Results 1 to 9 of 9

Math Help - 20.000 Bingo Cards... Just 1 winner (cheating??)

  1. #1
    Newbie
    Joined
    Mar 2011
    Posts
    4

    Question Probability on 20.000 Bingo Cards... Just 1 winner (cheating??)

    Hi..Im new here..and yes Im looking for someone to help me with this problem...

    There's a anual bingo game in my city, each player has a card with 15 numbers on it. The total of balls is 90.

    Every year they sell about more of 20.000 cards, and always they get only 1 winner...
    I dont know how is this possible, when they assure that the extraction of the numbers is fully tranparent and without cheating.
    They say that have a "secret formula" to make the cards for only 1 winner per time...

    can someone tell me something about that "secret formula" to make cards and not to cheat in the extraction of the numbers??...or is it just a trap well covered...

    thats all..
    thanks!
    Last edited by MarkPimi; March 25th 2011 at 09:48 AM.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Master Of Puppets
    pickslides's Avatar
    Joined
    Sep 2008
    From
    Melbourne
    Posts
    5,233
    Thanks
    29
    Is it possible that there is only one winner as all 20,000 cards are different? i.e. no 2 cards are the same?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Mar 2011
    Posts
    4
    Hi pickslides..thanks for your reply...
    with only 90 numbers there can be only 6 cards uniques that assure us 1 only winner...so how can they do this for thousands of cards??..
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Newbie
    Joined
    Jan 2015
    From
    Kent, UK
    Posts
    4

    Re: 20.000 Bingo Cards... Just 1 winner (cheating??)

    There are many many more than 20,000 unique combinations of 15 numbers out of a possible 90
    Follow Math Help Forum on Facebook and Google+

  5. #5
    MHF Contributor

    Joined
    Aug 2006
    Posts
    19,422
    Thanks
    1945
    Awards
    1

    Re: 20.000 Bingo Cards... Just 1 winner (cheating??)

    Quote Originally Posted by troyaaron View Post
    There are many many more than 20,000 unique combinations of 15 numbers out of a possible 90
    How many?? And how do you know that?
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Newbie
    Joined
    Jan 2015
    From
    Kent, UK
    Posts
    4

    Re: 20.000 Bingo Cards... Just 1 winner (cheating??)

    Take the Lotto odds to start (UK Lottery)
    You pick 6 number from a possible 49 - there are around 14 million combinations you can choose

    The above post suggests 15 random numbers out of a possible 90 (per ticket) - a far greater amount of combinations

    However, the number of unique tickets does not dictate a single winner - there could be a time when with just 20,000 tickets are in play that the win is shared. You would need every single combination of numbers in play in order to definitely produce only one winner and that would happen by just releasing 15 numbers.

    However(2) the fact they say they use a secret formula to ensure only 1 winner sounds iffy. Do they only 'release' 15 number? If so I guess they give out unique tickets and that way secure one winner.
    Follow Math Help Forum on Facebook and Google+

  7. #7
    MHF Contributor
    Joined
    Nov 2010
    Posts
    1,962
    Thanks
    798

    Re: 20.000 Bingo Cards... Just 1 winner (cheating??)

    Consider one card with the first row of numbers: 1, 21, 41, 61, 81.
    It is possible to create a second card with those same numbers, but put the 1 down to the second row and keep the 21, 41, 61, 81 the same. Now, that combination of numbers cannot win on both cards.
    The mathematics behind this is rather complicated to explain, but with computer generation, it is relatively simple to create an algorithm for creating cards that will guarantee unique winners by placing the numbers in locations so that no two people can win at the same time.

    In other words, each card has 12 winning scenarios (the five rows, the five columns, and the two diagonals). A winning combination consists of one of the following: five of the 18 numbers from one of the letters (B,I,N,G,O), one of the 18 numbers from each of the five letters, four of the 18 numbers from one of the letters plus the free space, or one of the 18 numbers from each of the letters B,I,G,O with the free space taking the middle number. There are WAYYY more than 20,000\times 12 = 240,000 different such winning combinations allowing the developers to spread them out among the different cards.
    Last edited by SlipEternal; January 9th 2015 at 04:55 AM.
    Follow Math Help Forum on Facebook and Google+

  8. #8
    Newbie
    Joined
    Jan 2015
    From
    Kent, UK
    Posts
    4

    Re: 20.000 Bingo Cards... Just 1 winner (cheating??)

    I don't believe that is the type of bingo ticket they are talking about as that is not a 15 number game
    Follow Math Help Forum on Facebook and Google+

  9. #9
    Newbie
    Joined
    Mar 2011
    Posts
    4

    Re: 20.000 Bingo Cards... Just 1 winner (cheating??)

    Hi everyone...
    thanks for the reply

    the way to win the big prize is completing the full board with all numbers.


    Imagine this scenario where the cards only have 6 numbers:

    Card 1: 1 22 29 35 44 88
    Card 2: 1 25 28 31 39 65
    Card 3: 1 40 49 54 59 81

    all share the number 1, what happens if after completing all other numbers, the next number to come up is number 1?
    what happens is that all 3 wins. but that never happen in the show...they always get 1 winner.
    cause they release sometime 60 numbers before getting a winner.

    this scenario makes me think that not all balls are on the wheel
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Bingo Probabilities
    Posted in the Statistics Forum
    Replies: 3
    Last Post: November 16th 2011, 06:14 PM
  2. probability of 5 correct cards out of 6 cards
    Posted in the Statistics Forum
    Replies: 8
    Last Post: May 20th 2011, 06:44 AM
  3. Replies: 2
    Last Post: October 2nd 2010, 03:09 PM
  4. Bingo probability question
    Posted in the Statistics Forum
    Replies: 11
    Last Post: June 5th 2010, 09:39 AM
  5. Help with finding an Average Rating Winner
    Posted in the Math Software Forum
    Replies: 1
    Last Post: October 7th 2008, 01:58 PM

Search Tags


/mathhelpforum @mathhelpforum