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Math Help - An apology...

  1. #1
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    An apology...

    So I'll start by saying sorry, because I'm hoping for some help but have nothing really to offer in return. I guess many people register on this forum with the same intent as I, I have no way of knowing whether there is a group consensus as to whether this is:

    a) Extremely annoying behaviour to be discouraged at all costs
    b) Just fine, we're all really helpful and just LOVE helping complete strangers with their problems
    c) All part of life's rich tapestry - what goes around, comes around

    So - my problem. I'm looking for a way of assigning grid positions in Kart racing to be as fair as possible. 35 Karts, 12 events, assume a purely linear grid with just 35 slots. I've tried incrementing each grid position by 3 for each of the 12 events and the results aren't bad, average grid position is 18, worst average was for Kart 35 which had average grid position of 20.6 (approx)

    Is there a better way? Can the average be somehow "smoothed"?

    Thanks in anticipation
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  2. #2
    MHF Contributor ebaines's Avatar
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    Re: An apology...

    By incrementing 3 for each race the karts are always in the same relative position compared to the car in front and behind - for example car 9 is always placed behind car 8 for all 12 races, which isn't fair. One thing you can do is after race #6 flip the relative positions of each group of 3 cars. For example consider the cars in slots 4, 5 and 6 for race 6: under your scheme for race 7 they would be in slots 1, 2, and 3, but instead put them in 3, 2, 1 reaspectively. Then continue with your regular scheme. This evens it out quite a bit, though it's still not perfect because you have 35 cars, and there is no way to make it totally fair over 12 races. However - if instead there were 36 cars it would be possible to make it perfectly fair.

    As for how the site works - no apology needed, as your option (b) is the way we work around here. This is a help forum, and the folks who answer questions here do it because they like to do it!
    Thanks from mash and Touchwood
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