.
3. Eclipse Phase: 1D100 under modified skill (+/-10,20, etc.). Both dice same result critical success. Versus winner highest successful roll, but critical success trumphs a higher number.
4. Fantasy Dice: Roll a number of skill die (D4 to D12) equal to the skill's associated attribute (average 2) with one bonus die for skill speciality. Must roll equal or over target difficulty from easy (2) to insane (12) or beat opponent - only highest die result counts (no addition or subtraction involved). Roll can be scaled up by sacrificing one die for each die type scaled up, or adding a die to the roll for each die type scaled down (example: 3D8 scaled up to 2D10 or even 1D12).
5. FATE: Same as fudge below or 2D6 where one is designated minus and one plus. Lowest result subtracted/added to skill and if both dice are the same then skill remains unmodified.
6. Fudge: 4Df, where f is six sided die with two +, - and blank sides. Moves traits (e.g. skills) up or down an adjective scale: Terrible, Poor, Mediocre, Fair, Good, Great, and Superb.
7. GURPS: 3D6 under modified skill (modifier runs -10 to +10). Has criticial success and failure on low and high rolls.
8. Hot War: Dice pool where highest roller wins and number of dice that defeat the opponent improves the degree of success.
9. JAGS: 4D6, where a 6 is treated as zero must be equal or less to the target number.
10. Mouse Guard: 1D6 where 1-3 fail & 5-6 success. Roll dice equal to skill and need successes equal to the obstacle which is typically 1-4.
11. One Roll Engine: Pool of D10s equal to Stat+Skill. To succeed must have matches above set difficulty (1-8). Penalty removes dice from pool. Contest won by having most matches or highest match.
12. PDQ: Simple situations are resolved with a comparison of Difficulty Rank with the character's Quality Rank (table for this). Complicated situations require a 2D6 roll + Modifier for the Quality Rank to match or beat a Target Number for the Difficulty Rank.
13. Savage Worlds: Trait (e.g. skill) represented as a die (1D4, 1D4+1, 1D6, etc.). 4 or greater, +/- modifiers, is success. Players and important NPCs get to roll additional 1D6 which if higher than trait die is used instead, but 1-1 is critical failure.
14. SIEGE: 1D20 + Attribute & Speciality versus 12 if within skill bundle, versus 18 otherwise. Difficulty modifiers adjust this from easy to impossible (-6, 0 +2, +6, +12, +18).
15. Ubiquity: Binary dice system, even numbers are successes, odds are failures.
16. Unisystem: Success if Attribute + Skill + 1D10 + Difficulty Modifier is nine or greater. On 10 roll again subtract five and if above zero add to result. On 1 roll again subtract five and if below zero subtract from result. These are open ended.

The end result of all of these systems is tragically the same. The set of possibilities for what you will roll is still predetermined by your initial pre-game choices. The key walkway is game dice systems seem to balance these three factors:

1. Statistics
2. Complexity and non-intuitiveness
3. Fun of rolling lots of dice

One key issue in game design is to let the player make meaningful choices. If the entire choice aspect is in pre-game work, though, the dice rolling is a mechanical exercise that-- stripped of the fun of tossing dice-- has a huge impact on the game result but little input by the player. The existence of dice-rolling smartphone apps is precisely because that task is easily replaced by a machine.

"Fantasy Dice" and a small group of other games do allow some element of choice, whether to sacrifice some dice (reducing your odds) to get a bonus to your success if you succeed. This adds a runtime component-- given a specific pregame loadout, you can make on-the-fly decisions to tweak your probability matrix for a given situation.

Tales from the Floating Vagabond adds a neat choice wrinkle to the mix. You have to roll low and you can only roll 1 die, but based on task difficulty, you choose the size dice you roll. An easy task means roll 1d4. A super heroic task or wishing more success than usual requires rolling low on 1d100. This inverts the usual conventions-- switching die size rather than number of dice-- while still keeping within dice culture norms.

In essence, for all adjustable systems, you can add risk to improve the magnitude of your success if it happens. This is an excellent addition in terms of game theory, because you are adding a meaningful choice.

However, since we are bad at math and probabilities-- Las Vegas casinos are based on that very fact-- the "meaningfulness" of the choice can be debated. As we're wired, if we have a high potential of success, we think rolls that fail to succeed 'robbed' us. So instead of 'neat interaction' we get a feeling the system was unfair, or we were unlucky. Feeling unlucky rarely equates to 'fun'.

This is not symmetric, in that we do not feel a lucky roll is unfair. In fact, lucky rolls are the very definition of 'fun'. In games with dice, making that low-probability roll succeed is a very positive emotion.

So if we get angry when the odds were in our favor but we didn't make the roll, but we feel perfectly justified when a one-in-a-hundred roll turns in our favor, are dice systems good game design? They are certainly ubiquitous, but the issue of whether they are 'good' is less important than the fact they are necessary.

Without some degree of randomization, games would be pre-determined. The larger army or strongest fighter or first to move would always win. We require randomness to add richness to games, and the balanced randomness of a good dice systems also mimics the real world behavior we expect our games to mimic.

You don't always nail the job interview-- but your odds are better if you prepared (and thus, metaphorically, get to roll more dice). You don't always win in ping pong, but over many sets the better player will win more. You may try something that's a long shot, but every now and then it pays off.

Dice systems have their problems-- predominantly that they don't allow for meaningful choices. Given reality also shares that same flaw, they are still the best approach to adding balanced randomness to games. The key of a good dice system is one of two approaches. Either keep it simple with a flat or few-dice bell curve, or make it very wacky so the players are ignoring the math and relying on our primitive, superstititious minds. Dice systems may not be perfect, but neither are we.

Until next month,
Sandy at rpg.net