Maths help in World Cup Nominate finalists market

You're miles off

It's actually a number so big that for me to count up to it would take longer than I have left on this earth,

but it's basically 8,000,000,000,000,000,000,000,000,000,000 different possible combinations of finalists.

Sorry, it's actually several times more than that, I missed about 15 zeroes off

Just kidding, I think its 528

31+30+29...+1 = 496

or (32*31)/2 = 496

Reasoning is there are 31 teams that Brazil can play.  Argentina can play 30 more teams other than Brazil.  Spain can play 29 teams other than Brazil or Argentina etc etc.

I made it 512 (might be wrong).  This evening I asked Betfair on live chat to add a "Any Other combination of finalists" as they have only 62 listed.

its more complicated than u think my first reaction was 496
32x31/2
but a team cant meet all teams in their group(in the final) as 2 go out

so is it  248 prob talking at my arse

You are over thinking it. Brazil for example can only meet 1 team in the final, they can't meet 3 teams in the final, which could be any of Mexico Croatia and Cameroon.

It's 512

Yesterday
"This evening I asked Betfair on live chat to add a "Any Other combination of finalists" as they have only 62 listed."

I gave a couple of examples of combinations that were not listed e.g. Brazil/Russia
So today what do I find?  Betfair now have Brazil/Russia added to the market (available at 5.2 if you are interested.)

I got on to Betfair chat a minute ago and again went through the situation, and asked them to add "Any other two finalists not listed"

It can't be more than 496 as there are only 496 combinations.  It can only be less if some of the combinations are not possible.  I believe that they are all possible.  In which case it can't be less either.

It's a mistake to add "Any other two finalists not listed" so I doubt they will.  When you get to the quarter finals you would at least hope that every option is available.   Imagine if 3 of the quarter finalists weren't listed (2002 SK Turkey and USA) then you'd only be able to bet on 10 of the possible 28 scenarios.

32!/(2!).(30!) = 496 as Clydebank correctly points out.

CLYDEBANK
If I understand your point correctly you are saying that if outsiders get into the semi-finals Betfair will then add the possible finalist combinations that are missing at that date.

If the semi-finalists are: Brazil; Costa Rica; Ivory Coast; Portugal
Only one of these is listed today afaik (Brazil V Portugal)

I think you are saying Betfair will then add the missing combos to the market

Brazil V Costa Rica (Any other finalists)
Brazil V Ivory Coast (Any other finalists)
Brazil V Portugal (Brazil V Portugal)
Costa Rica V Ivory Coast (Any other finalists)
Costa Rica V Portugal (Any other finalists)
Ivory Coast V Portugal (Any other finalists)

I would prefer the chance to bet now on the shock combinations and have a complete market.

kincsem they will likely add them at a later date, probably at the last 16 stage.

My first thoughts was the answer is 496
32x31/2
However, the possibility of England playing all three combinations(in the final) of England v Italy, England v Costa Rica or England v Uraquay as two of their opponents will be eliminated at the group stage.
Also after the group stage ,the winners of say group A will play the runners up of another group,therefore making it impossible for those two teams to meet in the final.
Perhaps im making this to complex.

We need a maths genius here!

after just reading all through this thread...

im going to have a very large whiskey, and forget it ever happened

The suggestion 496 is far to simplistic.
I was on the right lines with 248 but I missed the final part of the puzzle,which I will come to.
The answer is 124
32/x31/2/2/2

Explanation.....

First part 32 teams in the tournament who have potentially 31 opponents in the final.
Second part two teams in final therfore divide by two.
Third part at group stage each individual team will lose two potential opponents in final, therfore divide by two.
Fourth part,after group stage the next round will have 32 teams left  where sixteen teams will be played who they can no longer meet in the final.

Next round sixteen teams will be left where eight teams will be played who they can no longer meet in the final.

Next round eight teams left where four teams will be played who they can no longer meet in the final.

Next round four teams left where two teams will be played who they can no longer meet in final.

