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Lotto Probability

macgyver

Bacontologist
macgyver
Joined
May 4, 2006
Messages
317
I'm curious if this can be explained to a mathematically challenged individual like me:

Standard Lotto 6/49 draw where six unique numbers from a list of 1 through 49 are randomly drawn:

Is there any less chance that the same group of 6 numbers will be randomly generated more than once?

I would intuitively think that every drawing of 6 numbers has the same odds of occurring every time. So just because a certain series of 6 is drawn, doesn't mean there's any less of a chance of the same series of numbers being drawn again.

However, there's a part of the human psyche that wants to believe that "lightening never strikes twice" so your odds are better if you were to avoid any number combination that has already been picked in the past.

Is this strictly a psychological phenomenon, or is there some truth to it?
 
I think your speaking of the gambler's fallacy -

http://skepdic.com/gamblers.html

"The gambler's fallacy is the mistaken notion that the odds for something with a fixed probability increase or decrease depending upon recent occurrences."

ETA - the fallacy :-)
 
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macgyver said:
Is this strictly a psychological phenomenon, or is there some truth to it?
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Strictly psychological - how should the individual balls know and remember what other numbers have been drawn in previous games? (Especially since at least in Germany, they have many different machines and even more sets of balls.)

I think it was in the JREF forums recently, where I saw a map of lightning intensity. Some places are definitely more likely to be struck by lightning than others.

I was once told that if you went along the sides of a river after a thunderstorm, you could find many impact points, too.
 
Imagine the lottery consisted of a total of two balls to choose from (red and blue) and selecting the correct color of the one ball drawn wins. You have a 50% likelihood of winning. If the weekly drawing is red, the next drawing still contains the same two balls with the same 50% likelihood of either color being drawn.

It's the same idea except the 49 number lottery has more possible choices. The likelihood of any selection winning doesn't change between drawings.

I used colors instead of numbers to demonstrate that special number sequences are no more likely than if 49 colors were used to identify the selections.
 
yep it's the gambler's fallacy....

although you can use psychology to (very slightly) improve your EV....

These are the conclusions from a study http://news.bbc.co.uk/1/hi/sci/tech/240734.stm

avoid "lucky" numbers - 7 was chosen 25% more often than the least popular number 46

avoid low numbers - especially a low sequence such as 1,2,3,4,5,6, 10,000 people a week select this combination.


and generally avoid excessive use of numbers below 31 (as people often choose birthdays)

positioning on the ticket also makes some numbers more appealing -

The remarkable draw on 14 November 1995 when 133 tickets shared the £16 million jackpot prize is a clear example of the effects the team had deduced.

The winning numbers were 7, 17, 23, 32, 38, 42 and 48, all of which lie in central columns of the ticket, and the players won only £120,000 each. The average number of jackpot winners is five and the average amount won is £2 million.

Doing all this won't change your odds of winning, but if you do win, you'll proabably enjoy a bigger prize.....

and if you could give me a couple of quid if you do......:D
 
This Guy said:
I think your speaking of the gambler's fallacy -

http://skepdic.com/gamblers.html

"The gambler's fallacy is the mistaken notion that the odds for something with a fixed probability increase or decrease depending upon recent occurrences."

ETA - the fallacy :-)
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Yes, that's it exactly. What's embarrassing is that I even own that book!

I think this fallacy is probably very strong in the majority of people.

There are a few number combinations you could choose that theoretically have the same odds of winning, but nobody would believe you. Such as 1, 2, 3, 4, 5, 6

Also, if you were to have a combination win one week, and then tell somebody that they have the exact same chance of winning next week with the exact same combination...again no body would believe it.

Interesting...
 
macgyver said:
There are a few number combinations you could choose that theoretically have the same odds of winning, but nobody would believe you. Such as 1, 2, 3, 4, 5, 6
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The number combination 1, 2, 3, 4, 5, 6, 7 is by far the worst one to choose in Finnish national Lotto. Not because it is more unlikely than the others, but because you have to share your winnings with roughly 4000 other players.

The combination 5, 10, 15, 20, 25, 30, 35 is the second worst followed by 1, 7, 13, 19, 25, 31, 37. (The first column of the number grid) but exact statistics for these are not available online.
 
