Most high interactive competitive games are played with 2 sides, not just contact sports. Competitive games with 3+ sides and high interactions are very rare. A big issue with 3+ sides are metagame, where factors outside the game strongly influence the outcome. There are also many harder-to-check ways of breaking rules, like undue collusion and wintrading. Then there are also issue like lame duck (side that already lose but still have to try hard to keep the game balanced) and kingmaker (a side that can’t win but can help someone else win).
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