Therfore 32x31/2/2/2

The last part is comprised of 16 over 32, 8 over sixteen, 4 over eight, and two over four = 30 over 60 which is 1 over 2

I hope that makes sense.

the last part should be 8 over 16, then 4 over eight then 2 over four = 14 over 28 which is 1 over two,  please delete 16 over thirty two

England could meet Uruguay, Italy or Costs Rica in final, all are valid combinations, so 496

Phil, If England qualify they cant possibly play all the three possible combinations as two of the sides of Italy, Uruquay and Costa Rica will be eliminated at the group stage.
They cant all qualify can they.

but today, they could meet any of those teams in the final, so all are possible combinations

iprefertolay, of course teams go out, but any of the teams in this competition can play any of the others in the final.

We're talking possible combinations.

I have not followed the draw through but -
Can England and Uruguay qualify from their group?
Can England and Costa Rica get out of the group?
Can Italy and Uruguay get out of the group?

All of those teams can get out of the group, obviously in twos, like getting on Noah's Ark.
Can every one of the 32 teams get to the final?
Does that stop any other team getting to the final?

It is possible for any one team to play any other team in the final. Some combinations are unlikely, but not impossible.

Once the groups have been played it will be impossible for some teams to play other teams because each qualifying team will go into one or other half of the draw. At that stage it is impossible to play any team in your half of the draw in the final. But which half you go into is dependant on whether you finish 1st or 2nd in your group.

Up until then, it is possible for any team to play any other in the final.

Clydebank is spot on.  The number of subsets in a set is determined by the formula, N!/(N-n)! x n!

Where N is the value of the set & n is the value of the subset.

In this case N = 32 so N! = 32x31x30x29 etc.

n! = 2x1

The equation becomes 32!/(32-2)! x 2!

So 32!/30!x 2!

Which cancels out to 32x31/2 = 496

Lets take  Englands group as an example.
Lets assume England and Italy qualify.
It is then impossible for England to play Urugauy or Costa Rica in the final.

The 496 does not take this into consideration.
Also the fact that after the group stages teams playing each other can not possibly play each other in the final.

more whiskey required i feel

i know the answer 512

dead easy for example if brazil win group A then they can only play the runner up in group B = 1 times 4
then take croatia exactly the same 1 times 4
mexico 1 times 4
cameroon 1 times 4

that equals 16

there are 8 groups so thats 8 times 16 = 128

runner up in group is the same = 128

so total combinations is 256 not the 512 i stated thats 2 times 2 8 times = 512 which cant happen

the answer is 256

iprefertolay 25 May 14 00:00
Lets take  Englands group as an example.
Lets assume England and Italy qualify.
It is then impossible for England to play Urugauy or Costa Rica in the final.

The 496 does not take this into consideration.
Also the fact that after the group stages teams playing each other can not possibly play each other in the final.

This is the problem with your logic iprefertolay. Any of the teams can qualify so any of the combinations are possible

496 is the correct answer

Sorry

Mary,Mary quite contrary.
Lets have another go.
Its set in stone that two sides from each group dont qualify, agreed.
Now at this moment in time it is possible for England to play either Urugauy, Italy or Costa Rica in the final.
However,lets assume England qualify.
We now have a situation where TWO sides of either Italy, Uruguay or Costa Rica DONT QUALIFY,making it impossible for England to play the two sides that dont qualify.
Likewise its the same in every other group.
After the group stage, winners of groups will play runners up in other groups,thus making it impossible for teams playing each other meeting in the final.

Keeping it simple if England play Japan after the group stage they cant possibly play them in the final can they!

By the way Mary your post on World Cup reviews was terrific, im sorry to disagree with you, bless.

And to answer Phil ,its irrelevent whats possible today its what WILL occur as the rules state.
Bottom TWO sides DONT QUALIFY.

I must admit to being a little confused here but having thought about it for a while, I'm virtually certain that Mary is correct. Before a ball has been kicked, anything is possible. Of course, the real key to his debate is how you use the likely outcomes and group positions to consider whether there might be some value in a price you've seen for two teams to meet in the Final.

