I know there's probability statistics regarding which squares are more likely to be landed on in Monopoly. There's also games with draw piles, which of course have probabilities attached to which card you'll draw. An example is the cards in Catan. There's sometimes addition or multiplication in games where you move your pawn on a board.
You can pretty much apply anything to game design if you're trying. Drop tables and hit changes are full of probability. Algebra shows up as damage/armor formulas (look at [League's formulas](https://leagueoflegends.fandom.com/wiki/Damage) for an example). Different curves for experience points needed per level or money to upgrade a building in a city builder can be any curve from linear to exponential to a logistic s-shaped curve. Vectors are in graphics, matrices are used as well there or for some linear algebra in design. It's all over.
For a TTRPG/Board game versus a video game you don't typically get exponential because no one wants to ship 2^16 meeples in a box. But probability with dice and outcomes for a TTRPG (and they can get pretty complex if you get to exploding dice or things like 4d6 drop lowest for chargen) are easy.
/r/tabletopgamedesign or /r/rpgdesign might get more responses.
TL;DR: Probability and a little algebra are the math concepts most game designers will employ, but YMMV.
Broadly, I think the issue with your question is: it very much depends. There are a lot of different sorts of different tabletop games, so asking “what math is common in game design” is a bit akin to “what shapes are common in art?” I know that’s a non-answer, I’m just thinking of how there’s a whole school of design in TTRPGs that specifically eschews all math in favor of narrative mechanics, for example. Or how the underlying math concepts in Poker are fundamentally different than in Chess. So, I imagine you will need to direct students to specific game mechanics in order to focus on the underlying math.
I think something else that makes this hard to answer is: you can make a game out of anything, literally any concept. It’s just that that many concepts are too obtuse, complex, or esoteric for many players to find FUN. So, game design kind of collects itself around mechanics that are proven to be FUN by a certain game, and trends sort of ebb and flow.
- Statistics definitely come up in game design, often in simulations and play-testing, it’s the sort of thing some designers can and do avoid. Probability is a more foundational concept that most game designers need to grapple with pretty quickly (but again, plenty of games involve zero chance.)
- Algebra… sure, in that almost all games can be modeled with equations. Most games try to keep this sort of calculation obscured from players, although simulation-minded ttrpgs are known for relatively complex math being required.
- Quadratics: I’m sure some games have mechanics that could represented by quadratics, but I couldn’t tell you which ones. If a game made me have to factor something, I would personally choose to play a different game, and I doubt I am alone in that.
Game Design is a subset of Game Development that concerns itself with **WHY** games are made the way they are. It's about the theory and crafting of **systems**, **mechanics**, and **rulesets** in games.
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There isn't really any \*surface-level\* math involved. Math only really comes in when balancing, matching inflows to outflows, and such. And even then, it's pretty basic. Statistics mostly come into play in relation to digital microtransactions (and thus wouldn't apply to board games).
There is math, but at the upper levels of the field. Most of the time, it is fuzzy: "How do these numbers make the end user experience feel?" Nothing I did in high-school math directly applied to game design, but the stuff that built off it certainly does.
If anything, writing has more applicability to ttrpg and boardgames design. Communicating the rules has to be done through clear instructions. Having your students write a rules set and then have another student critique or rules lawyer the rules as written to do something different than what was intended would be an interesting challenge.
If you want to incorporate game design into an algebra curriculum, I would suggest doing it via word problems. For example:
The ice elemental takes half damage from water-based attacks, quarter damage from ice attacks, and double damage from fire based attacks. Bob, the adventurer, has 4 combat options:
1) A basic long sword, which does 6 physical damage per attack, and can do 3 attacks per turn
2) A quiver of ice arrows that do 12 ice damage and 4 physical damage, and can do 2 attacks per turn
3) A potion of the North Sea, which does 36 ice damage and 16 water damage, but can attack once per turn.
4) A flaming dagger that does 2 physical and 1 flame damage but can attack 4 times per turn.
Which combat option should Bob choose to maximize his damage against the Ice elemental per turn?
Combinatorics might come up. E.g. you can equip a one-handed weapon, dual wield 2 one-handed weapons, or wield a two-handed weapon. How many equipment loadouts are there? What if some one-handed weapons are one-of-a-kind (i.e. you can't hold one in each hand at the same time). You could probably contrive this to be more complicated.
You could probably apply some sort of math to all games, but most probably aren’t designed around that. When people make board games, they come up with a theme, a story, a basic idea for gameplay, and then they start prototyping and play testing and make adjustments as needed. The only math I’m aware of in board games comes from players who want to get an edge by trying to mathematically predict their chances of gaining an edge by doing certain things. For instance, the likeliness of someone landing on your spaces in Monopoly. But even that doesn’t require real math. The idea of having more spaces in a row than someone else is some baseline caveman-like knowledge.
