Quick Final Four math question??? (Kotysdad or others???)

[taoist]

How many permutations are left as of the beginning of the Ky v Mich St game??? I came up with 12...is that right?

 

[GM]

No, it's 6. I think you've counted each matchup twice.

Ill/NC
Ill/Ky
Ill/MSU
Louis/NC
Louis/Ky
Louis/MSU

After this game you're left with 4.

 

[taoist]

6 x's 2, because in any of those 6 games, you could have 2 winners.

...for example...

ILL/NC
Ill wins or NC wins...

...right? anyway, out of the 12 permutations that I came up with BleedDogerBlue gets in the $$ in 11 of 12 scenarios. Congrats tio him....

 

[GM]

Oh....ok. I didn't know by "permutations" you meant who could beat who. Took it to be who could play who. Yes, 12 then.

 

[KotysDad]

There was 16 possible outcomes going in.

 

[GM]

Heading into the day there were 16. Heading into this final game today there were 12.

 

[KotysDad]

No, heading into today there was 32, heading into the final game today there was 16, now there are 8.

However many games you have left, each game has 2 possible outcomes, so just multiply 2 by itself for however many games are remaining.

 

[GM]

Ok, can you list all 16 for me?

 

[GM]

This is what I come up with heading into the day...

Ill/NC
Ill/Wisc
Ill/MSU
Ill/KY
Louis/NC
Louis/Wisc
Louis/MSU
Louis/KY

8 matchups x 2 outcomes = 16 heading into the day. Have I missed something?

 

[KotysDad]

I understood Taoist's question to be 'How many possible "outcomes" are left at this point?' If that is the correct interpretation of his original post, then there are now 8 possible outcomes left.

Lou over UNC
UNC over Lou

Lou over MSU
MSU over Lou

Ill over UNC
UNC over Ill

Ill over MSU
MSU over Ill

3 games remaining.....2x2x2 possible outcomes.
4 games remaining.....2x2x2x2 possible outcomes

If MSU beats UK then list all 8 that I have above
If UK beats MSU, then replace MSU with UK in the 8 above.

That makes 16 possible outcomes possible.

 

[GM]

Yes, there are 8. But there weren't 32 going into today, there were 16. After one game played there were 12. And now there are 8. I think the confusion is in the fact that half of this round was played yesterday. Going into yesterday there were 32 combinations. Going into today however, there were only 16.

 

[KotysDad]

GM.....I dont know how else to put it.....going into yesterday there were 7 games remaining, therefore 128 possible outcomes to the eventual champion. With each game played, half the possible outcomes go away until there are 2 possible outcomes for the final game.

Going into today there were 32 possible outcomes.....after the UNC game ended, there were 16.

Bottom line is this.....in a single-elim tourney with n games remaining, there are 2 raised to the power of n possible outcomes.
Period.

 

[GM]

Alright, I think I see where you are coming from, and I don't think we were talking about the same thing.

For example, if you count NC beating Wisc, and Wisc beating NC, but you have either of them losing to MSU in the next round...you are counting those as two scenarios...I wasn't.

I was counting the number of potential matchups for the finals... not every possible combination of matchups along the way.