Probability Question

Everybody has 1 in 32 chance as the winner is not known before the event. If, however, you feel Spain were going to win the first to draw has a 1 in 32 chance of drawing Spain. If the first 31 don't draw Spain then the 32nd person to draw has a 100% chance of drawing Spain.

Exactly what I thought.  He thinks that just because he has a maths degree, he knows more than I do.  His theory is that numbers 2-32 may not have the opportunity to draw the winning team as it may have already been drawn reduces their chances...

Tricky question. 32 teams in the hat, realistically you had the favourites being Holland, Spain, Brazil, Argentina, Germany, Italy, France and to a certain extent Italy and England. That leaves 23 teams left in the hat that would have needed a miracle to win it.

It works out at around a 3.25 to 1 shot that the team you pick out (if you pick first) is going to be one of the favourites. Now, if you are fifth in line to pick and the first four people have all picked an outsider, your odds of getting a potential winner have shrunk.

It all depends on when the good teams get picked really, so there really isn't a right or wrong answer.

Myself? I'd probably want to be sventh or eighth to pick a team. That would mean that I have a good chance of getting a couple of outsiders out of the way, and unless a sheer amount of bad luck on my part, there should still be a few of the favourites.

You clearly have a 1 in 32 chance of picking the winner, no matter when you pick.

If you didnt open your slips until after the World Cup had taken place you wouldnt know who your team was. When you open your slips, whoever has Spain wins.

Clearly the chance of having picked Spain is totally unaffected by whether you go first, second or last, because the chance that Spain will come out last is exactly the same as them coming out 1st or (for example) 17th.

I completely agree, Mary.  Thank you!

marychain1 Joined: 05 Apr 05
Replies: 10423 14 Jul 10 19:00   


You clearly have a 1 in 32 chance of picking the winner, no matter when you pick.

Cant be true, if Spain had been picked first then anyone picking after had absolutely no chance of picking the winner did they

Whenever you pick, be it first or last, you have a 1 in 32 chance of picking Spain.

If you pick last, you would think you have much less chance of getting Spain because 31 times (on average) of 32, Spain will already have gone so you have 0% of picking Spain.

but the one other time, you will have a 100% chance of picking Spain.

You will find that the average still works out at the same chance as everyone else.

Where did he get his maths degree?

If i picked spain 1st, no one else had a chance of winning, so they never had a 1 in 32 chance, they had no chance of picking it because it's already gone

But that would only happen 1 in 32 times because you only have a 1 in 32 chance.

the other 31 times Spain would still be in there, and everyone else's chances of getting Spain have increased slightly.

fiftyfourminutes - that is true but you still have a 1 in 32 chance of picking it coming out first.  Are you saying that before the draw begins, that the odds are different for those further down the order?

Its OK prickard.  He only got a 2:2 :)

maybe next time you should do a sweepstake to decide the order that people draw out for the main sweepstake

There is nothing complicated about this question.  Its a 1 in 32 chance for everyone.  The probability of a team with a better chance of winning being picked out first is the same as a weaker team being picked out first, if you were to work out every combination and the probabilities of them being picked out in every combination, you would still end up with a 1/32 chance for each turn

before the world cup begins and the draw is made theoretically you have a 31/1 chance of winning, but afterwards if you find out that spain were drawn out first then you can then say that anyone picking after No1 had no chance

Clearly no advantage in picking in any particular position.

as long as the draw is random then odds are the same

It is extremely simple. Every picking position has an equal chance of picking Spain.

The fact that 1 in 32 times the person picking first will get Spain does not alter the fact that everyone has an equal chance of picking Spain or any time.

fiftyfourminutes, we are talking about whether any position has an advantage in a sweepstake.  Your point is irrelevant, surely you can see that?  Its like saying Brazil should have been 1000/1 because after the world cup we know that Spain won

marychain1 sums it up bang on. the odds are the same for everyone until the first pick, then spains odds will change one way or the other.

At any point, the probability of a participant winning is:

  If they not chosen:
    The sum of the probabilities of the unchosen countries divided by the number of participants yet to choose.

  If they have chosen:
    The probability of their team winning

So before any choices are made, for each participant it is 1/32.
After person 1 has chosen, the odds of winning will have shifted depending on the odds of the chosen team.  If a 7/1 shot has been pulled then the odds of any one person picking the eventual winner are 1/35.4

But if the first picker chooses a 100/1 shot then the odds will have narrowed to 1/31.3  This is because someone has taken out one of the duff teams, increasing the potential availability of the better teams that should - but might not - win it.

If everyone has chosen bar one person, then the odds they will pick the winner will be equal to the odds of the sole remaining team winning it.  Clearly a team like Spain, Brazil, England(!), Italy, etc. is still in the hat then your chances of picking the winner will be better than 1/32.

In conclusion, order of selection doesn't matter but the teams that are pulled before your pick does.

If you don't understand all of what I've written then betting is not for you.

I completely agree with you ascii but this was my friend's response:

I had to have it explained to me by three of my friends who argued long into the night about it but there is a small statistical different on your odds of pulling spain depending on where you drew. It was a very complicated explanation but in the end I had to concede they were right for two reasons. 1. They drew a graph and 2. All three of them have phd's in statistics with two of theres being in probability theory and the other in game theory.

It was mainly the graph that swung it for me

I have yet to see the graph lol!

The bit of paper doesn't know it has 'winner' written on it, it's clearly 1 in 32.
Tell him to hand his degree back to the polyversity he got it from

best to go to sweepstake halfway thru, ask if spain, italy etc has been taken. If not then enter the sweep.

If you pick somethink like germany then arb' it on betfair.

dirty arber

Its OK prickard.  He only got a 2:2 :)

Ah, young Desmond. No doubt he works in the City now.