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Trail: Putting It All Together
Lesson: BINGO!

## Traditional BINGO

> Traditional BINGO is played in person in a large hall. Players meet at the hall, pay a fee to get in, then the games begin. A night of BINGO consists of many BINGO games played continuously, one after another.

> A single BINGO game proceeds like this: Each player has a number of BINGO cards (players can usually play any number of cards). Each BINGO card has 5 rows and 5 columns thus providing 25 spaces.

> The columns are labeled from left to right with the letters: 'B', 'I', 'N', 'G', 'O'. With one exception (the center space is "free") the spaces in the card are assigned values as follows:

> - Each space in the 'B' column contains a number from 1 - 15.
> - Each space in the 'I' column contains a number from 16 - 30.
> - Each space in the 'N' column contains a number from 31 - 45.
> - Each space in the 'G' column contains a number from 46 - 60.
> - Each space in the 'O' column contains a number from 61 - 75.
> Furthermore, a number can appear only once on a single card.

> Here's a sample BINGO card:

> B | I | N | G | O
> 10 | 17 | 39 | 49 | 64
> 12 | 21 | 36 | 55 | 62
> 14 | 25 | FREE SPACE | 52 | 70
> 7 | 19 | 32 | 56 | 68
> 5 | 24 | 34 | 54 | 71

> The number of unique BINGO cards is very large and can be calculated with this equation:

> >     // the B, I, G, and O columns * the N column
> >     (15 * 14 * 13 * 12 * 11) ^ 4 * (15 * 14 * 13 * 12)

> While perhaps interesting to a statistician, the number of possible BINGO cards has nothing to do with player's chances of winning.

> You will note that there are 75 possible BINGO numbers:

> >     B1, B2, B3, ... B15, I16, I17, I18, ... I30, N31, N32, ... O74, O75.

> Each of these numbers is represented by a ball in a large rotating bin. Each ball is painted with its unique BINGO number. An announcer spins the bin, reaches in a selects a ball, and a announces it to the room. The players check all of their cards to see if that number appears on their card. If it is, they mark it.

> When a player has a BINGO (5 in a row, column, or diagonal), he or she calls out BINGO. The game pauses while the card is verified. If indeed a winner, the game stops and a new game begins. If the card wasn't a winner, the game proceeds where it left off. Each BINGO game proceeds until someone wins (there's always a winner).

### Chances of Winning

> Every BINGO game has a winning card, so a player's chances of winning depend on the number of cards in the game and how many cards s/he is playing. For example, if a player has 12 cards in a game with 1200 cards, the chances of winning for that player is 1 in 100.

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