Math is incredibly common in board games. It’s pretty necessary in most styles of games. The most common uses for math are totaling points and doing damage, and there’s a lot of different types of math that could end up being used, and you’d be surprised how much things change.

Addition

Adding numbers is easy, at least usually. It just adds up! For points, this is pretty useful. Every [thing] you get adds [number] points to your score. This helps keeps things straightforward, and can be very useful for complex games. But it’s also very boring and linear. Since something will always add the same number of points, nothing really every scales up or gets exciting, at least not inherently.

For calculating in-game stats, addition gets kind of weird. Increasing, for example, damage, by a flat amount can end up being extremely powerful. If they stack, they could end up getting very high very easily. If they don’t stack, then it can get kind of boring. This is most often a problem when games use very small numbers, so the smallest increases are still large, and games where the improved stat is used repetitively, like a game where you often attack multiple times using the same attack stat.

Multiplication

Multiplying is just so much fun. It doesn’t have to be direct multiplication, either. Triangular scoring is a common one (each item is worth the total value of all the previous items) as is a Fibonacci style number system. Multiplication’s primary use in game design is to reward specialization. Doubling something is only useful if you have a high enough number to start with. If you want to encourage players to do the same thing or focus on a single thing, use some form of multiplication.

With stats, multiplication is inherent with the system. Anything you want to do multiple times is essentially “multiplying” that action. That means that it’s actually fairly easy to figure out what the result of a multiplicative effect could be. Doubling an attack stat is going to mean they only need to attack half as much.

The other fun part of multiplication is how it interacts with addition. Adding something then doubling it is way better than doubling it then adding it. Giving players opportunities to carry out these changes in the right order can be very rewarding.

Subtraction

Let me address the inverse for a moment. Things that subtract as you get more can be interesting, as it encourages players to spread out. Subtractions can also have a hard limit, such as subtracting from a price. Reducing a price by 10 doesn’t matter much if it only cost 5 in the first place. This can work as a nice balancing tool, since it still provides an advantage, but not one that’s always better all the time.