| .g
90-Number Bingo |
| Last Update:
Feburary 23, 2005 |
How to
play 90 Ball Bingo
Do you
know what the favorite leisure activity of young women, 20
to 25 years of age, in the UK? It’s 90 Ball bingo. The game
is an absolute craze in the UK. Of course, if you’re from
the UK, you already knew that.
Naturally, since
all the young women are playing the game, you can find a lot
of men, both young and old, playing the game in earnest.
Online 90 Ball bingo has been an absolute phenomenon in the
UK and has been growing by leaps and bounds since 2005.
With the huge popularity of online 90 Ball bingo in the UK,
many Internet heavyweights such as Yahoo!, AOL UK, Virgin
and MSN UK have ventured into the market and now manage
their online bingo. Major British TV shows such as “Emmerdale,”
“Coronation Street,” and “I’m a Celebrity” have also jumped
on the online bingo bandwagon and now run their own games.
The game
is called 90 Ball bingo because 90 is the maximum quantity
of numbers that can be called in the game. It is played on
bingo cards which have three horizontal rows and nine
vertical columns.
The game begins with players buying their bingo cards where
numbers are spread out across the three rows. On each row,
only five of the nine spaces have numbers while four spaces
are blank. The numbers range from 1 to 90. The first column
has numbers from one to 10, the second column has numbers
from 11 to 20, the third column has numbers from 21 to 30
and so on until the ninth column.
Once all players have their cards, the dealer begins drawing
numbers at random from a container and calling these numbers
out. Players mark each number called on their cards. The
first player who completes each of three patterns shout out
“Bingo!” to indicate that he has won the game. The dealer
confirms the numbers on his card. Once the win is confirmed,
a new game begins.
The three basic patterns in 90 Ball bingo are One Line, Two
Line and Full House. The first player who crosses off a
horizontal line wins One Line, the first to cross off two
horizontal lines wins Two Lines and, finally, the player who
crosses off all three lines wins Full House. Prizes for each
pattern increase in value. Naturally, the biggest prizes are
awarded for Full House games because these are the most
difficult.
In 90 Ball bingo, each player can have as many as 48
tickets. Players can also purchase a strip of six tickets
which covers all numbers from 1 to 90. This way, he is sure
to cross out one number every time a bingo call is made.
The 90 Ball bingo game is much simpler than 75 number bingo,
which has many and more complicated themed patterns. It’s
also slower than the 75 Ball version, although it certainly
isn’t any less exciting.
Unlike American bingo with a 5 by 5 card with numbers from 1
to 75, in Europe and South America bingo is often played with a
3 by 9 card with numbers from 1 to 90. Below is an example.
As the example shows the card contains 3 rows and 9 columns.
On each row are exactly 5 numbers. The other four cells in each
row are blank, or free squares. From other examples I have seen
the first row contains the numbers 1 to 10, the second 11 to 20,
and so on, but mathematically this doesn't matter. Winning
events I have heard of all are based on covering rows only, so
mathematically speaking the game could played on a 3 by 5 card
with all numbers covered, the odds would be the same.
The purpose of this appendix is to show the probability of
covering (1) at least one row, (2) at least 2 rows, and (3) all
three rows, in any given number of calls from 5 to 90. For
example, the table shows the probability of covering at least
one row in 50 calls on any one card is 0.139289864, or 13.93%.
