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Old Lotto Probabilities

Page with "new" calculations

Lotto belongs to the most popular gambling games in Norway. Every weekend many thousands participate in a secret hope to become this weeks Lotto millionaire. You know, Lotto millionaires are not like other millionaires.

How to participate in the game

Go to one of the dealers, you find them at almost every corner, and fill in a lotto coupon. It consists of ten rows, each of them with numbered boxes in the range from 1 to 34. Tick of seven numbers per row, at least in two rows. Its only NOK 2.00 per row anyway. Next, give your coupon to the charming lady at the dealer's office. Now, if you really fall for the temptation to participate (probably due to the charming lady), sit down in front of your TV set at 7:25 pm next Saturday night, and tune in nrk1. Be prepared for the exciting moment when the Lotto official proudly announces that your happy moment is about to come: the lotto numbers are going to be drawn.

A big drum, containing 34 numbered balls, starts to rotate and releases randomly and one by one seven of the balls. All of it very fancy to watch. These balls are marked with the winning numbers. Next, two additional balls are drawn, containing the winning extensions. Now the exciting moment has come, compare these numbers with the numbers you have ticked off. Got all seven numbers right in one row?

Statistical outcome of the game

Let's look at the probability that you get them right. But first a brief repetition of probability calculations in general.

definition:Comb(n,k) = (n!)/(k!*(n-k)!)

If a set contains n elements, then there exist Comb(n,k)
combinations (subset) containing k elements...from the book 
'Probability and Statistics for the engineering, computing and Physical
Science' by Edward R. Dougherty, 1990, page 40

! mean faculty: n! = n*(n-1)*(n-2)* ...*3*2*1

ex:Comb(5,2) = (5*4*3*2*1)/(2*1*(3*2*1)) = 120/12 = 10

(7+0)
Your 7 numbers matches GO 7 main numbers
To answer this we must find out how many combinations you can draw 7 number out of 34
comb(34,7) = 34!/[7!*(34-7)!] = 5 379 616
You can chose to play between 5 379 616 different combinations.
Pobability(7+0) = favorable/possible = 1/5 379 616 = 0.0000001858868
You have 0.0000186 % chance of draw 7 out of the 7 main number
(6+1)
favorable = comb(7,6)*comb(2,1) = 7*2=14
possible = comb(34,7) = 5 379 616
Pobability(6+1) = favorable/possible = 14/5 379 616 = 0.0000026024
You have 0.00026 % chance of draw 6 out of 7 main number and 1 out of 2 extra number
(6+0)
favorable = comb(7,6)*comb(34-7-2,1) = 7*25 = 175
Pobability(6+0) = favorable/possible = 175/5 379 616 = 0.00003253
You have 0.0033 % chance of draw 6 out of 7 main number.
(5+0) and (5+1) and (5+2)
favorable = comb(7,5)*[comb(35-7-2,2)*comb(2,0)+comb(35-7-2,1)*comb(2,1)+comb(34-7-2,0)*comb(2,2)]
= comb(7,5)*comb(27,2) = 7371
Pobability(5+0,5+1,5+2) = favorable/possible = 7371/5 379 616 = 0.001370
You have 0.137 % chance of draw 5 out of 7 main number and 0,1 or 2 extra numbers

(4+1) and (4+2)

favorable = comb(7,4)*[comb(2,1)*comb(25,2)+comb(2,2)*comb(25,1)] = 35(2*300+1*25) = 21875

Pobability(4+1,4+2) = favorable/possible = 21875/5 379 616 = 0.004066

You have 0.4066 % chance of draw 4 out of 7 main number, and


If you are interested in playing poker on the internet, I recomend Everest Poker. By signing up with Everest Poker you get an USD 100 welcome bonus. I highly recommends this site where there is an excellent selection of tables and an unusually high proportion of fish (weak players)!

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