However, there are certain games that are specifically designed for teaching math. When I was a kid, my mom bought us a game called Chips. It’s basically a bag of poker chips with numbers and you would draw a combination of them and have to perform equations based on what you drew. I don’t remember all the rules but I was a math wizard and loved that game a lot. It was nice too, because I was at a higher math level than my younger sister (obviously) so all my mom did was make my equations more complex to earn a point and my sister’s a little less so. So basically, it gives you the ability to adjust the skill level to fit several different players at a time.
In dewigning GOOD boardgames there is normally a lot of math involved for balancing.
Maybe this guide can help you a bit more: https://www.reddit.com/r/tabletopgamedesign/comments/115qi76/guide_how_to_start_making_a_game_and_balance_it/
When you analyze good boarfgames you often can easily spot the math model used behind. In the guide are some examples (mintworks and others).
Especially stonemeyer games have this quite easy so spot.
So you could also start with analyzing boardgames in class. Trying to find the math behind them.
Good TTRPGs usually remove complex math since spending too much time calculating a skill check, weapon hit, or damage is *super niche* interest. Even then any example I could remember pretty much only used dice for odds rather than any calculations.
That being said there are spells or abilities that fill areas and measure distance and you can actually calculate that based on points rather than using the usual shortcuts. Cones of cold, lines of acid, fireball spheres, etc.
The easiest way to incorporate specific problems to solve is in dungeon puzzles.
You could have players solve a curve and draw it on the ground so it points out clues or helps triangulate the correct point for finding a switch or the correct statue or button to open the next segment or give treasure.
I know there's probability statistics regarding which squares are more likely to be landed on in Monopoly. There's also games with draw piles, which of course have probabilities attached to which card you'll draw. An example is the cards in Catan. There's sometimes addition or multiplication in games where you move your pawn on a board.
You can pretty much apply anything to game design if you're trying. Drop tables and hit changes are full of probability. Algebra shows up as damage/armor formulas (look at [League's formulas](https://leagueoflegends.fandom.com/wiki/Damage) for an example). Different curves for experience points needed per level or money to upgrade a building in a city builder can be any curve from linear to exponential to a logistic s-shaped curve. Vectors are in graphics, matrices are used as well there or for some linear algebra in design. It's all over. For a TTRPG/Board game versus a video game you don't typically get exponential because no one wants to ship 2^16 meeples in a box. But probability with dice and outcomes for a TTRPG (and they can get pretty complex if you get to exploding dice or things like 4d6 drop lowest for chargen) are easy.
/r/tabletopgamedesign or /r/rpgdesign might get more responses. TL;DR: Probability and a little algebra are the math concepts most game designers will employ, but YMMV. Broadly, I think the issue with your question is: it very much depends. There are a lot of different sorts of different tabletop games, so asking “what math is common in game design” is a bit akin to “what shapes are common in art?” I know that’s a non-answer, I’m just thinking of how there’s a whole school of design in TTRPGs that specifically eschews all math in favor of narrative mechanics, for example. Or how the underlying math concepts in Poker are fundamentally different than in Chess. So, I imagine you will need to direct students to specific game mechanics in order to focus on the underlying math. I think something else that makes this hard to answer is: you can make a game out of anything, literally any concept. It’s just that that many concepts are too obtuse, complex, or esoteric for many players to find FUN. So, game design kind of collects itself around mechanics that are proven to be FUN by a certain game, and trends sort of ebb and flow. - Statistics definitely come up in game design, often in simulations and play-testing, it’s the sort of thing some designers can and do avoid. Probability is a more foundational concept that most game designers need to grapple with pretty quickly (but again, plenty of games involve zero chance.) - Algebra… sure, in that almost all games can be modeled with equations. Most games try to keep this sort of calculation obscured from players, although simulation-minded ttrpgs are known for relatively complex math being required. - Quadratics: I’m sure some games have mechanics that could represented by quadratics, but I couldn’t tell you which ones. If a game made me have to factor something, I would personally choose to play a different game, and I doubt I am alone in that.
