Topic for a gaming-related maths research?

[Lucifer666]

Hiya,

This is one of the sadly increasing number of times I reach out to the temp for inspiration with college work. I take an advanced maths course and I have to produce a research on a similar level of complexity

One of the things they look for is personal engagement, i.e. how interested the student is in the topic. This is assessed by apparent enthusiasm in classes, as well as enthusiasm shown in the writing, and I figure this would be easy to do and I wouldn't have to fake it if I did it on something I'm genuinely interested in. Hence, gaming. Unfortunately I'm really uncreative and bad at coming up with ideas so here's where you guys come in.

If you wanna know what sort of maths I do, I've done all sorts from something as simple as arithmetic/geometric functions all the way down to implicit differentiation, integration by parts, the integration of radical functions, volumes of revolution, limits, infinite sums, integrating trig functions, etc.

I was thinking something along the lines of 'the mechanics behind RPGs' but I couldn't get much more specific nor could I find something complex on the maths scale. Also the body of the research should not exceed 2,000 words.

Any ideas?

Spoiler: If gaming is a bad idea here's some other stuff I'm into

• Computer programming (I know C++ and Java fairly well, and I'm kinda noobish at Python and BASIC), the focus HAS to be on maths though so if I'm to include code it should only be in the introduction to establish the topic of the research, not as part of the actual research itself
• Science fiction (namely Doctor Who, Bravest Warriors, and The Hitchhiker's Guide to the Galaxy)
• Collecting mini car models
• Electrical engineering (mostly repairing stuff, building computers, etc.)

Spoiler: Examples of previous stuff students taking my course have done

My teacher was telling me about a good research he read before where a student tried to work out the design/dimensions of a vase such that it can hold the most amount of liquid in comparison to the amount of material used to make it. The student obtained a function of the volume of the vase itself against the volume of the liquid it can contain and differentiated it to find a maximum point, etc. etc. you get the gist of it.

Another one was something to do with the probability factors behind the game minesweeper. But this was fairly un-complex and scored poorly as a result, even though it was interesting.

 

[FAST6191]

I usually encourage not using personal interests for research topics, mainly as they can be quite limiting and sometimes it can lead to assumed knowledge on the author's part; http://www.cracked.com/video_17500_a-helpful-tutorial-most-difficult-video-game-ever.html would be the extreme but even something as basic as "fire two fireballs as you land or you will lose a life" means less than you might imagine to someone that never played Mario before.

The obvious one is maths has a whole concept called game theory, and also mechanism design. That is a fairly in depth part of applied maths though (indeed many place it more in economics and psychology), and you did not mention it above so I would possibly consider not doing that unless you want to learn it. http://levine.sscnet.ucla.edu/general/whatis.htm
On the other hand if you want to take a look at a lot of games and show where they use elementary game theory concepts (these games show examples of the prisoner's dilemma, these hawk-dove... these games can be categorised as ???, unless you turn fog of war on and then it is **** which changes the mode of play....)

If you want to go back to the RPG mechanics then even something as basic as the first pokemon games yield results like http://www.dragonflycave.com/rbycapture.aspx
Computer games are tricky though as most people that are not casinos/gambling/eve online usually arrive at playable results by playtesting/brute force and a gut feeling in the first place than any underlying mathematical analysis, or if they do then it is possibly after the initial tests (this is our system, now make it playable/refined, or "meh they can grind"). Computer games will tend to hide these systems as well leaving you either having to work them out by analysis or look at the game code (hopefully it is open source or you will then have to explain disassembled code) to figure things out.

You mention minesweeper and that would be a poor choice (most of it is solvable but when it is not then it is usually reduced to something that is a very basic element -- it is random but as there is nothing near it then it is functionally the same as many things you would have seen before, now you might be able to generate a so called heuristics list and take that far but I would not suggest it). Card games on the other hand have a long history of this sort of thing ( http://www.solitairelaboratory.com/fcfaq.html ), board games are also good for it.

On science fiction. Sales data can probably be found and if you can not make a maths project out of that (does being called scifi help or hurt if different regions say different things, does it matter if there is a popular scifi/fantasy film out that year....) then you have gone very wrong somewhere.

Electrical engineering, especially the analogue stuff, has some insane maths you can play with.

"Collecting mini car models"... do these get to be pricey for rarer and harder to find things? Artificially controlled markets are frequently a great source of both data and trends you can look at.

As for the vase stuff I am now thinking about hoop stress so I will leave that one alone.

 

[Lucifer666]

-snip-

I've been wanting to reply to this for so long, but one thing led to the next and here I am 3 weeks later. thanks so much for your help

I've looked at the pokemon red/blue/yellow capture thing and while the level of maths is great, I can't possibly think of a research question to go with it

Good point about the science fiction, but I'm afraid with projects like statistics/sales data it is very difficult to go beyond just looking at analysing the data (mean, mode, standard deviation, etc.) which often ends up being pretty basic. I'm trying to think of something along the lines of "Is [fictional concept from a sci fi series] correct in its handling of mathematics?" with extensive mathematical research put into it to answer the question.

For example, "Is the 'Infinite Improbability Drive' from Douglas Adams' novel The Hitchhiker's Guide to the Galaxy a mathematically sound concept?"

That would be a LOVELY research question. Only problem is the HHGTG series doesn't give much of a description of how it works so there's nothing to work with there

Thanks for this. I'm still a bit undecided though and would appreciate more input from anyone who might have anything to say, even if they think it's a dumb suggestion.

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I'm all ears. Anyone got suggestions?