I also fell for this. I went through every drawing on the Power Ball for like a year, or 18 months (forget now), looking for numbers that had hit, trying to find the numbers that had hit the least. My logic (illogic;) was that those numbers would be more likely to be drawn next time.

The only pattern I could find was that there was none, and basically, as far as I could figure, any given number was as likely to come up on any given drawing.

Now I "invest"(cough) $1 per drawing via quick pick. I figure $104/year, to increase my odds from 0 to something isn't that bad, and it could happen ;)

ETA: My wording was a little off. I took those numbers from the web, and analyzed them. Only took a few hours of active time working on it, not 18 months :)
 
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macgyver said:
Also, if you were to have a combination win one week, and then tell somebody that they have the exact same chance of winning next week with the exact same combination...again no body would believe it.
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I've been told that once the Germyn lottery drew the exact same numbers (or 5 out of 6 of those numbers, or something) as the Dutch lottery in its previous drawing. The story continues that people living close to the border would often play the dutch numbers. Of course, peolpe didn't wain much that week, either.

I am rather hazy on the details, and I couldn't confirm the story online. Other than that: It's true.
 
My uncle always plays the numbers for Lost. I don't have the heart to tell him that if he does hit he'll be splitting his winning with hundreds of other Lost fans.
 
LW said:
The number combination 1, 2, 3, 4, 5, 6, 7 is by far the worst one to choose in Finnish national Lotto. Not because it is more unlikely than the others, but because you have to share your winnings with roughly 4000 other players.

The combination 5, 10, 15, 20, 25, 30, 35 is the second worst followed by 1, 7, 13, 19, 25, 31, 37. (The first column of the number grid) but exact statistics for these are not available online.
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I wasn't aware that statistics are available regarding how often number combinations are played in any lotteries. Do you have a link to any such statistics?
 
I wonder how popular the Lost numbers are now (they were really popular the first week after the episode entitled "Numbers")...
 
andyandy said:
well, the link i gave before http://news.bbc.co.uk/1/hi/sci/tech/240734.stm

is from a university study. You might have to chase up the raw stats....but the conclusions are summarized in the article.
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Thanks. The article is interesting, but the researchers did not have access to the actual lottery data. Rather: "They analysed how many tickets shared the jackpot each week and then compared that with the winning numbers. If a higher number of winners shared the jackpot, then the numbers they chose must be more popular, the scientists reasoned." Probably sound reasoning, but no substitute for having access to the actual data.
 
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The same numbers have won the Lotto more than once.

And the same people have won the Lotto more than once.

No correlation.
 
balrog666 said:
The same numbers have won the Lotto more than once.

And the same people have won the Lotto more than once.

No correlation.
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Any evidence of the same numbers winning the lotto more than once? I'm just curious if it has happened. The odds of it happening are just as bad as any combo of numbers, but it's still interesting to see it occur.
 
While there is an equal probability of any single number being chosen, there are some differences when you look at the probability for the numbers as a group. The result is a different gambler's fallacy, but fun to ponder.

The WA State lotto is a 6 pick system from numbers 1-49 and there is no special ball and numbers cannot repeat.

Take the number 1 (it also works for #1-5 and #45-49 respectively). While the chances of getting #1 should be equal to any other number, 1 appears less likely to be chosen because it can only occur in positions #1-44. #7 OTOH, has 5 more chances of being chosen since it can go in the positions of #1-49.

So if you take the odds of picking any of the 49 numbers (ping pong balls are used) each number should have an equal chance of being chosen. But if you calculate out the chance of each of the 6 positions individually, you get different odds. If you then add the odds of each position together, #1-5 and #45-49 should occur less frequently.

The reason it is a gambler's fallacy is while #1 cannot end up in position #45-49, it occurs more often in positions #1-#6 and vice versa for #45-49.


You can buy a group of numbers that increase your odds. In a 6 pick system, you can buy all the combinations for 7 numbers pretty inexpensively. When you start getting all the combinations for 8 or more the cost goes up pretty fast. I try to play the 7 number group even though it only increases the odds of winning by a tiny amount. But hey, that's at least a real increase and not a fallacious one. ;)

The number frequency charts are another means of increasing probability. They really only have meaning in a physical system where there are true variables in the system such as bouncing and bumping balls. If it is a computer generated random number, then you'd have to show something in the program was not truly random. Otherwise you'd just be seeing a coincidental difference in the number frequency and not a true variation.
 
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