Sports math

[KrazyHorse]

Fans buy in advance here too, but their money is returned if the remaining games are not played.

People would riot if they were forced to watch meaningless games instead of having their money refunded.

[flash9286]

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[Nacht]

0,15625

[KrazyHorse]

You are correct.

I'm afraid Dauphin's question ruined my test, though since he is familiar with a sport where the rules of play are different than those I had assumed were universal, it is not his fault.

[flash9286]

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[KrazyHorse]

Errr, no.

The trap was supposed to be 35/128

[Dauphin]

The trick is you are supposed to work out that chances of it going to the last game.

[Ecthy]

Very simple theory of probability, apart from the fact that the question wasn't put too well.

[Joe Kick Ass]

They'll play all the games in rugby too.

[Dauphin]

Originally posted by KrazyHorse
Fans buy in advance here too, but their money is returned if the remaining games are not played.

People would riot if they were forced to watch meaningless games instead of having their money refunded.

Yeah, but these fans have travelled across the globe to see a match. Whether it is academic is not of great concern compared to watching your team play abroad.

Similar thing in the football world cup, teams always play the three group stage games, even if they are knocked out after only the second game and the final game has no effect on who goes through.

[Nacht]

Originally posted by Dauphin
The trick is you are supposed to work out that chances of it going to the last game.

And dividing by two

[KrazyHorse]

Yeah. The best way to figure it is:

probability it will get to a point where one win for the right team will fulfill prediction * probability that team will win that game

So, for 4-3, your calc should be (6C3 / 2^6) * 1/2 = 5/32

where 6C3 stands for 6 choose 3 = 20

For 4-2, it would be (5C3 / 2^5) * 1/2 = 5/32

For 4-1 (4C3 / 2^4) * 1/2 =1/8

For 4-0 (3C3 / 2^3) * 1/2=1/16

Lo and behold, when we sum these probabilities we get 1/2, which is as it should be

[Dauphin]

Originally posted by Nacht

And dividing by two

That's the easy part.

[KrazyHorse]

Originally posted by Ecthy
Very simple theory of probability, apart from the fact that the question wasn't put too well.

You're an idiot. The question was put quite clearly outside of an English predilection to continue playing games even after the Australians have beat them (Rugby, cricket, etc)

[KrazyHorse]

Originally posted by Dauphin


Yeah, but these fans have travelled across the globe to see a match. Whether it is academic is not of great concern compared to watching your team play abroad.

Similar thing in the football world cup, teams always play the three group stage games, even if they are knocked out after only the second game and the final game has no effect on who goes through.

Round robin (group stage) games are understandable, and are there for that reason (in addition to providing a helpful seeding mechanism) but I find the idea of elimination round matchups played despite futility to be odd.