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Judge Roughneck
24 Feb 16 20:11
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Date Joined: 14 Aug 07
| Topic/replies: 105 | Blogger: Judge Roughneck's blog
Assuming the odds for the draw in each game was 25/1 - What would be the odds on a team in the 6 nations drawing twice in one tournament?

I make it about 75/1 but am not sure.........

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Replies: 10
By:
pumphol.
When: 24 Feb 16 21:29
nearly 67/1
By:
Judge Roughneck
When: 25 Feb 16 08:54
Would aybody care to share how this is worked out? Thanks.
By:
pumphol.
When: 25 Feb 16 11:46
5 matches played by each team any two from 5 = 10

so at 25/1 that's 26x26 divided by 10 = 67.6 that's 66.6/1

That obviously is taking one specific team to draw twice, if the bet was any of the six teams drawing twice then that becomes more problematic.
By:
Judge Roughneck
When: 26 Feb 16 08:43
Thanks pump.
By:
dunlaying
When: 06 Mar 16 20:06
If you mean twice and no more than twice then your answer is , I think, as follows. Assuming independence.

10* (1/26)^2*(25/26)^3 which comes to around 76/1.

I will give it some more thought though.
By:
dunlaying
When: 06 Mar 16 20:08
For 2 or more there are a few more calculations and my trusty Casio is displaying "low battery" so no can do.
By:
dunlaying
When: 07 Mar 16 10:21
12 minutes to log in today!

Clearly there will be 0,1,2,3,4 or 5 draws in your 5 selected matches. By the laws of probability;
P(0)+P(1)+P(2)+P(3)+P(4)+P(5)=1
then
P(2)+P(3)+P(4)+P(5)= 1 - {P(0)+P(1)}
then using Pascal/Binomial
P(0)= 1*(25/26)^5
P(1)= 5*(1/26)(25/26)^4

Using your calculator you should be able to do that easily enough. One of mine is without battery and the other went under my heel half an hour ago.....it kept giving me the answer as a fraction.


One objection raised against the 76/1 is that a double gives a return of 675/1. But you will have staked ten units to get it and so your odds of reward are 288/5, considerably less than 76/1.

I hope I am correct but do not guarantee to be so.
By:
dunlaying
When: 07 Mar 16 11:16
Sorry 333/5 not 288/5 .
By:
pumphol.
When: 07 Mar 16 15:10
333/5 is 66.6/1 which is what I said earlier.
By:
Mark1977
When: 07 Mar 16 15:59
Using binomial probabilities (n=5, p=1/26), the probability of getting exactly 2 draws is 0.013150834 or almost exactly 75/1. The probability of 2 draws or more is 0.013687 or 72/1.
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