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Old 09-03-2017, 05:17 AM   #1
ThePressure
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greyhound / horse racing probability

Hi,

I was wondering if someone could help me, I'm trying to work out how I do the calculations and probabilities for the below scenarios, any help would be great.

In a 6 dog race, what is the probability any given dog would finish in the top 2?
6 dog race, what is the probability with 2 selections, one will finish in top 2, and both finish in top 2?

same with 3 and 4 selections, chances of picking the winner, and chances of picking 1st and 2nd?

thanks, can't find any information about this online, I thought it would be easy to find.
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Old 09-03-2017, 06:46 AM   #2
md46135
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Re: greyhound / horse racing probability

assuming each dog has 1/6 probability of winning and 1/6 for any other place:

Quote:
In a 6 dog race, what is the probability any given dog would finish in the top 2?
2/6 = 33.33%

Quote:
6 dog race, what is the probability with 2 selections, one will finish in top 2, and both finish in top 2?
only one in top 2: 2C1*4C1/6C2 = 8/15 = 53.33%
both in top 2: 2C2/6C2 = 1/15 = 6.67%
both outside top2 : 4C2/6C2 = 2/5 = 40%

Quote:
same with 3 and 4 selections, chances of picking the winner, and chances of picking 1st and 2nd?
if you choose 3 selections:
you have both dogs in top 2: 2C2*4C1/6C3 = 1/5 = 20%
only one dog in top 2: 2C1*4C2/6C3 = 3/5 = 60%
no dogs in top 2: 4C3/6C3 = 1/5 = 20%


with 4 selections:
top 2 covered: 2C2*4C2/6C4 = 2/5 = 40%
only 1 dog in top 2: 2C1*4C3/6C4 = 8/15 = 53.33%
no dogs in top 2: 4C4/6C4 = 1/15 = 6.67%

Last edited by md46135; 09-03-2017 at 07:08 AM.
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Old 09-03-2017, 11:19 AM   #3
statmanhal
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Re: greyhound / horse racing probability

For those who rather see direct probability calculations: Assume pick is A and B

One in top 2: P(A in top 2)*P(B in bottom 4 given A in top 2) * 2 = 2/6*4/5*2=16/30 = 0.5333
(2 multiplier for the case B in top 2)

Both in top 2: P(A in top 2)*P(B in top 2 given A in top 2) = 2/6*1/5 = 2/30 = 0.0667

Neither in top 2: P(A in bottom 4)*P(B in bottom 4 given A in bottom 4) = 4/6*3/5 = 12/30 =0.400
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Old 09-03-2017, 11:50 AM   #4
ThePressure
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Re: greyhound / horse racing probability

both excellent responses thanks! what does all the 2C2 stuff mean?

also being greedy, what are the odds of picking a winner if you back 4 selections, 4/6 ? 66%? but thats more likely than having the top 2 covered from 4 selections? that doesn't make sense?
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Old 09-03-2017, 12:33 PM   #5
Didace
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Re: greyhound / horse racing probability

Quote:
Originally Posted by md46135 View Post
assuming each dog has 1/6 probability of winning and 1/6 for any other place
Don't overlook this. It is not true in the real world.
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Old 09-03-2017, 02:27 PM   #6
statmanhal
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Re: greyhound / horse racing probability

Quote:
Originally Posted by ThePressure View Post
both excellent responses thanks! what does all the 2C2 stuff mean?

also being greedy, what are the odds of picking a winner if you back 4 selections, 4/6 ? 66%? but thats more likely than having the top 2 covered from 4 selections? that doesn't make sense?
Why?

Requiring 2 of 4 to be in certain positions is more restrictive (=generally less likely) than requiring only 1 of 4.

2C2 is math shorthand for the number of combinations (ways) of selecting 2 things out of 2 things. In general

nCr = C(n,r) = n Choose r (Google nomenclature) = n! /(r!*(n-r)!)

where x! = x*(x-1)*(x-2)* … *3*2*1

C(5,2) =5!/(3!*2!)= 5*4/(2*1)= 10.

Search for math combinations on the internet for more detail.
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Old 09-06-2017, 01:11 AM   #7
akkopower1
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Re: greyhound / horse racing probability

Quote:
Originally Posted by ThePressure View Post
both excellent responses thanks! what does all the 2C2 stuff mean?

also being greedy, what are the odds of picking a winner if you back 4 selections, 4/6 ? 66%? but thats more likely than having the top 2 covered from 4 selections? that doesn't make sense?
2C2 measn how many ways can you choose two objects from two objects, here the order is nit relevant.

If there are two drinks in the fridge there is only one way you can choose two drinks. Take them both!!.

3C2, means if there are 3 drinks in the fridge (drinks A,B and C), how many ways can you choose 2.
You can take; AB, AC, BC, that is three different ways

8C3 means if there are 8 drinks how many ways can i choose 3, it would be 56 different combinations
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Old 09-07-2017, 09:13 AM   #8
davmcg
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Re: greyhound / horse racing probability

Quote:
Originally Posted by Didace View Post
Don't overlook this. It is not true in the real world.
This.

Because the odds are all different, you would be better designing a spreadsheet (that gives the odds of all 30 1st/2nd permutations - dog A first, dog B first of the remaining 5 runners, dog A first, dog C first of the remaining 5 etc) and inputting actual true odds.

The information is also basically useless for dogs as in many cases the probability of two dogs running well can be related ie they can interfere with each other (or not). Also the odds of the bookmakers on dog races are very poor value (although pooled bets can always offer opportunities).
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