December 7th, 2016 at 7:04:32 PM
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I work in Bingo Hall and I have a debate going on with the techs setting up our Bingo Computers. We have Level 1 and 2 computers that pay out different prizes. When setting up the computers, initially the vendor assigned the following series of cards to each type of computer. Card series 1-1,000,000 was assigned to Level 1 computers. Card series 3,333,334-5,000,000 were assigned to Level 2 computers.

Since more cards were assigned to Level 2 I believe the Level 2 computers are weighted heavier and will therefore win more often. The vendor tech is saying that isn't the case and number of cards assigned has no bearing on the frequency of wins on a computer.

Can someone confirm if my understanding is true? If so, how much more often would we expect those computers to win? What formula should be used to determine how this affects the odds of the computers? Assume 66 bingo cards per game and 50 Level 1 and 50 Level 2 computers sold.

Please let me know if more information is needed.

Since more cards were assigned to Level 2 I believe the Level 2 computers are weighted heavier and will therefore win more often. The vendor tech is saying that isn't the case and number of cards assigned has no bearing on the frequency of wins on a computer.

Can someone confirm if my understanding is true? If so, how much more often would we expect those computers to win? What formula should be used to determine how this affects the odds of the computers? Assume 66 bingo cards per game and 50 Level 1 and 50 Level 2 computers sold.

Please let me know if more information is needed.

December 8th, 2016 at 6:11:12 AM
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I assume that, for each game, each Level 1 computer uses one of its 1,000,000 cards, determined randomly, and each Level 2 computer uses one of its 1,666,667 cards.

However, that shouldn't matter; each card has an equal chance of winning, even if there was a Level 3 computer that used the same card every time (e.g. B 1-5, I 16-20, N 31-34, G 46-50, O 61-65, with all columns in order from top to bottom).

This is easy enough to prove for two cards where all of the numbers are different; for every drawing of the 75 numbers where Card A wins, swap each number on Card A with the number in the same position on Card B, and you have a "partner" drawing where Card B wins. It's when you have one or more numbers on both cards but in different positions that I'm still working out.

Then again, if each machine creates a selects card from its group without comparing them to the other cards in the game (to prevent duplicates), there is a slim advantage to playing a Level 2 machine in that you are less likely to have a duplicate card (and thus share the prize if you both win). If there are 50 Level 1 computers being used in a game, the probability that two or more have matching cards is about 1 / 817.

However, that shouldn't matter; each card has an equal chance of winning, even if there was a Level 3 computer that used the same card every time (e.g. B 1-5, I 16-20, N 31-34, G 46-50, O 61-65, with all columns in order from top to bottom).

This is easy enough to prove for two cards where all of the numbers are different; for every drawing of the 75 numbers where Card A wins, swap each number on Card A with the number in the same position on Card B, and you have a "partner" drawing where Card B wins. It's when you have one or more numbers on both cards but in different positions that I'm still working out.

Then again, if each machine creates a selects card from its group without comparing them to the other cards in the game (to prevent duplicates), there is a slim advantage to playing a Level 2 machine in that you are less likely to have a duplicate card (and thus share the prize if you both win). If there are 50 Level 1 computers being used in a game, the probability that two or more have matching cards is about 1 / 817.

December 8th, 2016 at 8:50:28 AM
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A few more key pieces of information:

1. Each computer (Level 1 & Level 2) have 66 cards loaded. So if we sell 100 of each type, there are 6600 Level 1 & 6600 Level 2 in play at the same time. If we sell 50 of each then we have 3300 Level 1 cards and 3300 Level 2 cards in play at the same time.

2. There is no cross checking of cards so duplicates may occur, There may be exact duplicates and there may also be duplicates in number only. Meaning, 2 cards have the same 25 numbers just in different positions. For example, there could be 5 cards all with B1, B2, B3, B4 and B5 on them but B1 is in the 1st, 2nd, 3rd, 4th and 5th position on each card. That would make the cards "different" in the eyes of the system.

3. We did an actual test playing 50 games with Double Bingo both ways and had a 7% increase in Level 2 winners and 7% decrease in Level 1 winners when we assigned the additional cards to Level 2. So I am fairly confident my theory is correct. However, I am looking for some more exact math to prove my theory.

My original theory was that we would see a 10% decrease in Level 2 winners when the cards assigned were adjusted since we change the % assigned to Level 2 by 10%. Our simulation run above of a 7% change seems to support my theory with some deviation.

Original Setup

60% Level 2

40% Level 1

Adjusted Setup

50% Level 2

50% Level 1

1. Each computer (Level 1 & Level 2) have 66 cards loaded. So if we sell 100 of each type, there are 6600 Level 1 & 6600 Level 2 in play at the same time. If we sell 50 of each then we have 3300 Level 1 cards and 3300 Level 2 cards in play at the same time.

2. There is no cross checking of cards so duplicates may occur, There may be exact duplicates and there may also be duplicates in number only. Meaning, 2 cards have the same 25 numbers just in different positions. For example, there could be 5 cards all with B1, B2, B3, B4 and B5 on them but B1 is in the 1st, 2nd, 3rd, 4th and 5th position on each card. That would make the cards "different" in the eyes of the system.

3. We did an actual test playing 50 games with Double Bingo both ways and had a 7% increase in Level 2 winners and 7% decrease in Level 1 winners when we assigned the additional cards to Level 2. So I am fairly confident my theory is correct. However, I am looking for some more exact math to prove my theory.

My original theory was that we would see a 10% decrease in Level 2 winners when the cards assigned were adjusted since we change the % assigned to Level 2 by 10%. Our simulation run above of a 7% change seems to support my theory with some deviation.

Original Setup

60% Level 2

40% Level 1

Adjusted Setup

50% Level 2

50% Level 1

December 11th, 2016 at 6:17:16 PM
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I'm still not sure I understand the question, but as long as the ball draw is totally random, meaning each ball has the same chance and the draw is independent of the cards, then each card should have the same chance of winning any given pattern.

I'm aware of games where the ball draw is electronic that are not random.

As per your test, I would need to see information on the sample size to rule out that it isn't just expected variance likely behind the change.

I'm aware of games where the ball draw is electronic that are not random.

As per your test, I would need to see information on the sample size to rule out that it isn't just expected variance likely behind the change.

"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)

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