Some Combinatorics of Epic Duels

Sun, 01/17/2010 - 18:28 by volleyballgy Tags:

I wrote this paper for a graduate course in Combinatorics (yeah, can you believe graduate math classes make you write papers?!?), and I figured, where better for it to be read by no one than on my blog at epicduels.com?

Note: Some of the mathematical expressions appear to have not been translated very well into MS Word, but if you know what they would mean, I have full confidence you're smart enough to figure out where they belong!

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Submitted by Darth Trumpetus on Mon, 01/18/2010 - 19:27.

Re: Some Combinatorics of Epic Duels

You could also add in 6 player free-for-all into the analysis (1vs1vs1vs1vs1vs1). What would be even cooler is to calculate not only all of the possible matchups given decks and players, but all of the possible deck draws within each of those matchups. How many different ways could a deck of 31 cards be shuffled and played out? Then factor THAT into the 16 million combination of decks/teams. I can't even fathom how large that number would be.

So, to sum up: endless possibilities. :D

Oh, and believe it or not, there is also Combinatorial Music, which I spent about 2 weeks studying during grad school in a music theory survey class. I couldn't tell you much about it now without looking it up.

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Your Skills Are Not Complete

Submitted by volleyballgy on Tue, 01/19/2010 - 12:59.

Re: Some Combinatorics of Epic Duels

The six-player free-for-all was considered in the 4th paragraph in the general sense (m-player FFA), but I do think the penultimate paragraph could be improved by adding a line mentioning that (something like, "... in addition to the previously calculated possibilities of 6-player free-for-alls" added to the last line about team games).

When I first outlined the paper, I had many more things in mind, one of which was the "first-turn beatdown" likelihood, which does involve counting shuffles. It turned out that I had much more to say about just counting the possibilities than I anticipated, though, and I was approaching the limit of how long the paper was to be. In general, counting a shuffle isn't difficult -- "# of cards factorial" (for 31 cards, that's on the order of 10^33); variations in the count of specific cards are what make a more interesting problem.

Submitted by Roman Farraday on Thu, 03/04/2010 - 11:26.

Re: Some Combinatorics of Epic Duels

You're such a geek, Tim. :-)

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Guess what? I've got a fever, and the only prescription is more cowbell!

Submitted by volleyballgy on Sat, 03/20/2010 - 23:49.

Re: Some Combinatorics of Epic Duels

Duly noted, proudly admitted!