Storms on Cloud 9

Storms on Cloud Nine #15:

The Odds, Part Two

by Scott Holliday
July 28, 2003

Last time, I laid out some important principals for randomness mechanics based on setting and genre. This week, I plan to examine some critical considerations and demonstrate with the systems that I will be using in Orphan Crown. Once again, although a computer can use complex algorithms to achieve the same result, I will be approaching the problem from the side of dice theory.

If you have much experience with table-top games, you've probably seen several different mechanics. Common systems are to roll once, roll and add/subtract dice, roll and take the highest (or lowest), or roll and consider each die separately. Although you can generate good random results with any of these mechanics, there are several important considerations:

How much importance is given to the roll? You've probably seen systems in which your character's abilities only matter slightly, since the roll is worth many times the advantage given by advantages/disadvantages. At the opposite end are systems where the roll only matters when the obstacle is very near your skill level. At the extreme, you have the diceless system in which you don't even get a roll.
How does the mechanic handle orders of scale? Ants can lift many times their body weight, so they are very strong. However, they can't individually lift a penny, so they are weak. What about a squirrel then? These kind of questions often come up for issues of strength, speed, or damage resistance. Some systems simply give bonuses if you are operating on different scales. Others give more dice or a scale multiplier. Most however just try to ignore the problem.
Does the mechanic tend toward the likely result? Single die mechanics, unless they use a chart or table, usually set all results to be of equal likelihood. In contrast, most other mechanics give a tendency to the average. Adding several dice together generates a curve centered in the middle. Typically, the more dice you add, the steeper the curve, so the more average the result. As an example, d20+4 will generate the same numbers as 4d6. However, in the latter case, you are not very likely to generate results at the extremes. Alternately, some mechanics are designed so that characters always operate at near their best potential. This is often done by rolling a number of dice and only selecting the highest.
Is there always potential for success/failure? Depending on your genre and setting, this question can be very important. Do bullets always bounce off superman? Many systems use this same approach when they really shouldn't. Just because you have superior skills and abilities does not mean you are flawless. A common adage from old dueling world is that the #1 dueler doesn't fear the #2 dueler... he fears the beginner: they are more likely to do something stupid that he won't expect. Systems which "add a number to your roll" often break down in this sort of situation. Once the number added passes a breakpoint, you can't fail at all anymore. As an example, I drive to work everyday. What are the odds that I will be in a wreck tomorrow? Given that I haven't been in a wreck since when I first learning to drive, I would say the odds are less than 1%. However, if I take a defensive driving class (improving my skills), would this mean the chance of a wreck would drop below 0?
Does the system provide the occasional "unlikely" result? This is better known as critical success/failure. Regardless of skill and situation, people sometimes make outrageous mistakes (or successes). This sort of mechanic in a game certainly adds more chance to a game, which is often a very good thing. A horde of insignificant obstacles suddenly looks a lot scarier if there is a constant chance that you might trip and fall on your head. One argument against such a mechanic is that it changes any operation into a "life-or-death" battle. The key here is to make sure to set the odds of critical results to be very, very low. As an example, imagine a battle between two sets of 500 peasants armed with clubs. If the odds of a critical failure is 5%, then after each "swing", 25 peasants one each side will drop their weapon? By the end of a short battle, only half will NOT have dropped their weapon? I hope this seems absurd... In contrast, what if there were more than one critical result? Imagine instead that you are using that 5% to generate an internal list of 100 things that might go wrong. For instance: drop weapon, hit self, hit neighbor, fall down, off balance (defense penalty), muscle injury, flee in terror, refuse to fight, surrender against orders, etc... This drops the odds of "you drop your weapon" to 0.05%, while keeping the odds of "something outrageously bad happens" at 5%.

I said I would use a system from Orphan Crown as an example, so I'd better keep my promise before this gets too long. For my first example, I'll look at the mechanics behind the spell research and combat system which I've mentioned before in Storms on Cloud 9, #7. This is just an internal game, but with competitions and tournaments (and rewards), I'm guessing that many players will spend a lot of time here. When the player casts a spell, the computer runs a seemingly-random algorithm to determine the characteristics of the effect... the spell's function, power, stability, element, and description. This gives some basic statistics used for interaction between spells. For instance, a spell that launches a cloud of splinters is easily countered by a protective wall of fire. In fact, a weak cloud of splinters isn't going to be able to break a strong defense of splinters. However, what happens when two spells hit each other that are of equal power? This is where the random element comes into play.

