Calculation of BINGO odds - help needed

[system13]

I'd be very grateful if some mathematician on this board could calculate odds of winning the prize in our Bingo game 15 from 90, I've searched for some kind of calculator but without luck.

Basically, the coupon has 90 numbers on it, it is consisted from 6 slips, and each of these slips makes an independant entity, arranged in 3 lines like shown below, vere the xx mark stands for a blank space.

f.e.

Slip1
Line1  xx 18  23 32 43  xx  xx  75  xx 
Line2  6  xx  27 38 xx  57  68  xx  xx
Line3  xx 16  21 xx xx  52  xx  72  84

You win the third prize if you match the numbers in one line (so called „Fiver“), if 2 lines are matched than it is a second prize („Tenner“) and obviously if you match all of them its BINGO.

But, the third and the second prize can be won only until 33 numbers are drawn from the container, afterwards you can hope only for bingo.

Now, I'm curious what are the odds of matching one line, 2 lines or even all 3 with 33 numbers drawn from 90.

TIA.

Cheers.

 

[johnph77]

I would assume by the description that all 90 numbers on the 6 slips are shown without duplicating any number in any line. Therefore the solution would have to be set up somewhat like Keno, where you have 5, 10 or 15 numbers out of 33 drawn from a field of 90. And that's relatively easy if rounding is allowed. I currently have spreadsheet formulas capable of doing this.

Is this what you were asking and describing?

 

[system13]

I would assume by the description that all 90 numbers on the 6 slips are shown without duplicating any number in any line. Therefore the solution would have to be set up somewhat like Keno, where you have 5, 10 or 15 numbers out of 33 drawn from a field of 90. And that's relatively easy if rounding is allowed. I currently have spreadsheet formulas capable of doing this.

Is this what you were asking and describing?

Yes, johnph77, this is exactly what I was describing or at least trying to, there are no duplicates, all 90 numbers are shown only once on 6 slips. Thanks.

Just one thing, what do you mean by if rounding is allowed

 

[johnph77]

Yes, johnph77, this is exactly what I was describing or at least trying to, there are no duplicates, all 90 numbers are shown only once on 6 slips. Thanks.

Just one thing, what do you mean by if rounding is allowed

Spreadsheets commonly in use, notably Excel, are accurate to 15 significant numbers - i.e. the 15 leftmost figures (only) of any number or calculation are used and returned, the rest are dropped. In your requested calculations, numbers can reach well over 100 figures - I really haven't started on them yet but 90! (factorial) is a large number with which to deal.

In layman's terms the rounding to 15 significant figures more than likely wouldn't have any effect on the final percentage or odds - less than 1/100 of a percentage point at most. What it will do is truncate the display of any number over 999,999,999,999,999 to where any figure beyond the leftmost 15 figures will be "0". Normally, this is acceptable for most applications. But I like to check before I start.

 

[system13]

Oh, I see now what you meant, johnph77, thank you for the explanation.

As a non-mathematician, I am not after a 100% accuracy here, I'd like to have just a raw picture what the odds are, so rounding to 15 numbers like you've described seems far more than enaugh.

Thank you very much for your time and efforts, it is much appreciated.

Cheers.

 

[johnph77]

system13 -

Tables:

15 Spot - 33/90 Hits Possibilities Odds - 1:: 45795673964460800
0 22057981462440 2076.15
1 253923274974600 180.35
2 1292700308961600 35.43
3 3858949811196480 11.87
4 7550119195819200 6.07
5 10248885206239700 4.47
6 9964193950510800 4.60
7 7059181136950800 6.49
8 3670774191214420 12.48
9 1399532643709200 32.73
10 387562885950240 118.16
11 76448939767200 599.04
12 10381954783200 4411.08
13 914773638240 50062.30
14 46672124400 981221.12
15 1037158320 44154950.20
45795673964460800

10 Spot - 33/90 Hits Possibilities Odds - 1:: 5720645481903
0 43183019880 132.47
1 296883261675 19.27
2 872473258800 6.56
3 1442489121216 3.97
4 1484915271840 3.85
5 993750989616 5.76
6 437500435680 13.08
7 125000124480 45.77
8 22159112976 258.16
9 2198324700 2602.28
10 92561040 61804.03
5720645481903

5 Spot - 33/90 Hits Possibilities Odds - 1:: 43949268
0 4187106 10.50
1 13035330 3.37
2 15449280 2.84
3 8707776 5.05
4 2332440 18.84
5 237336 185.18
43949268

The tables are deceptive in one way - they only take the one-line odds into consideration. Therefore, in order to calculate the odds of the 5 and 10 number hits for each ticket, multiply the number of possibilities by 3 and divide the odds by 3. This does not apply to the 15 number possibilities and odds.

Then, since you have 6 tickets, multiply all the possibilities by 6 and divide the odds by 6. That should give you the true odds of the game.

gl

j

 

[system13]

johnph77, thank You very much sir

 

[johnph77]

system13 -

Do you have the bets and payouts for this game? If so I'll post the figures on my website. Also, if there are any other lottery games in Croatia I'd appreciate receiving the same information for the same purpose. Thanks in advance.

gl

j

 

[system13]

system13 -

Do you have the bets and payouts for this game? If so I'll post the figures on my website. Also, if there are any other lottery games in Croatia I'd appreciate receiving the same information for the same purpose. Thanks in advance.

gl

j

No problems johnph77, its the least I can do, I just came back from the business trip from Brussels,though so I'll post infos on all our lotteries as soon as possible (6/45+bonus, 7/39+bonus, bingo)

Thanks again for your kindness and willingness to help.

Cheers.

 

[system13]

johnph77, I dont know if you'll find this info helpful because all croatian lotto games and bingo are pari-mutual, so there are no fixed prizes and the players share 50% of total payment, in different percentages for various games and prizes.

For Bingo 15/90

BINGO 60 %
from 15. to 33.drawn number _ 100% from 60% (BINGO33)
from 34. to 36. drawn number _ 70% from 60% (BINGO 36),
from 37. to 39. drawn number _ 50% from 60% ( BINGO 39),
from 40 drawn number _ 30% from 60%(BINGO 40+)

If BINGO33 is not drawn, the remaining ammount from reduced prizes of other bingo types (bingo36,39 and 40+) is carried out in the next round.

As I said, tens and fives can be won only until 33 numbers are drawn (or if someone gets BINGO33 before, say f.e. after 28th drawn number)
TEN 15 %
FIVE 25 %

For lotto 6/45+b :

"jackpot" - 25,0%
"5+b" - 5,0%
"5" - 15,0%
"4" - 17,5%
"3" -37,5 %

For lotto 7/39+b

"jackpot" - 30%
"6+bonus" - 5%
"6" - 15%
"5" - 15%
"4" -35%


Cheers

 

[johnph77]

system13 -

TYVM for info - only 2 other things needed - unit of currency (Euro?) and minimum bet. I can go with the rest of the info. I really appreciate this - it helps.

gl

J

 

[system13]

johnph77,

croatian currency is Kuna (HRK), exchange rate is 1 EURO=7.5 HRK(on average).

For lotto 6/45 and 7/39, price of one combination is 1.5 HRK, minimum bet is 2 combinations.

For bingo, price of one whole coupon (with 6 slips) is 8 HRK, minimum bet is half of coupon (3 slips)=4 HRK.


Cheers.

 

[johnph77]

system13 -

Sorry for delayed reply - was on road.

TYVM - will print and publish info on my return home. If I have any other questions then I'll let you know. Much appreciated.

gl

j