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

1. ## 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!

2. Is it possible that there is only one winner as all 20,000 cards are different? i.e. no 2 cards are the same?

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??..

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

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

Originally Posted by troyaaron
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?

6. ## 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.

7. ## 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.

8. ## 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

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

Hi everyone...

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