Importance of the Roll? This system is meant to be a strategy game - with distinct advantages and disadvantages based on your action. With this in mind, the roll should not be very important - only deciding situations when they are nearby in potential.
Handling of scale? I'm basically assuming that the spell effects are not based on the scale of the user. However, the resistance/health of a target very well could be...
Tendency? I've already limited the importance of the roll, however it seems like magical effects should not tend toward the middle. Decision is to use a linear (single-die) mechanic.
Always Potential for Success & Failure? No. If you've cast a good counter-spell, you will always succeed. Likewise, if you cast a hopeless attack against a sturdy wall, you will always fail.
"Unlikely" Results? No. Since it meant to be a game, I don't want any outrageous results sneaking in and messing up the sense of simple strategy.

Given this list of qualities that I'm aiming for, it is fairly simple to come up with a mechanic. After generating the base characteristics of the spell, I add a small random factor to the spell's power and stability. For instance, perhaps the spell's power varies by 1-10%.

All right, that was too simple. Mainly because it's designed as a sub-system with very distinct strategy rules (and not as much chance). For my second example, I'll look at the system that I use for most everything else. Combat, Crafting, Exploration, Searching, and NPC interaction. One dice mechanic to handle almost any situation.

Importance of the Roll? Since this is an almost universal mechanic, I want skill to be more important than the roll. A highly skilled person should be able to do things that an unskilled person just doesn't have any chance at. However, the roll should still be important enough to give a wide range of potential capabilities.
Handling of scale? Luckily, I don't have to worry too much about scale in Orphan Crown. In areas where scale often matters (strength, speed, toughness), vastly different scales will not be interacting. Although the Fae player characters are tiny (think of pixies or sprites), they will not be in direct competition with their human wards. And assuming this does occur, I guess I'll mostly ignore the problem given that they are supernatural beings. Along the same lines, although humans may be in competition with larger humans, bears, giants, dragons, and such... the difference in scale is not significant or I can ignore it with the "supernatural being" excuse. It seems like the setting of fairie tales would allow the hero (or heroine) to wrestle a giant or outrun a horse. It should be hard, but should not be impossible based solely on scale.
Tendency? It is a faerie-tale world, however this does not mean that people aren't real. Even in faerie-tales, characters generally operate at their norm. Likewise, players will be looking at the world from the bias of reality. Given these facts, it is pretty clear that I should use a system which tends toward the norm. Either simulate the roll of multiple dice to be added, or use mathematics to set my own curve based on a single roll.
Always Potential for Success & Failure? No, there are going to be levels of skill unreachable without the requisite skill. Until you learn to read letters, reading a book should be impossible. Likewise, once you can read a book, failing to recognize a single well-scribed letter seems unreasonable. However, characters will still have a range of results - moderate skill may vary between sometimes being able to read letters and sometimes being able to read a book.
"Unlikely" Results? Absolutely. Faerie-tales are often based in unusual (and unlikely) sets of coincidences. Though, these coincidences should be presented as just that - rare enough to be considered strange. Unfortunately, providing a computer-ready set of strange coincidences for each and every random test is nigh impossible. Instead, I'll just add in the chance of an "unlikely" success or failure. Using the example above, a illiterate character might somehow have memorized that book previously. Likewise, a well-read character might not be paying attention (or might refuse to follow orders) such that he fails to read a single letter. Unfortunately, the only way to approach this (without building such a list of coincidences for every random test) is to simply state that "Somehow you succeed/fail against all odds", or something along those lines.

There's the basis. As far as the mechanic itself, since I'm using a computer, I prefer to generate only one random number and then alter it mathematically. There are two reasons for doing it this way. The first reason is that computers often fail spectacularly at consistently generating repeated random numbers. Since many random number generators are based on the current time of the computer, if you ask for a set of random numbers all at once, a computer will often generate patterns of numbers. The second reason is simply that by using mathematics instead of dice mechanics, I can exercise a greater level of control over the shape I generate. Likewise, it is easier to get advanced shapes. What if the odds of a critical success/failure were directly proportional to the odds of basic success? Or what if the shape (or area of tendency) of the curve is based on the skill of the character? For instance, perhaps as skill increases, the tendency of the character should be to operate more and more often towards their highest potential.

All right, I realize I started getting really complex near the end. In any case, in both examples, I'm trying to avoid the actual formula that will be used. My thought is that players would rather not have to deal with the calculation themselves, and would prefer it if the workings are kept somewhat hidden. I certainly wouldn't want the game to devolve to the point where a player can calculate their exact odds of succeeding at a certain action. In my mind, half the fun is learning from experience where your character can excel (or fail).