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Horse Racing

  • 22-08-2016 10:52am
    #1
    Smiles35
    Registered Users, Registered Users 2 Posts: 1,749 ✭✭✭


    If 75% of winners come from the first 5 in the betting forcast. And 28% of winners are the favorite. What percentage or winning chance have the 3rd and 4th in the betting forcast?


Comments

  • #2
    reunion
    Registered Users, Registered Users 2 Posts: 1,334 ✭✭✭reunion


    Smiles35 wrote: »
    If 75% of winners come from the first 5 in the betting forcast. And 28% of winners are the favorite. What percentage or winning chance have the 3rd and 4th in the betting forcast?

    A range between 16.6667% to 35.3333%

    To get an exact solution you would need to know the odds of the second and 5th horses (or a better explanation of the question).

    a = favourite = .28
    b = 2nd
    c = 3rd
    d = 4th
    e = 5th
    f = 6th and subsequent horses = 0.25 (75% of winners are the top 5)

    a + b + c + d + e + f = 1

    0.28 + b + c + d + e + 0.25 = 1

    c + d = 1 - 0.28 - 0.25 - b - e

    c + d = 0.53 - b - e

    The minimum solution:
    Since b can't be higher than 0.28 it's max value is 0.28
    c + d = 0.53 - 0.28 - e

    c + d + e = 0.25

    as this is the minimum solution we assume c = d = e (e's max value)
    0.25 / 3 * 2 = c + d = 16.6667%


    The max solution:
    f is an infinite number of horses, therefore e approaches 0.
    So c + d = 0.53 - b
    As this is the max solution b = c = d (i.e. b's lowest possible value)
    0.53 / 3 * 2 = c + d = 35.3333%


  • #3
    Smiles35
    Registered Users, Registered Users 2 Posts: 1,749 ✭✭✭Smiles35


    75% of all races are won by the first five in the betting forcast. Fav' win 34% of races. 2nd favs win 20% of races. 3rd favs win 14% of races. 4th favs win 5% of races. 5th favs win 3% of races.

    Going on the above figures what percentage chance of winning, backing the 2nd and 3rd favs together.


  • #4
    bit of a bogey
    Registered Users, Registered Users 2 Posts: 528 ✭✭✭bit of a bogey


    Smiles35 wrote: »
    If 75% of winners come from the first 5 in the betting forcast. And 28% of winners are the favorite. What percentage or winning chance have the 3rd and 4th in the betting forcast?

    b+c+d+e = 1-0.53 = 0.47

    bmax = 0.28
    bmin = (0.47/4) = 0.1175
    emin > 0

    Calculating [c+d]max;
    b+c+d+e = 0.47
    And if e=0, b+c+d = 0.47
    If b=c=d= (0.47/3) = 0.1566,
    so [c+d] = (0.1566*2) = 0.313

    Calculating [c+d]min;
    0.28+0.28+[c+d]+e+0.25=1
    [c+d]+e = 0.19
    If c=d=e= (0.19/3) = 0.063,
    so [c+d] = (0.063*2) = 0.126

    So the chances of the 2nd or 3rd horse in the betting winning are between 12.6% and 31.3%.

    But as reunion says, you really need more information and have too many unknowns.
    Smiles35 wrote: »
    75% of all races are won by the first five in the betting forcast. Fav' win 34% of races. 2nd favs win 20% of races. 3rd favs win 14% of races. 4th favs win 5% of races. 5th favs win 3% of races.

    Going on the above figures what percentage chance of winning, backing the 2nd and 3rd favs together.

    If you back the 2nd and 3rd fav, you’ve a 34% chance of collecting.


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