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Tags lotteries , math puzzles , probability , probability puzzles

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Old 30th January 2012, 02:04 PM   #1
Undesired Walrus
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1,2,3,4,5,6 in the lottery

For years, I've been telling people that it's as likely for you to get the above numbers as something like 35,32,18,16, 28, 21.

People can't seem to believe it. Is this actually the case, or am I making a fool of myself?
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Old 30th January 2012, 02:08 PM   #2
kajata
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Not only is it the same but if you won you'd probably share the jackpot with thousands of other people who play those numbers to make a point to their friends at the convenience store.
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Old 30th January 2012, 02:15 PM   #3
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Yes, the likelyhood of winning is the same. But in the event of a win, you share it with others who played the same numbers. So you want to avoid picking numbers that other people are likely to pick.
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Old 30th January 2012, 02:19 PM   #4
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I used to play 15, 16, 17, 18, 19, 20, just so when I asked for it, I could hear the cashier say "what are the odds of that?"

Originally Posted by Almo View Post
Yes, the likelyhood of winning is the same. But in the event of a win, you share it with others who played the same numbers. So you want to avoid picking numbers that other people are likely to pick.
Good point.
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Old 30th January 2012, 02:26 PM   #5
dasmiller
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Originally Posted by Undesired Walrus View Post
For years, I've been telling people that it's as likely for you to get the above numbers as something like 35,32,18,16, 28, 21.

People can't seem to believe it. Is this actually the case, or am I making a fool of myself?
[pedantic] It depends on what you mean by "something like." <1,2,3,4,5,6> should be exactly as likely as <16, 18, 21, 28, 32, 35>, but to the typical lottery player, there are several billion sequences "like" <16, 18, 21, 28, 32, 35> while there's only one sequence "like" <1,2,3,4,5,6>, and maybe ~40 case that are "like" <12, 13, 14, 15, 16, 17> (i.e. sequential numbers).

Of course, once you've picked one particular sequence, the "like" part becomes inconsequential; <16, 18, 21, 28, 32, 35> should have the same chance of winning as <1, 2, 3, 4, 5, 6>

[/pedantic]
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Old 30th January 2012, 02:26 PM   #6
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Originally Posted by Almo View Post
Yes, the likelyhood of winning is the same. But in the event of a win, you share it with others who played the same numbers. So you want to avoid picking numbers that other people are likely to pick.
For the same reason, you shouldn't choose numbers that represent dates, or numbers you get from fortune cookies and the like.
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Old 30th January 2012, 02:36 PM   #7
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The data is available from you local lottery office on the number of minor prizes for partial matches in each lottery drawing. From that you can calculate the probabilities that someone would pick any sequence of numbers for that lottery. I did this for the first couple of years that we had a lottery here but quickly lost interest because I never play.
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Old 30th January 2012, 02:36 PM   #8
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I read that people tend to avoid filling out numbers which make a geometric shape on the ticket, like

***
**
*

in a corner -- because it seems "doubly unlikely".

Of course the likelyhood of that winning is ther same as 1,2,3,4,5,6 or 35,32,18,16,28,21 or any other sequence, but apparently if you DO win your pot is less likely to be split. And fewer people would do so to make a point, unlike 1,2,3,4,5,6.
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Old 30th January 2012, 02:50 PM   #9
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What are the chances that all the numbers for a couple major lotteries could be found in a random 1000-digit block of pi?


Pretty good so far, as it turns out.
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Old 30th January 2012, 03:01 PM   #10
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Every possible set of numbers has exactly the same probability of being drawn. About the only thing you could count on is a lottery drawing the same set of numbers as they had drawn previously. That would be like doubly astronomically impossible.
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A text message was found to have been sent at 8:35PM of November 1st by KNOX's number to that of her co-defendant Patrick, in which she wrote "Ci vediamo dopo" ["See you later" or lit: "We'll see each other after"] thus confirming that in the following hours KNOX would find herself with Patrick in the apartment where the victim was. -- Prosecutor Giuliano Mignini (Order for arrests)

Last edited by Dan O.; 30th January 2012 at 03:04 PM.
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Old 30th January 2012, 03:53 PM   #11
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In a 6/49 lottery the combinations that have some sort of obvious looking pattern or sequence count for only a very small number of the 14 million possible combinations so it's more likely that a draw won't have any obvious sequence but every combination has an equal chance of showing up.

