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swinburne

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I have a question which I'm hoping someone in here might be able to answer, it would help resolve a debate at work.

The question is in relation to a type of sports sweepstakes that we organise at work, and whether there is an equal probabliity of finishing first or last.....

It revolves around The Premiership (English soccer league)......Here's how it works........

There are 20 teams in the league.

Each team plays each other twice, so the competition runs for 38 weeks.

There are 20 players in the sweepstake.

Each player puts in a fixed sum at the start of the season.

Every two weeks there is a draw and each player is randomly allocated a team for that 2 weeks.

The player is credited with the goals which that team scores during that time.

At the end of the season whoever has accumulated the most goals takes half the pot, and whoever has accumulated the least gets the other half.

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As stated above, the question is, is there an equal probability of finishing first or last??? Common sense tells most people "yes" but I guess you guys in here know all about that.

What I can say is that experience down the years has seemed to indicate that it's actually harder to finish last!! We've been doing this now for about a dozen years and it always seems to follow the same pattern; 1 or 2 people are out in front at the top end from about 2/3 of the way through the season, but the battle for last is always a huge scramble between 6 or so people.

I hope there is enough information above to allow the question to be answered. I have a suspicion that the fact that soccer is such a low scoring game (it's not at all unusual for a team to score 0 in a game) means there's more likely to be more people down at the bottom than the top, but I haven't got the maths to prove it!!!

Thanks.

Gareth. Dublin - Ireland.