A local pool hall features weekly 8-ball and 9-ball double-elimination tournaments, and the different tournaments are described as:
- Race to 4
- Race to 4/3
- Race to 2
What do these terms mean?
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According to Wikipedia, the term race in billiards means:
A predetermined, fixed number of games players must win to win a match; "a race to seven" means whomever wins seven games first wins the match.
Here is a file with some more examples:
First competitor to win 3 matches (race to 3)
First competitor to win 4 matches (race to 4)
First competitor to win 5 matches (race to 5)
First competitor to win 6 matches (race to 6)
As for your "race to 4/3" example, I believe that is specific to double-elimination tournaments in which you play a different number of games depending on whether you are in the winner's bracket or the loser's bracket. So "race to 4/3" means it's a "race to 4" in the winner's bracket and a "race to 3" in the loser's bracket. Here's a page where it mentions a different "race" for the winner's and loser's brackets in one tournament:
Race to 3 winner’s side. Race to 2 on the loser’s side.
If a double-elimination tournament has the same number of games for both the winner's and loser's brackets, then you could call it a "race to N/N". An example of that can be found here:
race to 3/3 double elimination
But instead of calling it a "race to 3/3", you could just call it a "race to 3". An example of that can be found here:
Double Elimination – Race to 3