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Math Help - Strategy: Picking the right numbers from the right groups

  1. #1
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    Strategy: Picking the right numbers from the right groups

    Forgive me if I've chosen the wrong forum, but I have absolutely no background in mathematics to even realize where my question fits.
    I'll bravely ask anyway.

    You have 10 groups of numbers:
    Group 01: { 91, 72, 59, 57, 54, 48, 35, 32, 22, 21 }
    Group 02: { 91, 76, 73, 51, 40, 39, 35, 32, 30, 23 }
    Group 03: { 113, 103, 49, 46, 39, 36, 35, 33, 31, 28 }
    Group 04: { 97, 73, 71, 59, 59, 59, 57, 51, 40, 40 }
    Group 05: { 59, 59, 42, 39, 36, 34, 22, 21, 21, 20 }
    Group 06: { 73, 42, 41, 36, 36, 31, 30, 28, 27, 21 }
    Group 07: { 86, 71, 65, 59, 57, 57, 52, 45, 42, 36 }
    Group 08: { 78, 63, 48, 46, 46, 37, 35, 29, 26, 25 }
    Group 09: { 82, 82, 59, 53, 51, 43, 37, 32, 28, 27 }
    Group 10: { 74, 73, 72, 40, 32, 32, 28, 23, 22, 21 }

    The task is that by random order, 10 people will begin picking a number, until all the numbers have been pick. Each person can only pick one number from each group. After all the numbers have been selected, the person with the highest sum of his or her numbers is the winner. Without thinging, most people will start picking the highest number available from a group that they have not yet selected from. My question is, is there some kind of formula I can come up with to get an advantage? And how does this formula change as numbers are selected ? How much more valuable is that 73 in Group 6 compared to that 73 in Group 4?

    Does anyone have any ideas that may help give me an advantage in a game such as this?

    Thanks in advance.
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  2. #2
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    Quote Originally Posted by balste View Post
    Forgive me if I've chosen the wrong forum, but I have absolutely no background in mathematics to even realize where my question fits.
    I'll bravely ask anyway.

    You have 10 groups of numbers:
    Group 01: { 91, 72, 59, 57, 54, 48, 35, 32, 22, 21 }
    Group 02: { 91, 76, 73, 51, 40, 39, 35, 32, 30, 23 }
    Group 03: { 113, 103, 49, 46, 39, 36, 35, 33, 31, 28 }
    Group 04: { 97, 73, 71, 59, 59, 59, 57, 51, 40, 40 }
    Group 05: { 59, 59, 42, 39, 36, 34, 22, 21, 21, 20 }
    Group 06: { 73, 42, 41, 36, 36, 31, 30, 28, 27, 21 }
    Group 07: { 86, 71, 65, 59, 57, 57, 52, 45, 42, 36 }
    Group 08: { 78, 63, 48, 46, 46, 37, 35, 29, 26, 25 }
    Group 09: { 82, 82, 59, 53, 51, 43, 37, 32, 28, 27 }
    Group 10: { 74, 73, 72, 40, 32, 32, 28, 23, 22, 21 }

    The task is that by random order, 10 people will begin picking a number, until all the numbers have been pick. Each person can only pick one number from each group. After all the numbers have been selected, the person with the highest sum of his or her numbers is the winner. Without thinging, most people will start picking the highest number available from a group that they have not yet selected from. My question is, is there some kind of formula I can come up with to get an advantage? And how does this formula change as numbers are selected ? How much more valuable is that 73 in Group 6 compared to that 73 in Group 4?

    Does anyone have any ideas that may help give me an advantage in a game such as this?

    Thanks in advance.

    The person who goes first and picks the highest number ( or 1 of the highest pair of numbers) from each group will have have the highest total at the end.

    The 73 in Group 6 is equal in value to the 73 in Group 4?

    Is there some additional clarification available?.
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  3. #3
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    Quote Originally Posted by balste View Post
    The task is that by random order, 10 people will begin picking a number, until all the numbers have been pick.
    WHAT is "at random"?
    10 names put in a hat, then names drawn?
    Or is it the group numbers that are assigned randomly,
    like 8-3-1-6-10-2-4-9-5-7?
    Do the 10 pickers keep original pick order, or is it changed after each
    picking session?
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  4. #4
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    Another question.
    Is everyone aware of everybody else's running score?
    Like, can strategies be involved, like everybody ganging
    in on the leader by going to a row the leader hasn't been
    in yet, and leaving him the smallest number?
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  5. #5
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    To clarify, the 10 people are numbered randomly from 1 to 10.
    Person #1 then picks a number from any grouping.
    Person #2 then picks as number from any grouping (but the number picked by Person #1 is now gone).
    then Person #3 and so on through #10...

    That completes the first round. In the second round, they pick in reverse order from Person #10 to #1. In the third #1 to #10 again, and it repeats through 10 rounds and each number is picked.

    A simpler example would be:
    Group A: {90, 80, 70}
    Group B: {80, 80, 50}
    Group C: {70, 40, 30}

    In this case, it would seem to me that the 70 in group C is more valuable than the 90 in group A, and if I had the first overall pick, I may go for the 70. What I would like to know is if there is a formula I can create that would indicate which exact value is the most valuable, and have it change as numbers are picked.

    Each player would be able to see who picked which number, but I would think ganging up on one person, and trying to block them from selecting from columns they have not would be to the detriment of the group. There can only be one winner, so each person would probably be picking the number that helps them the most.
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