| 90 Number Bingo
Probabilities |
| Calls |
One Row
Probability |
Two Rows
Probability |
Three Rows
Probability |
One Row Inverse
Probability |
Two Rows Inverse
Probability |
Three Rows Inverse
Probability |
| 5 |
0.0000000683 |
0 |
0 |
1 in 14649756 |
|
|
| 6 |
0.0000004096 |
0 |
0 |
1 in 2441626 |
|
|
| 7 |
0.0000014335 |
0 |
0 |
1 in 697607 |
|
|
| 8 |
0.0000038226 |
0 |
0 |
1 in 261603 |
|
|
| 9 |
0.0000086008 |
0 |
0 |
1 in 116268 |
|
|
| 10 |
0.0000172017 |
0 |
0 |
1 in 58134 |
1 in 1906881827301 |
|
| 11 |
0.0000315364 |
0 |
0 |
1 in 31709 |
1 in 173352893391 |
|
| 12 |
0.0000540623 |
0 |
0 |
1 in 18497 |
1 in 28892148899 |
|
| 13 |
0.0000878511 |
0.0000000001 |
0 |
1 in 11383 |
1 in 6667418977 |
|
| 14 |
0.000136657 |
0.0000000005 |
0 |
1 in 7318 |
1 in 1904976850 |
|
| 15 |
0.0002049848 |
0.0000000016 |
0 |
1 in 4878 |
1 in 634992301 |
1 in 45795673964460800 |
| 16 |
0.0002981578 |
0.0000000042 |
0 |
1 in 3354 |
1 in 238122146 |
1 in 2862229622778800 |
| 17 |
0.0004223859 |
0.0000000102 |
0 |
1 in 2368 |
1 in 98050336 |
1 in 336732896797506 |
| 18 |
0.0005848332 |
0.0000000229 |
0 |
1 in 1710 |
1 in 43577969 |
1 in 56122149466251 |
| 19 |
0.0007936849 |
0.0000000484 |
0 |
1 in 1260 |
1 in 20642236 |
1 in 11815189361316 |
| 20 |
0.0010582143 |
0.0000000969 |
0 |
1 in 945 |
1 in 10321154 |
1 in 2953797340329 |
| 21 |
0.0013888484 |
0.000000185 |
0 |
1 in 720 |
1 in 5406350 |
1 in 843942097237 |
| 22 |
0.0017972335 |
0.0000003391 |
0 |
1 in 556 |
1 in 2948945 |
1 in 268527030939 |
| 23 |
0.0022962984 |
0.0000005999 |
0 |
1 in 435 |
1 in 1666818 |
1 in 93400706414 |
| 24 |
0.0029003168 |
0.0000010285 |
0 |
1 in 345 |
1 in 972330 |
1 in 35025264905 |
| 25 |
0.0036249674 |
0.000001714 |
0.0000000001 |
1 in 276 |
1 in 583414 |
1 in 14010105962 |
| 26 |
0.0044873918 |
0.0000027852 |
0.0000000002 |
1 in 223 |
1 in 359038 |
1 in 5927352522 |
| 27 |
0.0055062482 |
0.0000044234 |
0.0000000004 |
1 in 182 |
1 in 226072 |
1 in 2634378899 |
| 28 |
0.006701763 |
0.0000068803 |
0.0000000008 |
1 in 149 |
1 in 145342 |
1 in 1223104489 |
| 29 |
0.008095776 |
0.0000105007 |
0.0000000017 |
1 in 124 |
1 in 95232 |
1 in 590464236 |
| 30 |
0.0097117813 |
0.0000157493 |
0.0000000034 |
1 in 103 |
1 in 63495 |
1 in 295232118 |
| 31 |
0.0115749612 |
0.0000232459 |
0.0000000066 |
1 in 86 |
1 in 43018 |
1 in 152377867 |
| 32 |
0.0137122121 |
0.0000338066 |
0.0000000124 |
1 in 73 |
1 in 29580 |
1 in 80950742 |
| 33 |
0.0161521615 |
0.0000484952 |
0.0000000226 |
1 in 62 |
1 in 20621 |
1 in 44154950 |
| 34 |
0.0189251748 |
0.0000686847 |
0.0000000405 |
1 in 53 |
1 in 14559 |
1 in 24674825 |
| 35 |
0.0220633488 |
0.0000961302 |
0.0000000709 |
1 in 45 |
1 in 10403 |
1 in 14099900 |
| 36 |
0.0256004928 |
0.0001330566 |
0.0000001216 |
