On July 18 I purchased one Oregon Megabucks ticket (two lines, each with 6 numbers from a pool of 48) and one PowerBall ticket (one line of 5 numbers from a pool of 59, plus one number from a pool of 35), all quick picks by the computer. Although both tickets (all three lines) were not winners, all three lines did contain the same three numbers, 01,11,48 (the PowerBall line had the three numbers in the group of 5). I think the odds of this happening are astronomical, maybe even as high as winning the jackpot, but I don't know how to figure it with multiple games. Anyone?
Statistically, each number has an equal probability of appearing on each line. So the odds of this happening are exactly the same as if the numbers were unrelated.
Lets say you roll a dice. You have a 1/6 chance of rolling a 4. You roll a dice again and you once again have a 1/6 chance of rolling a 4. Therefor the probability of your rolling two 4s in a row is 1/36. Then the probably of rolling a 3rd 4 is 1/216 and so on. BUT, The probability of rolling lets say a 3, a 6 and a 2 in sequence is also 1/216.
SO, applying that to the lottery you mentioned!
The probability of lets say a 7 coming out of the computer is 1/59. The the probability of a 4 coming out is 1/58. The probability of them coming out in sequence is 1/3422.
In the end the probability of any particular sequence of numbers coming out the machine on one line is 1/589843296. Apply that to three lines and the probability of a specific sequence of numbers (Lets say 16, 17, 21, 34, 63 on one line then some other random numbers on the next etc.) coming out across those 3 lines as a whole is:
1 in 4467443448548230000000000000000000 (If my calculations are correct!) - Now thats regardless of what those sequences are. There's nothing special about recurring patterns in random selections I'm afraid to say. Imagine these 3 lines of numbers came up on the lottery:
5, 2, 18, 45, 12, 25
36, 48, 13, 27, 4, 32
53, 18, 15, 24, 6
They look like nothing special. However the probability of those numbers coming up in that exact sequence is EXACTLY the same as if the numbers came up like this:
1, 2, 3, 4, 5, 6
1, 2, 3, 4, 5, 6
1, 2, 3, 4, 5
These sequences have no difference. However one registers with us as a similar pattern and therefor seems significant even though it's not (At least in the sense of the lottery).
I hope that helped. (Although I could be completely wrong so if anybody could confirm my calculations I'd appreciate it)
Sadly not nearly as unlikely as you think. Remember that in a group of 23 people it is more likely than not that 2 of them will share a birthday. And that's with a choice of 365 options!
Bear in mind that the odds of matching 3 numbers with the final draw are about 1 in 55. So that's also the odds of having two lines picked by the computer containing 3 common numbers. Obviously having all 3 of 3 lines containing 3 common numbers seems that bit rarer but it's certainly not approaching the astronomical in probability terms.
Of course the other thing you might have to take into account is that random numbers are notoriously unrandom in computers, even when they are working properly. Do not entirely discount the possibility that that machine left you all but certain to achieve this feat!
answered Jul 20 '12 at 13:53