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What are the most critical aspects of mathematics for a game designer to understand?

For the purpose of the question, let's assume our imaginary designer doesn't have any current qualification beyond high-school maths.

This question is aimed at those who have some experience of RPG design: what areas of mathematical study did you find most useful in your efforts at game design? Illustrations by example from your - or existing - games are appreciated.

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closed as unclear what you're asking by the dark wanderer, Oblivious Sage, Thomas Jacobs, user17995, Wibbs Jun 4 '17 at 21:09

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    \$\begingroup\$ I'm concerned this is more of a discussion-starter and opinion poll rather than something we can reasonably provide a correct/best answer to, so I'm closing this as primarily opinion based. You can ask about this on a forum. \$\endgroup\$ – doppelgreener Jun 1 '17 at 11:58
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    \$\begingroup\$ @doppelgreener Well, if there is an audience of RPG designers on this site, they could provide their specific expertise on how much mathematics was needed. But I can see why you are concerned, and of course the answers could be too much opinion based or of not good enough quality. \$\endgroup\$ – Francesco Jun 1 '17 at 12:42
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    \$\begingroup\$ It would not; it is a matter of opinion what the "best" area is. Good subjective, bad subjective, our guidepost for subjective posts, suggests that "Great subjective questions invite sharing experiences over opinions" and "Great subjective questions insist that opinion be backed up with facts and references". I'm not sure how we can get facts and references and experience on this beyond "here's my opinion of what's important." This is also my concern for the "most critical aspects" and "what should they learn?" questions. \$\endgroup\$ – doppelgreener Jun 1 '17 at 13:00
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    \$\begingroup\$ @doppelgreener "Mechanics X, Y and Z from popular games A, B and C all depend on mathematical concept N which is therefore worth learning" \$\endgroup\$ – Bob Tway Jun 1 '17 at 13:02
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    \$\begingroup\$ If there are any professionals in the field of game design who frequent here they may be able to offer an objective answer. Additionally, I find it highly unlikely that someone would need to be able to utilize various infinities or imaginary numbers in RPG design, so there certainly is some semblance of an objective "right answer". \$\endgroup\$ – Tom Dacre Jun 1 '17 at 13:35
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Probability and optimization are the two main areas that I can see playing a role in the design of the mechanics of a new RPG. Also some economics (and related game theory) can help to model some imbalances in the world one is designing.

That said, I don't think that a good game (as in "fun and nice to play") requires deep mathematical knowledge (on the other hand, a good mathematical basis is nice to have and doesn't hinder RPG design!)

I base this on creating a lot of games for my kids and holding a PhD in Physics: but my RPG design experience is limited to text-based MUDs of which I wrote a couple "in the good old days".

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If your game uses dice, or similar random number generators, you should have enough understanding of probability that your mechanics actually do what you intend. I've encountered several home-brewed RPGs that could not manage that.

Be aware that trying to fool your players with mathematical tricks is not a good idea. I was once asked to help design a dice-pool mechanic for a cinematic game where taking more dice in exchange for a higher target number would give the impression of taking greater risks, but actually increase the probability of success. Even if the players didn't spot this instantly, they'd soon learn from experience that doing this made things easier, which would destroy the tension the mechanic was supposed to create.

If you have a copy-editor, which is always a good idea, they should try to clean up statements that are mathematically dubious or ambiguous. For example, in d20-based games, some people will think that "+1 to hit always increases your chance of hitting by 5%." Well, yes, in one sense that's true. But if your chance was only 5%, adding 5% doubles your chance. The problem is with the boundary between English and mathematics, and avoiding the pitfalls along that border is a good idea.

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    \$\begingroup\$ We've seen various professional RPGs which couldn't get it right either, possibly most famously D&D 4e... \$\endgroup\$ – Philip Kendall Jun 4 '17 at 18:14

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