I've noticed that in some games I've been playing lately (mostly classics) that taking a little time off to the side to do some math work (and simplifying the process via Excel) has improved the quality of my gameplay here and there, be it in the output of my gaming, or learning something new in the process.
For example, through some simple functions, applied correctly, I've been able to determine all kinds of stuff with my games, and make use of the information to better aid my progress; and through Excel, making the process of calculating other things I wanted to know as simple as changing the value of a cell or few.
I've tried looking around different sites and such to find out if anyone has explored other neat applications of math in gaming (besides using Rocket Science in Kerbal Space Program; that seems too obvious to require mentioning), and I couldn't really find anything relevant. If you found a good use of math or a mathematical formula for a game (optimizing damage or speed or something), then feel free to post it.
Some decent examples of math in action:
Rollercoaster Tycoon -- Through the use of the formula
( y/xz ), I was able to optimize my line waiting times for all of my rides that had some serious car/train distribution issues, which needless to say, led to tons of customer complaints about waiting in the line for ages. Log Flume's template "Logger's Revenge" is guilty of this, and a good proof of concept. Since the ride was
4m51s (291s) long
(Y-value), and it also has
9 cars/trains (4 passengers each) active at all times
(Z-value), then we need the best distribution possible by setting the MIN/MAX waiting times for the ride itself
(Solve for X).
X = roughly 32(.33333) seconds minimum and maximum. It'll continuously cycle at equal intervals, and with
5 queue tiles lined up, we have an average time of 6 minutes of waiting for the customers, and I have yet to hear any whining about waiting in line yet. As a secondary perk, in case the station brakes fail, there's more breathing room between cars/trains to allow the repairman some time to fix it before things go from bad to worse. Needless to say, it also looks more aesthetically pleasing, and like an actual theme park ride more (at least, the times I went to parks, it looks more familiar now).
I've also applied the Pythagorean Theorem for the starmap navigation in Starcon 2, along with taking Quasi-Space into account, which has not only helped me save fuel, but also time (In-game, and Real Life. Those numbers were also figured out using the same formula, converted for time); which ended up giving me an unique ending which keeps everyone alive;
Ilwrath and Thraddash alike, with the Utwig still providing coreward aid, and possibly able to intervene in their zealous battle with the Ultron in hand to set the Ilwrath and Thraddash minds in line again, overall.
X-Com has also used a few tricks here and there to optimize my manufacturing (what sells the best (maximum (80 engineers) production rate and value-wise), what's the most optimal engineer output (40 or 80 is the magic number for me, depending on the project and need/value), and so on). I have yet to get the math down to optimize interception distribution for maximum effect (timing arrivals and the like, with fuel and ammo to spare). The engineer thing, I noticed allows me to spare my engineering a bit more so I can have others set on smaller projects to allow for more income along with the main project (most-all profitable small production jobs average within 3-4 hours per-project with 80 engineers assigned; having at least 240 engineers and enough space makes for a profitable base (due to having up to 3 3-4 hour long jobs working simultaneously, and selling upon completion of a unit. Watching the funds ticker slowly climbing is a beautiful sight to behold; unless you timed it so each project is offset by 1 hour each, and makes it rapidly climb instead.)). Since I also had sites that were overstocked with engineers (about 250 of them at 1 or 2 bases each), this came really handy in mass-production as a global effort, making the monthly expenses the only bottom-line to worry about (But when you're producing upwards to 5M-10M (10M-20M with 2 bases doing it) monthly, making medi-kits, motion detectors, and alien laser rifles (Final Mod; no material cost to produce), why worry?), permitting me to go to ridiculous lengths in UFO defense. Global surveillance, interceptors at nearly every base, losing a ship being a minor loss... the list goes on. Things got so insane, I needed a base for excess goods to use as an emergency fund cache. One of my bases effectively turned into a scrap yard, complete with 2 troops and 2 dogs, and maybe a laser tank. Good luck getting your weapons back, aliens. Beauty of it is, I can adapt this same principle to TFTD (and/or X-Piratez even), and give T'Leth a Terror From the Surface of their own.
Got any neat ideas, math formulas, games you want some math help with or want some ideas applied, to apply to any games (something that can be applied to all games, or even just a few specialized ones) to help out, feel free to post it.
EDIT:
I think the application of math also aided in me making a bomb in SS13 so powerful, the bomb range couldn't even contain the blast. That was a fun experiment. I think my numbers (provided by the admin) was something along the lines of (15,30,60) or something of the sort. In other words, the bomb range was nothing more than it's main support frame (and only the said frame remained), and atmos got knocked hard enough, a good chunk of it needed to be rebuilt. Hell, even the observation pod for the bomb range had it's windows blown off, and knocked my character to the ground, thanks to the shockwave. I think it also was large enough to lag the server for a moment. That was a good time. Kinda wish I took a screenshot of the damage.
EDIT EDIT:
Another nice perk of optimizing the ride time is also the fact that the income for the ride, based on the rate of customer use, is now stabilized to a more consistent number to track, meaning you shouldn't expect the income rate to increase or decrease, unless you directly adjust the price. Which is a new avenue I ought to check out; price adjustment as the ride (or ride type) ages. Some have rapid decay, others not. Finding this out will be a new place to look, but will unfortunately, take some time to learn/figure out. But this info will help tremendously with parks that need to be done by Year 4 (4 hours of playing) that may have a few pretty old rides in it already. So yeah, adjusting for diminishing interest.
All I know is that an ideal Year 1 value is equivalent to the excitement rating, but what's the depreciation rate? When would be the best times to lower prices to keep popularity/satisfaction up, and by how much (percent-wise) should it be adjusted per-year, if at that rate? I noticed that the fewer variables I am worrying about since doing this, the more finer details, like depreciation of rides (interest/income wise), I'm noticing that I also want to tinker with.
What will truly rock will be if I can do all this and get an optimal amount of guests at my parks (at least 1.5k by goal time or Year 2 even, depending on park), while retaining a minimum of 95% park rating the whole time.
EDIT EDIT EDIT:
Thanks Ludorum Rex for teaching me a new word. Title updated.
While at it, looking up the term 'Theorycraft' has given me much more relevant material in the same places I looked around previously for this topic. There goes my afternoon.