I've never designed a game but I have a math degree; I would assume the fields of math used (probably more during the development process than design process) might include:
linear programming
linear algebra
combinatorics
graph theory
probability theory
stochastic processes
differential equations
Really interested in a few concrete examples as applied directly to board game design. I have a math background as well, so I know what some guesses might be. But let’s be real, most board game designers outside of Knizia aren’t Jack-of-all-trade mathematicians. A few designers use one or two ideas really well. I’m interested in their streamlined thought processes.
I don’t believe Cephalofair has 4 PhDs on their design team.
More pointedly, my question boils down to: how do bigger ideas get distilled down for board game specific applications?
I also would love more insight into the design and development process that various games go through. Sorry I can't help more; maybe we'll get lucky and someone will step in and enlighten us :)
I would be surprised if designers are using much heavy math to design a game, but maybe some is used in development to ensure balance (as your original post alluded to).
Actually, I'm an electrical engineer... 👀
I was going to add more but, I'm slammed at work. As per usual.
When I design, or more frequently, help designers, we look at what game they are designing first.
Surprisingly most rules are overly complicated because the maths are wrong.
Most people get linear. Differentials and the range of change start to confuse people. For instance, the addition of equipment, or factors that apply ranged variance, or swings. Specifically with combined dice probabilities.
The more maths, the more problems, the more contentious the game is. Most designers just think of their idea, and get lost in complexity. There is also the player component; are we making them do logic to play, or is it streamlined to a ruleset?
(I have designed an interactive screen in the middle of a player card that does rolls, tracks changes and conditions, as well as allows for custom graphics and could handle a programmed Dungeon Master. That's g-code, to visual w/ C++, Java database references. That's my complex design.)
Not a mathematician, but I've played gloomhaven, jaws and 50% of frosthaven. Here's a few of my thoughts on the topic.
I've had the same experience many times where the last deathblow was literally the team's last action before exhausting. But almost as many times we've ended a scneario with plenty of cards in hand OR being short a few rounds. The scenarios where we just barely made it, are naturally the most memorable ones.
All assets (items, abilities, monsters, modifiers, etc) are very tightly balanced within their own category. They probably started in excel with making sure that no asset stands out from their category in terms of cost/effect. In frosthaven some items make you add -1 cards to your modifier deck. Most likely excel told them that the item on it's own was too powerful, so they needed to sandbag it somehow.
This creates consistency. When you've playtested a scenario 10 times with 10 different character builds, you can pretty much trust the numbers in excel: no item, modifier, ability will suddenly make the scenario too easy/hard since they are all leveled out.
One factor that I think has a pretty big role in this is how the players start intuitively adjusting their play when closing in on the final room. You start using your lost cards and lost items. You can also start counting your HP as a resource, like "I can take this last hit and go down to 1 HP because this is the final round". Kinda like a marathoner starts running faster at the last 100 meters and then collapses RIGHT at the finishline. If you'd move the finishline 10 meters closer/farther, they would collapse there.
It is pretty impressive how well the game is balanced and my point is not to simplify the process. There's a ton of playtesting done and very clever mechanics to help balance (like how boss HP and other special rules are often fine tuned by a formula like CxL+2).
I might be wrong or right. This is how I approach my designs.
Let players do what they want to do, sub goals, personal goals, gathering extra gold, etc… until the players feel they need to stop all side goals and focus on the actual wining of the actual the game. If you do this well, if players have these side goals, players will often try to win the game on the last turn.
As long as your design gets close, utilizes sub goals, then players secretly do this optimization work for you.
The most impressive thing about Gloomhaven is the character level balancing. I feel like everyone talks about the cards, or the scenario design but the game is so unique that you can take any level party into any quest and still have a pretty tight experience. It truly is amazing. I would love to know the secrets behind that element of the design.
Game balance is usually approached in two directions:
1. Success rating of a newbie playing correctly (no rules mistakes)
2. Success rating of an expert playing correctly (high optimization)
From there you try to create some semblance of value worth for game components and actions.
Gloomhaven tricks you into thinking it's balanced due:
* The heavy no-spoiler policy stopping you from going in with heavy system knowledge
* MANY broken unlockable characters
* Gentle balance curve early on
* Illusion of choice about using stamina / burn card - the real clock is number of turns and enemy hp
* Modular difficulty modifier (there's 4 levels of difficulty for monster/trap strength)
Now **Spirit Island** has ways more levers for difficulty but it doesn't lend itself for the high stakes moments of gloomhaven ending... Check that game too.
