Three sided football

Triolectique / Triolectics from Pied La Biche on Vimeo.

Three sided football, via faraimadzima.com. 

Good theory of the strategy of the game from a commenter 'Rotaryfan' on Gizmodo.com

Say the ball is in zone A. there are two teams on the offense, and one on defense. Teams B and C don't want the ball to shift zones because it means that theres a 50% chance it will go toward their zone. instead, it is in the best interest of both teams to hammer at team A because it is the least risky, and because they are already in an offensive position. In the event that team A is beating teams B and C, and B and C are close in score, it is best for B and C to work together to keep the match close. If the three teams are separated from each other by a significant margin, the leading team will work to pit the weaker teams against each other or will side with the weakest team to secure a defensive advantage while risking little by giving that team an offensive advantage by providing defense when the middle scoring team is in an offensive position.

when the game is very close or tied, the defensive advantage you are suggesting is an illusion, because even if three teams are in zone A, both teams B and C are attempting to help defend team A against the other team, but trying to keep posession to themselves, meaning they are really still both playing offensively. Breakaways should be much more powerful because the teams must return to their zones to play defense, reducing the number of defenders by half. 

The best defense in this game is definitely a powerful offense that keeps the other teams on regular defense. fewer dedicated defenders means more shots on goal.

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