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Page with 7+2 calculations (before 7+3 calculated here)
With three(new) instead of two(old) extra drawn numbers, the probability for winning * 7 same * 6+1 increase with 50% (14 -> 21 ) * 6+0 decrease with 4% (175 -> 168 ) * 5 same * 4+1 increase with 44 % (21875 -> 31535) This means * There are 9960(31535-21875) more ways to win out of 5379616 possible ways * There are 2.82% bigger chance of winning (966000/29436 = 32.82) * But still you will only have a 0.73% (3909600/5379616) chance of winning, up from previously 0.55% (2943600/5379616) (ie you will win 1 out of every 138 time)
Probability (%) | |
7 | 0.0000186 |
6+1 | 0.00039 |
6 | 0.0031 |
5 | 0.137 |
4+1 | 0.586 |
Not winning | 99.27 |
If you play a lot of games, what is the probability to win?
Lotto - a regressive tax in Fattiges toppskatt (Norwegian text) Dagbladet, 2002-09-21, page 52
Video-lotto machines - gambling's crack-cocaine in Hard luck story The Economist, 2002-09-14, page 55
Date: Wed, 27 Jan 1999 16:31:15 +0100 From: "Helgesen, Rita" rita.helgesen@norsk-tipping.no
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Lotto is run by Norsk Tipping
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
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
favorable = comb(7,6)*comb(3,1) = 7*3=21
possible = comb(34,7) = 5 379 616
Pobability(6+1) = favorable/possible = 21/5 379 616 = 0.0000039...
You have 0.00039 % chance of draw 6 out of 7 main number and 1 out of 2 extra number
favorable = comb(7,6)*comb(34-7-3,1) = 7*24 = 168
Pobability(6+0) = favorable/possible = 168/5 379 616 = 0.0000312...
You have 0.0031 % chance of draw 6 out of 7 main number.
favorable = comb(7,5)*[comb(34-7-3,2)*comb(3,0)+ comb(34-7-3,1)*comb(3,1)+ comb(34-7-3,0)*comb(3,2)] = comb(7,5)*(276+72+3) = 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
favorable = comb(7,4)*[comb(34-7-3,2)*comb(3,1)+ comb(34-7-3,1)*comb(3,2)+ comb(34-7-3,0)*comb(3,3)] = comb(7,4)*[828+72+1] = comb(7,4)*901 = 31535
Pobability(4+1,4+2,4+3) = favorable/possible = 31535/5 379 616 = 0.005861...
You have 0.586 % chance of draw 4 out of 7 main number, and at least one extra number
NOT winning = (5379616-39096)/5379616=5340520/5379616=99.27%
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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)! |