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In most professional sporting events that involve some form of ranking system to determine an overall winner, or progression into later stages, there are a series of tie-breaker rules to determine a winner / loser when the primary ranking metric is tied across two or more competitors.

For example, for the 2018 FIFA World Cup, the tie-breakers for the group stage were as follows:

  1. greatest number of points obtained in all group matches;
  2. goal difference in all group matches;
  3. greatest number of goals scored in all group matches.

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  1. greatest number of points obtained in the group matches between the teams concerned;
  2. goal difference resulting from the group matches between the teams concerned;
  3. greater number of goals scored in all group matches between the teams concerned;
  4. greater number of points obtained in the fair play conduct of the teams based on yellow and red cards received in all group matches;
  5. drawing of lots by the FIFA.

https://www.fifa.com/worldcup/news/tie-breakers-for-russia-2018-groups

Quite a lot of these tie-breakers end a coin toss, or another "luck of the draw" type scenario, to determine the "winner".

My question is: has any professional sporting event ever had to use its final "it's down to luck" tie-breaker?

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There are a number of examples of this, but mostly from the days when they didn't have nearly as many tiebreakers before the "coin toss". Some football examples:

The latter two would these days have been settled by a penalty shootout; the former would probably have used one of the "disciplinary record" tie-breakers but I haven't looked into the details.

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