What's the fewest number of games it would take to name one champion out of six teams?

[b0mbrman]

Suppose you have six teams and need a champion out of them.

Suppose further that you need to have one "championship game" between the top two teams. What is the fewest number of games you'd need to produce a clear winner?


My thoughts in a minute...

 

[nakedfrog]

Forty two.

 

[ScottFern]

6

 

[Alkaline5]

Can we assume that this is a post-season scenario, or are these six teams playing a regular season schedule?

edit: if it's post-season, then I say 5.

 

[nycxandy]

5

 

[b0mbrman]

Originally posted by: Alkaline5
Can we assume that this is a post-season scenario, or are these six teams playing a regular season schedule?

edit: if it's post-season, then I say 5.

Let's say that these teams have never played each other before

 

[KLin]

nvm

 

[ElFenix]

Originally posted by: b0mbrman

Originally posted by: Alkaline5
Can we assume that this is a post-season scenario, or are these six teams playing a regular season schedule?

edit: if it's post-season, then I say 5.

Let's say that these teams have never played each other before

it's still 5. logic is, whoever lost in the first round wouldn't have beaten the team that won in the second round anyway. then the two winners from the second round meet up.

 

[iamme]

what's the game?

maybe they can play a free for all with all six teams at once........last team standing wins answer = 1 bloody game :evil:

 

[kstu]

7 is fairest

divide into 2 sets of 3. round robin in each group to determine two finalists (with tiebreaker in case each team goes 1-1), then finalists face for the championship

 

[SpanishFry]

5, just like NFL playoffs

 

[sciencewhiz]

I predict another thread proposing a college football playoff in less then 15 minutes.

 

[kstu]

Originally posted by: SpanishFry
5, just like NFL playoffs

5 gives two teams a bye

how do you determine who gets a bye if the 6 teams have never played before?

 

[jpeyton]

One cage match, winner take all.

 

[Garet Jax]

Originally posted by: kstu
7 is fairest

divide into 2 sets of 3. round robin in each group to determine two finalists (with tiebreaker in case each team goes 1-1), then finalists face for the championship

This is the fairest.

The least fair is 0. Stick all names in a hat and randomly draw one.

 

[Garet Jax]

Originally posted by: kstu

Originally posted by: SpanishFry
5, just like NFL playoffs

5 gives two teams a bye

how do you determine who gets a bye if the 6 teams have never played before?

Agreed. You have to randomly choose two teams. If this is a sport that involves some sort of attrition, then it is exceedingly unfair.

 

[jersiq]

OP never stated you needed to have a playoff, so one game.

The number one seed vs. the number two seed.

 

[kstu]

Originally posted by: Garet Jax

Originally posted by: kstu

Originally posted by: SpanishFry
5, just like NFL playoffs

5 gives two teams a bye

how do you determine who gets a bye if the 6 teams have never played before?

Agreed. You have to randomly choose two teams. If this is a sport that involves some sort of attrition, then it is exceedingly unfair.

i suppose if it was single elimination (i.e. 5 games), you could argue if 1 beat 2 then 3 beat 1, then 3 would have beaten 2 as well. but then you get into bad games or differing styles of play, etc. etc.

 

[Alkaline5]

Originally posted by: kstu

Originally posted by: SpanishFry
5, just like NFL playoffs

5 gives two teams a bye

how do you determine who gets a bye if the 6 teams have never played before?

The OP didn't say the teams hadn't played before, just that they hadn't played each other.

 

[GasX]

Round 1: 3 games

winners progress

Round 2: 3 game round robin

Winner declared based on record backed up by an assortment of tie breakers, total score, differential, head to head, etc...

6 games

 

[Matthias99]

Originally posted by: Garet Jax

Originally posted by: kstu
7 is fairest

divide into 2 sets of 3. round robin in each group to determine two finalists (with tiebreaker in case each team goes 1-1), then finalists face for the championship

This is the fairest.

Whether that is the 'fairest' structure is debatable. Would having all the teams play each other round-robin be 'fairer'? After all, in the 2x3 setup some teams still never play each other at all. If several teams are very evenly matched (so that a game between them is close to a coinflip), single elimination in any form becomes quite 'unfair'. Baseball uses playoff series because a single game is not deemed enough to decide which team is superior.

If you want a single elimination tournament (and you assume teams play headsup matches), you need at least five games -- one team is eliminated per game. Of course, two teams must get byes if you do that. That format is used for American football mostly because you can't reasonably have teams play games fewer than 5 or 6 days apart, and if they did something else the playoffs would take much much longer.

Edit: several other posters mentioned previous records, seedings, etc. -- the OP didn't really provide any information on that sort of thing. If you assume all the teams should start out 'equal', single elimination of randomly paired teams is clearly not going to be very 'fair'.

 

[kstu]

by the way, fairest = most fair

Originally posted by: Mwilding
Round 1: 3 games

winners progress

Round 2: 3 game round robin

Winner declared based on record backed up by an assortment of tie breakers, total score, differential, head to head, etc...

6 games

but he specified there must be a championship game

 

[TuxDave]

If we turn the question into a logic question where the better team will ALWAYS beat a worse team, LAST game played HAS to be #1 vs #2, and no two teams are equal.

At most 9 games using the quick sort.

Divide into 2 groups of 3, round robin and rank = 6 games total
Take the best from each group and play against each other to find the #1 team = 1 game
Take the loser and play against the next highest in the winner's group to find the #2 team = 1 game
Play the #1 against the #2 game just so the last game is between the #1 and #2 = 1 game

9 games total. We already know the outcome of the last game but we just have to do it for the sake of the OP's requirements.

 

[her209]

At least 1

 

[b0mbrman]

Originally posted by: iamme
what's the game?

maybe they can play a free for all with all six teams at once........last team standing wins answer = 1 bloody game :evil:

Game is softball...I'm not sure how a softball free-for-all would work