has a great concise thing about this, with a few references for further reading: raphkoster.com/gaming/gdca200
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Hm this is basically discrete math and complexity theory 101. I didn’t get much intuition about game design.
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Did you get to the examples of each problem used in various games? That said, I wouldn’t have started here either. :)
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I liked the first few slides, reminded me of OODA loop models. But the rest.. I mean I get the connection between for eg knapsack problem and inventory style games, but it doesn’t get at what makes particular knapsacks interesting for eg. But perhaps that’s too domain specific?
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Like I’m aware of a result that Tetris with only z and S pieces is np hard so Tetris tuning knob becomes percentage of those pieces. But are there principles for coming up with those 6 tiles (s, z, L, J, I, T, o) as a great game set?
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In the case of Tetris, it’s literally every permutation of four units. Five would be too many, three is trivial. And board size matters too. So yeah, there’s a significant tuning factor even once you identify the problem, defining the extent of the problem.
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Ah yes. So some mix of number theory and insight
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Yup. The real trick, I think, lies in coming up with the relationships. Suits/numbers axis (poker). Four units and 2D topology (Tetris). Pathing problems and permutations (Tsuro). Arcs and fixed distance barriers (flappy bird)
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As far as the OODA loop stuff you may want to look at Theory of Fun
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I should note that math problems are only one of the core problem types in games... particularly tabletop games. You may also be interested in my talks on game grammar. raphkoster.com/games/presenta is one of several.
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I have several down those lines, and you may want to look into the similar work of Dan Cook, perhaps starting with “Chemistry of Game Design.” There is also a bunch of good work by Joris Dormans on a systems driven modeling language
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