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been mentioned, but its limited card set causes problems for the emerging online Bingo culture. Larger patterns, e.g. a diamond pattern consisting of cell positions B3, I2 and I4, N1 and N5, G2 and G4, and O3, are often used by online Bingo games to permit large number of players while ensuring only one player can win. (A unique winner is further desirable for online play where network delays and other communication interference can unfairly affect multiple winning cards. The winner would be determined by the first person to click the "Bingo!" button (emulating the shout of "Bingo!" during a live game).) In this case the number of unique winning cards is calculated as (15*(15*14)/2) = 260,465,625 (260 million). The division by two for each of the "I", "N", and "G" columns is necessary to once again remove redundant number combinations, such as and in the N column.
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septillion cards need to be in play. Any given set of numbers in a column (e.g., 15, 3, 14, 5, 12 in the "B" column) can be represented in any of 5! (for the "B", "I", "G", and "O" columns. 4! for the "N" column) or 120 different ways. These combinations are all statistically redundant. Therefore, the total number of cards can be reduced by a factor of (5! * 4!) = 4,976,640,000 for a total unique winning card set of 111,007,923,832,370,565 or 111 quadrillion. (Still impossibly enormous, but our eager printer described above would only need 1.29 days to complete the task.)
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the third, fourth, and fifth rows. Thus, the number of unique "B" (and "I", "G", and "O", respectively) columns is (15*14*13*12*11) = 360,360. The combinations of the "N" column differ due to the use of the free space. Therefore, it has only (15*14*13*12) = 32,760 unique combinations. The product of the five rows (360,360 * 32,760) describes the total number of unique playing cards. That number is 552,446,474,061,128,648,601,600,000 simplified as 5.52x10 or 552
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The challenge of a multiple-pattern game is selecting a winner wherein a tie is possible. The solution is to name the player who shouts "Bingo!" first, is the winner. However, it is more practical and manageable to use card sets that avoid multiple-pattern games. The single-pattern #3 row has already
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to print just one set. However, while the number combination of each card is unique, the number of winning cards is not. If a winning game using e.g. row #3 requires the number set B10, I16, G59, and O69, there are 333,105,095,983,435,776 (333 quadrillion) winning cards. Therefore, calculation of the
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calculations. In its simplest sense, the number of unique "B" columns assumes that all 15 numbers are available for the first row. That only 14 of the numbers are available for the second row (one having been consumed for the first row). And that only 13, 12, and 11 numbers are available for each of
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Before the advent of printing machines, numbers on bingo cards were either painted by hand or stamped using rubber stamps onto thick cardboard. Cards were reusable, meaning players used tokens to mark called numbers. The number of unique cards was limited as randomization had to occur by hand. Before
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Perhaps the most common pattern set, known as "Straight-line Bingo" is completing any of the five rows, columns, or either of the main diagonals. In this case the possibility of multiple winning cards is unavoidable because any one of twelve patterns on every card can win the game. But not all 552
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Players use cards that feature five columns of five squares each, with every square containing a number (except the middle square, which is designated a "FREE" space). The columns are labeled "B" (numbers 1–15), "I" (numbers 16–30), "N" (numbers 31–45), "G" (numbers 46–60),
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For example, in a simple one-pattern game of Bingo a winning card may be the first person to complete row #3. Because the "N" column contains a free space, the maximum number of cards that guarantee a unique winner is (15*15*15*15) = 50,625. Because the players need to only focus on row #3, the
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In UK bingo, or Housie, cards are usually called "tickets." The cards contain three rows and nine columns. Each row contains five numbers and four blank spaces randomly distributed along the row. Numbers are apportioned by column (1–9, 10–19, 20–29, 30–39, 40–49,
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A popular Bingo myth claims that U.S. Bingo innovator Edwin S. Lowe contracted
Columbia University professor Carl Leffler to create 6,000 random and unique Bingo cards. The effort is purported to have driven Leffler insane. Manual
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156:." The game operated very much like a modern lottery as players placed bets on the chances of certain numbers being drawn. By the 1700s, a version of Lo Gioco del Lotto d'Italia was played in
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remaining numbers in rows #1, #2, #4, and #5 are statistically insignificant for purposes of game play and can be selected in any manner as long as no number is duplicated on any card.
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the advent of online Bingo, cards were printed on card stock and, increasingly, disposable paper. While cardboard and paper cards are still in use, Bingo halls are turning more to "
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In the early 1500s the people of Italy began to play a game called "Lo Gioco del Lotto d'Italia," which literally means "The game of lotto of
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is an onerous and time-consuming task that limited the number of Bingo cards available for play for centuries.
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number of Bingo cards is more practical from the point of view of calculating the number of unique
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are playing cards designed to facilitate the game of Bingo in its various forms around the world.
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Printing a complete set of Bingo cards is impossible for all practical purposes. If one
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The bingo queens of Oneida : how two moms started tribal gaming in
Wisconsin
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337:. Statements consisting only of original research should be removed.
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The Great
Depression in America: A Cultural Encyclopedia, Volume 1
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There are two types of Bingo cards. One is a 5x5 grid meant for
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Crossland, Drake. "Bingo:A Game's
Journey Through History".
693:"bingobonuspage:What are the different Bingo game types?"
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50–59, 60–69, 70–79 and 80–90).
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625:(First ed.). Wisconsin Historical Society Press.
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The calculation of random permutations is a matter of
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a printer would require more than seventeen million
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137:Bingo card with markers covering called numbers
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353:Learn how and when to remove this message
291:Learn how and when to remove this message
109:Learn how and when to remove this message
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484:. Greenwood Publishing Group, 2007.
229:adding citations to reliable sources
47:adding citations to reliable sources
377:principally relying on the use of
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599:Andrew Bowser (25 October 2006).
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672:"Bingo Myths: Fact or Fiction?"
480:Young, William H. and Nancy K.
216:needs additional citations for
193:and "O" (numbers 61–75).
34:needs additional citations for
574:. VirtualBingo. Archived from
528:. VirtualBingo. Archived from
470:(also known as a "bingo card")
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430:A typical housie/Bingo ticket
393:cards could be printed each
333:the claims made and adding
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572:"Types of Bingo Cards"
464: – Game of chance
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674:. My Casino Strategy
621:Hoeft, Mike (2014).
578:on September 6, 2008
532:on September 6, 2008
526:"Bingo Card History"
225:improve this article
43:improve this article
699:on December 6, 2015
468:Reader service card
439:Other types of card
422:90-ball bingo cards
188:75-ball bingo cards
182:U.K. style "Housie"
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368:random permutation
318:possibly contains
184:or 90-ball Bingo.
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603:. How Stuff Works
601:"Bingo Equipment"
512:EZinearticles.com
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457:Bingo (card game)
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240:"Bingo card"
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218:verification
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99:January 2016
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58:"Bingo card"
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36:verification
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142:Bingo cards
678:2012-12-08
607:2012-12-08
582:2012-12-08
557:2012-12-08
536:2012-12-08
475:References
445:Break Open
384:septillion
375:statistics
327:improve it
251:newspapers
129:bingo card
69:newspapers
656:April 18,
497:Footnotes
379:factorial
343:July 2023
331:verifying
281:July 2023
719:Category
703:12 April
451:See also
391:trillion
166:flimsies
406:cards.
404:winning
395:second,
325:Please
265:scholar
148:History
83:scholar
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158:France
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399:years
272:JSTOR
258:books
154:Italy
90:JSTOR
76:books
705:2016
658:2024
627:ISBN
486:ISBN
462:Keno
244:news
62:news
329:by
227:by
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