#### Small Numbers in Tabletop Game Mechanics

In a computer game you can have numerical variables that span any range, that are even non-linear, and otherwise very complex. But in a tabletop game, the players have to do the math themselves (or consult tables) and must track everything too. Tracking if variable states is especially tough with miniatures, or anything with many units. The burden of tracking leads most strategy game designs to go granular: reducing the spread of variables to a very small range. But this creates other ramifications. How do you maintain the mechanics you want, with extrmeely limited mathematical optons?

As an example, consider hit-points. In an RPG, or game with few units, you might have 10 hit-points per unit. But in a minitaures game, you will scale this down to 1 HP for most units: each is either alive or dead. This eliminates any book-keeping for HP, except for the rare multi-HP units.

But this means damage must scale down too. In the RPG comparison, a typical blow might do 1 damage, taking 10% of a units HP. But this isn't possible with 1-HP minis. If you round up, every attack destroys the defender; if you round down, attacks do nothing. I see three main ways to address this, and still model a familiar kind of attack-damage dynamic.

## Use Randomness

Instead of doing 10% damage, you could have a 10% change of destroying a 1-HP unit. Easily implemented with dice usually: although you still have a limited range of values (only certain dice are manufactured), you buy roughly an order of magnitude smaller granularity.

Obviously, introducing randomness has major implications for how the game plays. If you have only a modest number of units, it may cause a given play-through to be overly determined by luck, diffusing strategic choices and skill. Introducing dice also increases the "handling time" of actions; somewhat defeating the advantage of not tracking HP in the first place.

Randomness may then perform best (for this specific purpose) at a sweet spot of game-element-complexity: not with a dozen units, and not with a hundred; rather, somewhere in between.

## Use Interactions Between Unit Types

Here, an attribute of every unit limits what units can successfully attack one another. Or it could be an interaction of different attributes, like attack and defense types. There are two major sub-approaches:

• Hierarchy of Unit Power: More powerful units can damage lesser ones, but not vice-versa. Or you can compare attack and defense strengths (like in naval wargames).
• Rock-Paper-Scissor Interaction: One-way interactions between otherwise equal units, or weapons and armor (e.g., pierce versus slash damage).

The RPS approach is more flexible, and ensures that any unit can always be defeated. A strict hierarchy is trickier to pull off: there has to be some utility to lower-powered units, possibly some way for them to "punch above their weight." Exceptions to their normal limitations, with special points or one of the other methods described here, could work. Extreme (exponential) expense for stronger units might also help.

## Use Situation

A unit can only do damage in the right situation, which it creates with the right tactics. Two major examples:

• Position: Damage can be done at the right angle (facing) or range. A mech might be able to damage another from the rear or side, for instance, but not head-on.
• Outnumbered: Multiple units can gang-up and overpower another. This can be combined well with the heirarchy option above; giving small units a way to be useful--but it could be used on its own too.

Tactical choices become emphasized with this approach: setting up the right situation, and judging the enemy's moves can't be sacrificed for raw power. This could make the game harder for novices, and take longer to play out.

The above methods can obviously be combined as well, sometimes very logically. Some attacks (for example) could be allowed by virtue of position or unit interaction, while some others are possibly only with the right random effect. Alternately, randomness by always be involved, with the other options enhancing a player's roll. And so on.

Unlike in a computer game, board game mechanics must be enacted by pople. Small numbers are indespensible for making this feasible -- but you may need every trick available to generate the kinds of dynamics you want, while still keeping things simple.