For example, the draw is worked out so that winners of Groups A, C, E and G, and winners of Groups B, D, F and H will play each other before the Final (if they get past the next stages). So if you think Brazil and Germany will win their groups, you should know that they cannot meet in the final. Brazil are 1/4 to win Group A and Germany are 4/7 to win Group G. The double, for both to win, is therefore around about a 20/21 chance (a fraction of odds-on). The price for these two to meet in the final is 18/1, so you need to work out whether that represents value, given that one of them would need to win and the other come second in their group, and then both would need to win all of their remaining matches...

Why stop after the group stage? Why not take your argument to its logical conclusion and say that there is only one possible combination, the two teams that get to the final?

Of course that is ridiculous. As is saying that some combinations are NOT POSSIBLE before a ball had been kicked.

EVERY team in EVERY group has the POSSIBILITY to get through to the final against ANY other team.

Of course, some teams getting through mean others can't but that doesn't mean that any combination is IMPOSSIBLE, which is what you are saying.

At the risk of this being a wind up, Marychain is obviously correct, if you walked into a bookmakers and asked for a price about any 2 named teams making the final, they would quote one as it's a possibility. How many possibilities are there.....(32*31)/2 = 496, they would quote on any as they are all possible on this day.

Yes, and for anyone that doesn't believe it, try to write out a single combination that isn't possible...

zzzzzzzzzzzzzzzzzzzz. it's 496. (still)
iprefertoignoreadvice

Now I'm pretty much convinced the thread must be a wind up

another large one please, hic

If anyone likes to try it out you can use this chart to prove that 1st and 2nd in a group can meet in the final.  I did it for Italy and England
I had to suspend reality with England beating Colombia, Spain, Argentina before the final with Italy.
http://www.telegraph.co.uk/sport/football/world-cup/10501412/World-Cup-2014-Wallchart-Predictor-Game.html

kincsem, thanks for wallhart info, on my predictions for matches I finished up with the following result.

1.Brazil
2.Argentina.
3.Spain.
4.Germany

Probably miles out!

As long as there are no upsets in the entire tournament, that's exactly how it will finish.

my answer of 256 is way out.but in fact if you can lay 496 -256 = 240 you will be very rich, but you cant do it as sums will be astronomical in real odds as the betfair max is 1000.lets say iran v costa rica final which can happen the true odds of that happening is in the millions to 1,so you cant lay it

but my 256 from 496 is of more value = 1.9375 chance of happening if you know how

so (in their infinite wisdom), to this point, betfair have chosen all but four combinations of 12 teams and then thrown in brazil/russia just for kicks.

I pointed out to Betfair the market was far from complete,they said they will add runners if need be at there discretion.
They added Brazil Russia to appease me I guess.

Feck sake guys.  I claim the Brazil/Russia addition.
I used it as an example on Betfair chat when I was trying to get "any other finalists" added.

iprefertolay
24 May 14 22:38
Joined:
16 Sep 02
| Topic/replies: 459 | Blogger: iprefertolay's blog
Phil, If England qualify they cant possibly play all the three possible combinations as two of the sides of Italy, Uruquay and Costa Rica will be eliminated at the group stage.
They cant all qualify can they.

i take it you work with your hands for a living?

marychain1
26 May 14 11:03
Joined:
05 Apr 05
| Topic/replies: 22,542 | Blogger: marychain1's blog
Why stop after the group stage? Why not take your argument to its logical conclusion and say that there is only one possible combination, the two teams that get to the final?

Of course that is ridiculous. As is saying that some combinations are NOT POSSIBLE before a ball had been kicked.

EVERY team in EVERY group has the POSSIBILITY to get through to the final against ANY other team.

Of course, some teams getting through mean others can't but that doesn't mean that any combination is IMPOSSIBLE, which is what you are saying.

as succint and accurate an explantion as you could want

they can't all qualify, can they?

ffs, hihm for this tit please

I am delighted with odds of 370 on Italy/Netherlands for €18.75 stake.

sad thread

appalling

There are 32 teams
Before a ball is kicked any 2 teams could theoretically reach the final
There are 496 different combinations
So the answer is   ...  496