1 in 39 |
1 in 7516 |
1 in 8224942 |
| 37 |
0.0295720915 |
0.0001822611 |
0.0000002045 |
1 in 34 |
1 in 5487 |
1 in 4890506 |
| 38 |
0.0340152517 |
0.0002472336 |
0.0000003378 |
1 in 29 |
1 in 4045 |
1 in 2960043 |
| 39 |
0.0389686274 |
0.0003322973 |
0.000000549 |
1 in 26 |
1 in 3009 |
1 in 1821565 |
| 40 |
0.0444723213 |
0.0004427703 |
0.0000008784 |
1 in 22 |
1 in 2259 |
1 in 1138478 |
| 41 |
0.0505677613 |
0.0005851526 |
0.0000013851 |
1 in 20 |
1 in 1709 |
1 in 721962 |
| 42 |
0.0572975481 |
0.0007673395 |
0.0000021546 |
1 in 17 |
1 in 1303 |
1 in 464118 |
| 43 |
0.0647052697 |
0.0009988639 |
0.0000033089 |
1 in 15 |
1 in 1001 |
1 in 302217 |
| 44 |
0.0728352824 |
0.0012911709 |
0.0000050204 |
1 in 14 |
1 in 774 |
1 in 199188 |
| 45 |
0.081732452 |
0.0016579252 |
0.0000075306 |
1 in 12 |
1 in 603 |
1 in 132792 |
| 46 |
0.0914418539 |
0.002115356 |
0.0000111744 |
1 in 11 |
1 in 473 |
1 in 89490 |
| 47 |
0.1020084273 |
0.0026826381 |
0.0000164124 |
1 in 10 |
1 in 373 |
1 in 60930 |
| 48 |
0.1134765801 |
0.0033823132 |
0.0000238726 |
1 in 8.8 |
1 in 296 |
1 in 41889 |
| 49 |
0.1258897424 |
0.0042407513 |
0.0000344046 |
1 in 7.9 |
1 in 236 |
1 in 29066 |
| 50 |
0.1392898636 |
0.0052886518 |
0.0000491494 |
1 in 7.2 |
1 in 189 |
1 in 20346 |
| 51 |
0.1537168505 |
0.0065615844 |
0.0000696283 |
1 in 6.5 |
1 in 152 |
1 in 14362 |
| 52 |
0.1692079444 |
0.0081005673 |
0.000097856 |
1 in 5.9 |
1 in 123 |
1 in 10219 |
| 53 |
0.1857970345 |
0.0099526798 |
0.0001364834 |
1 in 5.4 |
1 in 100 |
1 in 7327 |
| 54 |
0.203513905 |
0.0121717032 |
0.000188977 |
1 in 4.9 |
1 in 82 |
1 in 5292 |
| 55 |
0.2223834172 |
0.0148187832 |
0.0002598433 |
1 in 4.5 |
1 in 67 |
1 in 3848 |
| 56 |
0.2424246244 |
0.0179631039 |
0.000354908 |
1 in 4.1 |
1 in 56 |
1 in 2818 |
| 57 |
0.2636498229 |
0.0216825599 |
0.0004816608 |
1 in 3.8 |
1 in 46 |
1 in 2076 |
| 58 |
0.2860635412 |
0.0260644094 |
0.000649682 |
1 in 3.5 |
1 in 38 |
1 in 1539 |
| 59 |
0.309661472 |
0.031205888 |
0.0008711645 |
1 in 3.2 |
1 in 32 |
1 in 1148 |
| 60 |
0.3344293554 |
0.037214755 |
0.0011615527 |
1 in 3 |
1 in 27 |
1 in 861 |
| 61 |
0.3603418208 |
0.0442097423 |
0.0015403199 |
1 in 2.8 |
1 in 23 |
1 in 649 |
| 62 |
0.387361203 |
0.0523208636 |
0.0020319114 |
1 in 2.6 |
1 in 19 |
1 in 492 |
| 63 |
0.4154363465 |
0.0616895391 |
0.0026668837 |
1 in 2.4 |
1 in 16 |
1 in 375 |
| 64 |
0.4445014202 |
0.0724684766 |
0.0034832766 |
1 in 2.2 |
1 in 14 |
1 in 287 |
| 65 |
0.4744747683 |
0.0848212433 |
0.0045282596 |
1 in 2.1 |
1 in 12 |
1 in 221 |
| 66 |
0.5052578274 |
0.0989214474 |
0.0058601006 |
1 in 2 |
1 in 10 |
1 in 171 |
| 67 |
0.5367341493 |
0.1149514356 |
0.0075505143 |
1 in 1.86 |
1 in 8.7 |
1 in 132 |
| 68 |
0.568768574 |
0.1331003983 |
0.0096874523 |
