Arbitrary numbers grant the Game Master a wellspring of inspiration to provide a seamless game environment for players. For game designers, they allow for the creation of a flexible system where Game Masters can take control and claim as their own. Still, what exactly are arbitrary numbers and how do they affect game design?
In mathematics, an arbitrary constant is undetermined and does not hold a specific value, whereas in other venues, something that is arbitrary represents unlimited or unrestricted power. In still other forays, it is capricious or unreasonable. When applied to a decision, an arbitrary outcome depends solely on the discretion of one person. Sound a bit dangerous? Sound a bit like the role of a Game Master?
Unfortunately, in many roleplaying systems, arbitrary numbers rarely exist. Many roleplaying games make use of statistics and modifiers, with each number representing a specific game application. A magical weapon might provide a bonus to represent its value in combat; a skill rank modifies a task roll when performing an action associated with the skill; and difficult terrain reduces speed, yet another defined number to represent just one thing. Speed represents how quickly you may move in a given amount of time, though not how deft you are.
While these restrictions are necessary to form the backbone of any solid roleplaying game, they also often make it difficult for the Game Master to . . . well, master the game. Sure, if the situation is favorable, a Game Master can grant a +2 bonus to a player to represent a beneficial circumstance. Though, this bonus only serves to promote "roll" playing rather than "role" playing since the player needs to roll dice to make use of the modifier.
That is the crux of the problem. Though, how can arbitrary numbers solve this quandary? To begin with, arbitrary numbers can represent anything rather than just one thing and since it represents a multitude of options, you can apply it to nearly everything.
Skill ranks, for instance, act as a modifier in many roleplaying systems. Generally, it augments a die roll that represents the aptitude of a character. The idea behind the modifier mechanic is if one is better at a task, the more likely he or she will succeed performing that task. While this theory is sound, what if a skill rank or proficiency bonus could be much more than just a modifier to a die roll? What would happen if a skill rank represented a plethora of things, limited only by the imagination of the Game Master?
Let us look at Survival as a skill (or its general equivalent depending on the system). In addition to the rank or proficiency bonus being a modifier for task resolution, let us explore what else it may lend itself to resolve. The most obvious task is gathering food and water. Instead of a player initiating the action of hunting and gathering, followed by a die roll or other form of task resolution, then finally the Game Master interpreting the result, why not have the rank or bonus be the result?
If a character has a Survival skill rank or proficiency bonus of 2, why not interpret that as a character possessing enough expertise to find enough food and water for two people? If the character needs or wants to find more beyond their capability, then initiate a task roll. What if the character is in the desert or a plagued city devoid of fresh food and water? Assign an arbitrary number, let's say 5. While someone with a background in desert survival or medicine might respectively still find enough food and water for two people, another person not so trained must have at least a skill rank or proficiency bonus of 5 to find enough for themselves without the need for a roll. On the other hand, maybe you allow the character to survive for up to two days before making a check. Then, as a Game Master, ask the player to describe how his or her character survived those two days.
What if the area is bountiful? Again, assign an arbitrary number. In this case, let us say 1. Now, the same character with a Survival skill rank of 2 can find enough food for three or four people depending on the judgement of the Game Master. Either the character finds additional food and water equal to the difference or increases the sustenance found by his or her rank for each step in difference. Therefore, a character with a Survival rank of 3 would find enough food and water for either five or nine people, depending on the decision or arbitration of the Game Master.
What about climbing? A character with an Athletics rank or proficiency bonus of 3 can roughly climb 15 feet without making a check (using a multiply of 5 feet for favorable conditions). How about a multiply of 10 feet when a character makes use of a rope or 15 feet with proper climbing gear or 2 feet when facing a difficult climb or even 1 when the surface is also slippery?
How does these arbitrary numbers affect the game? It allows the Game Master to do what he or she does best, weave a story and build upon an adventure without multiply interruptions due to incessant dice rolls or skill checks. For the players, it brings a sense of heroism and accomplishment and builds upon the virtues of their character.
Arbitrary numbers need not be restricted to just skills. What about abilities or ability modifiers? A character with a +3 Charisma bonus (or Charm score in the Aspyrias Adventuring System), might influence three of the diplomats at the council meeting through roleplay, but might require a check if he is going to convince the fourth to his side. What if a character gets into a bar fight and has a modifier of +4? Allow the player to weave a story of how her character takes down four of the patrons before making a Strength check to face the fifth or sixth drunkard to join the fray.
How about weapon proficiencies? Take a fighter with a +2 weapon proficiency in the longsword. Perhaps the warrior can easily kill two minions or minor foes in the first round of combat without the need of an attack roll; the Game Master allowing the player to describe the actions of his hero in vivid detail as he does so.
This makes for interesting roleplay and creates a better game environment for all involved, the players as well as the Game Master. Arbitrary numbers are one of the key ingredients in the game design behind the Aspyrias Adventuring System. Although, as you can see, arbitrary numbers applies to a variety of roleplaying systems without the need to tinker with existing rules.
However, feel free to adjust the rules a bit. It is, after all, your game, isn't it? You forked over your hard earned cash to buy the core rulebook, right? Let me leave you with one last example on how to use numbers in an arbitrary fashion: a simple arm-wrestling match.
A player character challenges the town champion during the Spring fair. The crowd gathers and bets are made. The character has a Strength of 15, while the champion has a Strength of 17. Instead of opposed dice rolls, the player has to make a choice: either lose the match to the stronger opponent or sacrifice a couple points of Strength to overcome his foe and be declared champion. For each point of Strength sacrificed, all will return to normal in an equivalent amount of hours as his body heals from the muscle strain.
The character, not knowing the Strength of the champion, sacrifices 3 points. This temporarily increases his Strength to 18, long enough to unseat the champion and win the match. Now, his Strength score will be 12 for the next three hours. Just shy of his Strength returning, the fair is attacked by raiders. What makes a more memorable roleplaying moment: a simple dice roll or the struggle to make a decision? Which more defines a character?
Something to mull over the next time you sit at the table, eager to roleplay. Until next time, happy gaming.