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The following dialogue is between two chess players at the end of a game. Does it mean "you have lost 4 games so far, what is your idea about going for the 5th game and developing the competition to 8 games"?

Dialogue:

A: Checkmate! Care to try for best five out of eight?

B: No, Thank you.

The source: http://www.clockwork-comics.com/2012/09/06/i-like-the-way-you-think-schlumberger/

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To me, it just seems A is asking for a match of 8 games. If you exclude the possibility of draws, you'll need 5 wins to win such a match. This is similar to the best-of-X formats used in playoffs in many sports.

In any case, it's not terminology specific to chess. You might have more luck on English Language & Usage or English Language Learners.

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Essentially, you would not ask for "best five out of eight" unless you have, excluding draws,

  1. lost 4 points
  2. can win 5 points within 8 games.

But these together are mathematically impossible, as that would require 9 games.

It doesn't get better if draws are allowed.

The reply should be "best 5 out of 9."

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