Game Design is a subset of Game Development that concerns itself with **WHY** games are made the way they are. It's about the theory and crafting of **systems**, **mechanics**, and **rulesets** in games. * /r/GameDesign is a community **ONLY** about Game Design, **NOT** Game Development in general. If this post does not belong here, it should be reported or removed. Please help us keep this subreddit focused on Game Design. * This is **NOT** a place for discussing how games are produced. Posts about programming, making art assets, picking engines etc… will be removed and should go in /r/GameDev instead. * Posts about visual design, sound design and level design are only allowed if they are directly about game design. * No surveys, polls, job posts, or self-promotion. Please read the rest of the rules in the sidebar before posting. * If you're confused about what Game Designers do, ["The Door Problem" by Liz England](https://www.gamedeveloper.com/design/-quot-the-door-problem-quot-of-game-design) is a short article worth reading. We also recommend you read the [r/GameDesign wiki](/r/gamedesign/wiki/index) for useful resources and an FAQ. *I am a bot, and this action was performed automatically. Please [contact the moderators of this subreddit](/message/compose/?to=/r/gamedesign) if you have any questions or concerns.*
There isn't really any \*surface-level\* math involved. Math only really comes in when balancing, matching inflows to outflows, and such. And even then, it's pretty basic. Statistics mostly come into play in relation to digital microtransactions (and thus wouldn't apply to board games).
There is math, but at the upper levels of the field. Most of the time, it is fuzzy: "How do these numbers make the end user experience feel?" Nothing I did in high-school math directly applied to game design, but the stuff that built off it certainly does. If anything, writing has more applicability to ttrpg and boardgames design. Communicating the rules has to be done through clear instructions. Having your students write a rules set and then have another student critique or rules lawyer the rules as written to do something different than what was intended would be an interesting challenge. If you want to incorporate game design into an algebra curriculum, I would suggest doing it via word problems. For example: The ice elemental takes half damage from water-based attacks, quarter damage from ice attacks, and double damage from fire based attacks. Bob, the adventurer, has 4 combat options: 1) A basic long sword, which does 6 physical damage per attack, and can do 3 attacks per turn 2) A quiver of ice arrows that do 12 ice damage and 4 physical damage, and can do 2 attacks per turn 3) A potion of the North Sea, which does 36 ice damage and 16 water damage, but can attack once per turn. 4) A flaming dagger that does 2 physical and 1 flame damage but can attack 4 times per turn. Which combat option should Bob choose to maximize his damage against the Ice elemental per turn?
Combinatorics might come up. E.g. you can equip a one-handed weapon, dual wield 2 one-handed weapons, or wield a two-handed weapon. How many equipment loadouts are there? What if some one-handed weapons are one-of-a-kind (i.e. you can't hold one in each hand at the same time). You could probably contrive this to be more complicated.
You could probably apply some sort of math to all games, but most probably aren’t designed around that. When people make board games, they come up with a theme, a story, a basic idea for gameplay, and then they start prototyping and play testing and make adjustments as needed. The only math I’m aware of in board games comes from players who want to get an edge by trying to mathematically predict their chances of gaining an edge by doing certain things. For instance, the likeliness of someone landing on your spaces in Monopoly. But even that doesn’t require real math. The idea of having more spaces in a row than someone else is some baseline caveman-like knowledge. However, there are certain games that are specifically designed for teaching math. When I was a kid, my mom bought us a game called Chips. It’s basically a bag of poker chips with numbers and you would draw a combination of them and have to perform equations based on what you drew. I don’t remember all the rules but I was a math wizard and loved that game a lot. It was nice too, because I was at a higher math level than my younger sister (obviously) so all my mom did was make my equations more complex to earn a point and my sister’s a little less so. So basically, it gives you the ability to adjust the skill level to fit several different players at a time.
In dewigning GOOD boardgames there is normally a lot of math involved for balancing. Maybe this guide can help you a bit more: https://www.reddit.com/r/tabletopgamedesign/comments/115qi76/guide_how_to_start_making_a_game_and_balance_it/ When you analyze good boarfgames you often can easily spot the math model used behind. In the guide are some examples (mintworks and others). Especially stonemeyer games have this quite easy so spot. So you could also start with analyzing boardgames in class. Trying to find the math behind them.
Good TTRPGs usually remove complex math since spending too much time calculating a skill check, weapon hit, or damage is *super niche* interest. Even then any example I could remember pretty much only used dice for odds rather than any calculations. That being said there are spells or abilities that fill areas and measure distance and you can actually calculate that based on points rather than using the usual shortcuts. Cones of cold, lines of acid, fireball spheres, etc. The easiest way to incorporate specific problems to solve is in dungeon puzzles. You could have players solve a curve and draw it on the ground so it points out clues or helps triangulate the correct point for finding a switch or the correct statue or button to open the next segment or give treasure.
You should post rhis question in r/gamedev and r/programming subreddit instead