6/49 number % question.

Reply #11

JADELottery — Tue, 14 Jul 2015 14:37:30 GMT

It's a well known combinatorial function.

You can learn more about combinations at https://en.wikipedia.org/wiki/Combination

Reply #10

RJOh — Tue, 14 Jul 2015 14:07:47 GMT

Works equally well for 5/39 games too

WHEEL COVERAGE AND PERCENT

LOTTERY POOL SIZE 39

COMBINATION SIZE 5

575757 POSSIBLE COMBOS - Wheel Size - Percent Cover - Possible Combinations

No. %COVER Combos No. %COVER Combos

________________________________________________________________________________

39 = 100.000000% 575757 38 = 87.179313% 501941

37 = 75.708328% 435896 36 = 65.477623% 376992

35 = 56.383509% 324632 34 = 48.328722% 278256

33 = 41.221557% 237336 32 = 34.9... [ More ]

Reply #9

RJOh — Tue, 07 Jul 2015 01:40:47 GMT

I no longer has to do my figuring the hard way thanks to Jade's formula. Comb(n, r) = n! / (r! (n - r)!)

I wrote a 10 line program in QB64 that will give me the coverage percentage for any lottery matrix for every group size.

Thanks Jade.

Reply #8

RJOh — Mon, 06 Jul 2015 15:03:21 GMT

I did my figuring the old fashion way, I took the 1323 Classic Lotto drawing results and checked the match6 I got with 49 and less numbers and then divided the results by 1323.

Problem is with my method you need a data file of a game with the appropriate matrix. Jade's formula works with any matrix and can be plugged into your computer calculator with the scientific view.

Reply #7

paul762 — Mon, 06 Jul 2015 14:06:17 GMT

My initial thought was that it might be around 42 numbers RJOH, which is why I asked for confirmation, looks like I was a out a bit

Reply #6

SergeM — Mon, 06 Jul 2015 00:42:06 GMT

Combin(n,0) = 1, while truly = 0.

Reply #5

JADELottery — Sun, 05 Jul 2015 19:20:04 GMT

For any N / R lottery and Q / R wheel the percent probability S drawn numbers are in Q wheel numbers.

P(N, R, Q, S) = 100% Comb(Q, S) Comb(N - Q, R - S) / Comb(N, R)

N - Lottery Pool Size

R - Lottery Pick Size

Q - Wheel Pool Size

S - Quantity of Drawn Numbers Matching the Wheel Numbers

Where Q N and S R; Comb(n, r) = n! / (r! (n - r)!); n! = n (n - 1) (n - 2) ... 3 2 1 and 0! = 1.

Reply #4

RJOh — Sun, 05 Jul 2015 16:12:51 GMT

You would think having 85% of the 49 numbers or 42 would cover all six numbers 85% of the time but I checked that theory using the last 1323 drawings of Ohio's Classic Lotto(6/49) and it turns out it only covered all six numbers 40% of the time. You need to use 48 of the 49 numbers to cover all six number 85% of the time. The following is a chart showing percentage of coverage for other groups sizes.

*Looks like Jade's chart is right on.

49/49 = 100%

48/49 = 87%

47/49 = 76%

46/49... [ More ]

Reply #3

SergeM — Sat, 04 Jul 2015 21:59:27 GMT

I thought that it would be something like that without calculating.

Reply #2

JADELottery — Sat, 04 Jul 2015 20:14:18 GMT

Quantity of Numbers you use Percent of time 6 drawn numbers match your numbers.

Q 100% Comb(Q, 6) / Comb(49, 6)

6 0.000007%

7 0.000050%

8 0.000200%

9 0.000601%

10 0.001502%

11 0.003304%

12 0.006608%

13 0.012271%

14 0.021475%

15 0.035791%

16 0.057266%

17 0.088502%

18 0.132753%

19 0.194024%

20 0.277178%

21 0.388049%

22 0.533567%

23 0.721884%

24 0.962513%

25 1.266464%

26 1.646403%

27 2... [ More ]

Reply #1

SergeM — Sat, 04 Jul 2015 17:20:44 GMT

Do a random test, that should be close to the mathematical answer.

6/49 number % question.

paul762 — Sat, 04 Jul 2015 13:01:40 GMT

How many numbers would I need to use to guarantee that I have the 6 winning numbers in my selections 85% of the time? What would be the best way to select those numbers