Predicting the Premier League Table

mattmath123

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Aug 6, 2015
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Hi everyone,

I made an account here just to ask this question...

Okay so, this morning my friend texted me telling me about a bet he had taken. William Hill are offering 25,000,000/1 for anyone who can predict the exact order of the Barclays Premier League table this year. He asked me if this was a good bet...

So I told him that because there are 20 teams, the are 20! (about 2.4 x 10^18) different possibilities so it's a pretty bad bet! But obviously a lot of these possibilities are pretty unrealistic... Chelsea are not gonna get relegated for example. So I tried to come up with a more realistic answer.

First I divided the table into 4 groups of 5, using the assumption that the top 5 will finish in some random order, but they will all finish in that same top group (obviously this isn't true, but I was simplifying as much as possible). I did the same for the remaining 3 groups. So then I was left with 5! possibilities for the top group, 5! for the second, 5! for the third, 5! for the fourth. Therefore using this system, there are 5! x 5! x 5! x 5! which is about 2 x 10^8 possibilities. Is the maths here correct? I know I've over simplified, but in principle is the reasoning sound?

And finally, I wanted to work out how sure you would have to be with each guess to make it a "fair" bet. So for example, if I was 50% sure Chelsea would finish top, 50% Arsenal would finish second and so on, would this be fair? Well for that ended up with the equation:

1/X^20 = 25000000

This gives X as around 42%. Is my reasoning sound here? I'm pretty sure it's not, but I'm not sure why...

Anyways, hope someone here is as sad as me and has some time to think about this
wink.png


Any thoughts/advice would be great!

Thanks,
Matt
 
I was surprised to see these odds offered by William Hill, it would be a huge loss if they had to pay out, especially if to many winners. However it is not accurate to talk of odds 25,000,000 to 1.
Looking at the terms, the fixed payout of £ 50,000,000 (for £2.00 stakes) will be shared by any multiple winners. Also William Hills has reduced the opportunity for a punter to cover all permutations by limiting each to 250 entries and accepting only 1,000,000 entries in total. So they are expecting to receive £ 2,000,000, probably paying out nothing and knowing that the limit to their losses if any. Maybe still a good bet, but not really as good as 25,000,000 to 1.
 
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