The Element Games (Essen Tasch) in "A Gathering of Shadows": This otherwise lovely book has a 36-person tournament which proceeds in:
- two single-elimination stages
- a round-robin group of three which is decided by points scored (so you could lose two and still proceed, I think), and
- a three-way championship match
Azad in "Player of Games": two 10-player matches, and several 2-player matches (including the championship), but the dreaded 3-player match is thrown in. Some political justification in letting the dominant third ("apex") gender kick out males and females in the first round, which is a 10-player match. The purpose of the second 10-player match is less clear; perhaps this could serve to demonstrate that top Azad players can engage in coalition-forming, a useful real-life skill. But from a practical point of view, it's better to run both the 10-person matches immediately--- otherwise you need host a lot of two-player matches. There's no attempt at an excuse for three-player matches and it's a non-event in the book.
Triwizard Tournament in "Harry Potter and the Goblet of Fire": a purely arbitrary (and easily rigged) magical sorting artifact reduces the competitors to just three in a single stage. While this allows more challenging (and expensive) trials to be set up, there seems little justification for believing that the cup has really selected the best competitor from each school. There is little drama, either, and the fans would probably appreciate seeing a larger field to start.
The tournament itself resembles a decathlon, with competitors engaging in various tasks and challenges. But rather than an objective scale of point awards, or purely time-based scoring, the judges engage in further arbitrary decision-making based on "spirit" which allows them to promote their favorites. (The tasks are spaced out over the course of a year for no good reason.)
The blatant point-rigging is OK, because the points don't matter anyway, serving as only an insignificant handicap on the final task, a labyrinth.
(Quidditch, surprisingly, appears to have a fairly standard tournament structure--- all the misdesign was saved for the game itself.)
Assumption in "Last Call" (Tim Powers). This looks like a poker game. But the real object is to lose the "assumption" all-or-nothing side bet after merging hands with your victim. As a poker game this is a real mess, and virtually no spectators will understand who has actually won.
Hunger Games in "The Hunger Games": while theoretically designed for showmanship, the actual structure of this battle-royale tournament doesn't lend itself well to televised drama, requiring frequent intervention by the Gamemakers. The Cornucopia is an obvious "rules patch" to force early conflict and reduce the large number of contestants. (Otherwise, an equilibrium strategy is likely to wait for others to become injured.) Unwatchable in real-time, this blood sport probably gets cut down to just the 18 minutes of real action for most viewers (similar to a compressed baseball game.) Unfortunately, there's only one per year. Would be much improved by scheduling smaller weekly matches, but then the poorer Districts wouldn't feel quite so oppressed. Which, to be fair, seems to be the point of the exercise anyway---- the Capital is nobly willing to forgo entertainment value to promote heavy-handed social allegory.