1 in 1.76 |
1 in 7.5 |
1 in 103 |
| 69 |
0.6012066069 |
0.153561752 |
0.0123784113 |
1 in 1.66 |
1 in 6.5 |
1 in 81 |
| 70 |
0.6338740649 |
0.1765296538 |
0.0157543416 |
1 in 1.58 |
1 in 5.7 |
1 in 63 |
| 71 |
0.6665770642 |
0.2021944733 |
0.0199742546 |
1 in 1.5 |
1 in 4.9 |
1 in 50 |
| 72 |
0.6991024401 |
0.2307370275 |
0.0252306373 |
1 in 1.43 |
1 in 4.3 |
1 in 40 |
| 73 |
0.7312186968 |
0.262321349 |
0.0317558022 |
1 in 1.37 |
1 in 3.8 |
1 in 31 |
| 74 |
0.7626776074 |
0.2970857299 |
0.0398293112 |
1 in 1.31 |
1 in 3.4 |
1 in 25 |
| 75 |
0.7932165977 |
0.3351317439 |
0.049786639 |
1 in 1.26 |
1 in 3 |
1 in 20 |
| 76 |
0.8225620687 |
0.3765109088 |
0.0620292551 |
1 in 1.22 |
1 in 2.7 |
1 in 16 |
| 77 |
0.8504338369 |
0.4212086067 |
0.077036333 |
1 in 1.18 |
1 in 2.4 |
1 in 13 |
| 78 |
0.8765508925 |
0.4691248258 |
0.095378317 |
1 in 1.14 |
1 in 2.1 |
1 in 10 |
| 79 |
0.9006387073 |
0.5200512338 |
0.1177326101 |
1 in 1.11 |
1 in 1.92 |
1 in 8.5 |
| 80 |
0.9224383526 |
0.5736440281 |
0.1449016739 |
1 in 1.08 |
1 in 1.74 |
1 in 6.9 |
| 81 |
0.941717722 |
0.6293919373 |
0.1778338726 |
1 in 1.06 |
1 in 1.59 |
1 in 5.6 |
| 82 |
0.9582851926 |
0.686578675 |
0.2176474261 |
1 in 1.04 |
1 in 1.46 |
1 in 4.6 |
| 83 |
0.9720060987 |
0.7442390568 |
0.2656578878 |
1 in 1.03 |
1 in 1.34 |
1 in 3.8 |
| 84 |
0.9828224403 |
0.801107902 |
0.3234096025 |
1 in 1.02 |
1 in 1.25 |
1 in 3.1 |
| 85 |
0.9907762969 |
0.8555607343 |
0.3927116602 |
1 in 1.01 |
1 in 1.17 |
1 in 2.5 |
| 86 |
0.9960374767 |
0.9055451845 |
0.4756789123 |
1 in 1.004 |
1 in 1.1 |
1 in 2.1 |
| 87 |
0.9989359891 |
0.9485018727 |
0.5747786857 |
1 in 1.001 |
1 in 1.05 |
1 in 1.74 |
| 88 |
1 |
0.9812734082 |
0.6928838951 |
1 in 1 |
1 in 1.02 |
1 in 1.44 |
| 89 |
1 |
1 |
0.8333333333 |
1 in 1 |
1 in 1 |
1 in 1.2 |
| 90 |
1 |
1 |
1 |
1 in 1 |
1 in 1 |
1 in 1 |
Methodology: The probability of covering m marks in c
calls is
combin(15,m)*combin(75,c-m)/combin(90,m).
Using that you can find the probability of covering a card as
combin(75,90-m)/combin(90,m). To get the probability of covering
1 or 2 rows I determined the probability that m marks would
cover 1 or 2 rows. The chart below shows those probabilities,
which is based on basic probability.
| Rows Covered by Number
of Marks |
| Marks |
0 Rows |
1 Row |
2 Rows |
3 Rows |
Total |
| 5 |
0.999001 |
0.000999 |
0 |
0 |
1 |
| 6 |
0.994006 |
0.005994 |
0 |
0 |
1 |
| 7 |
0.979021 |
0.020979 |
0 |
0 |
1 |
| 8 |
0.944056 |
0.055944 |
0 |
0 |
1 |
| 9 |
0.874126 |
0.125874 |
0 |
0 |
1 |
| 10 |
0.749251 |
0.24975 |
0.000999 |
0 |
1 |
| 11 |
0.549451 |
0.43956 |
0.010989 |
0 |
1 |
| 12 |
0.274725 |
0.659341 |
0.065934 |
0 |
1 |
| 13 |
0 |
0.714286 |
0.285714 |
0 |
1 |
| 14 |
0 |
0 |
1 |
0 |
1 |
| 15 |
0 |
0 |
0 |
1 |
1 |
|
