In his Philosophical Investigations, Ludwig Wittgenstein famously argued that the word “game” defies definition. “Game”, for Wittgenstein, is used to describe a family of different human activities that have a certain family resemblance, but for which there are no definitive rules for including some activities and excluding others.
Nothing daunted, I’d like to offer a definition of game playing that I’ve found useful. Games are, for me, not so much things as activities, so I’ll define “game play”:
Game play is the pursuit of arbitrarily-assigned value. Continue reading “Playing Games”
Elimination tournaments of various kinds have been the subject of most of the posts here, and that might make it appear that I’m a big fan of elimination formats. But I’m not. In fact, I really dislike elimination tournaments, and I’ll take time out to explain why.
The one distinctive thing about elimination tournaments is that they’re ruthlessly efficient in eliminating people, and that, to my mind, is not necessarily good. Continue reading “A Nation of Losers”
On his website tournamentdesign.org, Joe Czapski has some ingenious tournament ideas.
One of his chief thoughts is to try to equalize the treatment of the upper and lower brackets in double- (and even triple- and quadruple-) elimination tournaments. He has a suite of Excel-based brackets for download. None of the ones I looked at looks like anything I’ve ever seen.
I’ve analyzed the “balanced” bracket for a 16-team double elimination so that I can relate it to the more conventional brackets already discussed. Continue reading “A Balanced Bracket”
As promised in yesterday’s post, I ran simulations to see if the 32 bracket would behave the way the 16 bracket did, showing a fairness advantage for the unshifted format where the tournament is seeded. It did.
A number of these bracket simulations have been run now, and I thought it would be good to gather them together in one place so that they can be compared, and tentative inferences drawn. Continue reading “The Results So Far”
Another surprising result today.
I ran a 16DE through the simulator, this time seeding the entries – all of my previous runs have been blind draw. On the basis of what I’ve seen so far, I decided to run only the shifted bracket, which is in line with my conclusion that the shifted bracket is, or at least should be, preferred. But there’s more to the story. Continue reading “Seedy and Shiftless”
The bracket-shifting technique illustrated in the case of a 16 DE tournament can be generalized to larger brackets, but there are some additional considerations.
The bracket shift works, essentially, by taking two adjacent rounds of drops, which would ordinarily be separated in the lower bracket by a non-drop consolidating round, and pushing them into earlier rounds of the lower bracket, causing there to be one fewer round in the tournament as a whole.
In a 32 bracket, there are two ways to do this. You can either shift the C and D drops earlier, leaving the E drop in its usual relative position, or shift D and E drops earlier, leaving the C drops in place: Continue reading “Shifting a 32 Bracket”
What of the complaint that a bracket with shifted drops is lopsided? What sort of complaint is it, anyway, fairness (A), fairness (B), or fairness (C)? Potentially, at least, all three kinds of fairness might be of concern. Continue reading “Fairness and the Lopsided Bracket”