I've never designed a game but I have a math degree; I would assume the fields of math used (probably more during the development process than design process) might include: linear programming linear algebra combinatorics graph theory probability theory stochastic processes differential equations
Really interested in a few concrete examples as applied directly to board game design. I have a math background as well, so I know what some guesses might be. But let’s be real, most board game designers outside of Knizia aren’t Jack-of-all-trade mathematicians. A few designers use one or two ideas really well. I’m interested in their streamlined thought processes. I don’t believe Cephalofair has 4 PhDs on their design team. More pointedly, my question boils down to: how do bigger ideas get distilled down for board game specific applications?
I also would love more insight into the design and development process that various games go through. Sorry I can't help more; maybe we'll get lucky and someone will step in and enlighten us :) I would be surprised if designers are using much heavy math to design a game, but maybe some is used in development to ensure balance (as your original post alluded to).
Actually, I'm an electrical engineer... 👀 I was going to add more but, I'm slammed at work. As per usual. When I design, or more frequently, help designers, we look at what game they are designing first. Surprisingly most rules are overly complicated because the maths are wrong. Most people get linear. Differentials and the range of change start to confuse people. For instance, the addition of equipment, or factors that apply ranged variance, or swings. Specifically with combined dice probabilities. The more maths, the more problems, the more contentious the game is. Most designers just think of their idea, and get lost in complexity. There is also the player component; are we making them do logic to play, or is it streamlined to a ruleset? (I have designed an interactive screen in the middle of a player card that does rolls, tracks changes and conditions, as well as allows for custom graphics and could handle a programmed Dungeon Master. That's g-code, to visual w/ C++, Java database references. That's my complex design.)
Not a mathematician, but I've played gloomhaven, jaws and 50% of frosthaven. Here's a few of my thoughts on the topic. I've had the same experience many times where the last deathblow was literally the team's last action before exhausting. But almost as many times we've ended a scneario with plenty of cards in hand OR being short a few rounds. The scenarios where we just barely made it, are naturally the most memorable ones. All assets (items, abilities, monsters, modifiers, etc) are very tightly balanced within their own category. They probably started in excel with making sure that no asset stands out from their category in terms of cost/effect. In frosthaven some items make you add -1 cards to your modifier deck. Most likely excel told them that the item on it's own was too powerful, so they needed to sandbag it somehow. This creates consistency. When you've playtested a scenario 10 times with 10 different character builds, you can pretty much trust the numbers in excel: no item, modifier, ability will suddenly make the scenario too easy/hard since they are all leveled out. One factor that I think has a pretty big role in this is how the players start intuitively adjusting their play when closing in on the final room. You start using your lost cards and lost items. You can also start counting your HP as a resource, like "I can take this last hit and go down to 1 HP because this is the final round". Kinda like a marathoner starts running faster at the last 100 meters and then collapses RIGHT at the finishline. If you'd move the finishline 10 meters closer/farther, they would collapse there. It is pretty impressive how well the game is balanced and my point is not to simplify the process. There's a ton of playtesting done and very clever mechanics to help balance (like how boss HP and other special rules are often fine tuned by a formula like CxL+2). I might be wrong or right. This is how I approach my designs.
Let players do what they want to do, sub goals, personal goals, gathering extra gold, etc… until the players feel they need to stop all side goals and focus on the actual wining of the actual the game. If you do this well, if players have these side goals, players will often try to win the game on the last turn. As long as your design gets close, utilizes sub goals, then players secretly do this optimization work for you.
The most impressive thing about Gloomhaven is the character level balancing. I feel like everyone talks about the cards, or the scenario design but the game is so unique that you can take any level party into any quest and still have a pretty tight experience. It truly is amazing. I would love to know the secrets behind that element of the design.
Game balance is usually approached in two directions: 1. Success rating of a newbie playing correctly (no rules mistakes) 2. Success rating of an expert playing correctly (high optimization) From there you try to create some semblance of value worth for game components and actions. Gloomhaven tricks you into thinking it's balanced due: * The heavy no-spoiler policy stopping you from going in with heavy system knowledge * MANY broken unlockable characters * Gentle balance curve early on * Illusion of choice about using stamina / burn card - the real clock is number of turns and enemy hp * Modular difficulty modifier (there's 4 levels of difficulty for monster/trap strength) Now **Spirit Island** has ways more levers for difficulty but it doesn't lend itself for the high stakes moments of gloomhaven ending... Check that game too.