Another way of looking at it and shows how unlikely it is to win the lottery is that any random sequence you select has exactly the same odds of being drawn as 1,2,3,4,5,6

The best you can do if you do play is to choose a sequence that is less likely to be chosen by other people so that if you do win then you share the jackpot with fewer people, so don't use birthdays/use at least 1 number above 31, avoid making lines and patterns on the ticket or having incremental steps of your numbers.

Another thing is that instead of playing every draw, playing 2 tickets every second draw or 10 tickets every ten draws etc. increases your chances slightly though if you do that and play the same numbers each time it could be a bit disappointing if one of your tickets comes up in the draws you don't play in so maybe better to choose different numbers each time you play instead.
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Old 30th January 2012, 05:55 PM   #12
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I figure the longer I go without ever once participating in the lottery, the better the odds are that the day I do I will be the winner of hundreds of millions of dollars. Yep.
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Old 30th January 2012, 05:57 PM   #13
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Originally Posted by kajata View Post
Not only is it the same but if you won you'd probably share the jackpot with thousands of other people who play those numbers to make a point to their friends at the convenience store.
This is the problem using obvious number combinations with shared pots.
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Old 30th January 2012, 06:00 PM   #14
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Originally Posted by alexi_drago View Post
... though if you do that and play the same numbers each time it could be a bit disappointing if one of your tickets comes up in the draws you don't play in so maybe better to choose different numbers each time you play instead.


"Quick Picks" exist for a reason!
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Old 30th January 2012, 06:02 PM   #15
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Originally Posted by alexi_drago View Post
In a 6/49 lottery the combinations that have some sort of obvious looking pattern or sequence count for only a very small number of the 14 million possible combinations so it's more likely that a draw won't have any obvious sequence but every combination has an equal chance of showing up.

Another way of looking at it and shows how unlikely it is to win the lottery is that any random sequence you select has exactly the same odds of being drawn as 1,2,3,4,5,6

The best you can do if you do play is to choose a sequence that is less likely to be chosen by other people so that if you do win then you share the jackpot with fewer people, so don't use birthdays/use at least 1 number above 31, avoid making lines and patterns on the ticket or having incremental steps of your numbers.

Another thing is that instead of playing every draw, playing 2 tickets every second draw or 10 tickets every ten draws etc. increases your chances slightly though if you do that and play the same numbers each time it could be a bit disappointing if one of your tickets comes up in the draws you don't play in so maybe better to choose different numbers each time you play instead.
There are number wheels that give you slightly better odds playing. So for example you can play 7 numbers in a 6 number game and cover most combinations so that instead of playing with 6 numbers you are essentially playing with 7. But it's expensive just to cover that many combinations so most of the wheels give you 3 or 4 numbers picked if any of the 7 are drawn. The increase in odds is so tiny however, it may not be worth the extra effort.
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Old 30th January 2012, 06:33 PM   #16
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Originally Posted by alfaniner
What are the chances that all the numbers for a couple major lotteries could be found in a random 1000-digit block of pi?
Or even that the beginning of pi could be found in pi?

pi = 3.1415926...19729715941700531415926095214704122509...

Position 50,366,472.

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Old 30th January 2012, 06:36 PM   #17
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Originally Posted by Halfcentaur View Post
I figure the longer I go without ever once participating in the lottery, the better the odds are that the day I do I will be the winner of hundreds of millions of dollars. Yep.
Yep, don't play for 14 million draws and save the price of a ticket each time, then wait for the jackpot to exceed 14M and use your savings, guaranteed win, you might get unlucky and have to share it though. There was someone who did that (well not save up each draw), there were 3 winners but with all the lower prizes he still made off it.

Originally Posted by Horatius
"Quick Picks" exist for a reason!
There is that but
Originally Posted by Skeptic Ginger
There are number wheels that give you slightly better odds playing. So for example you can play 7 numbers in a 6 number game and cover most combinations so that instead of playing with 6 numbers you are essentially playing with 7. But it's expensive just to cover that many combinations so most of the wheels give you 3 or 4 numbers picked if any of the 7 are drawn. The increase in odds is so tiny however, it may not be worth the extra effort.
the wheels can be used to slightly improve the odds on the lower prizes although it is tiny and it won't make any difference to the chances on the jackpot other than the number of tickets your playing. Might be worth it for a syndicate to do some wheeling instead of having each person make up their own numbers.
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Old 30th January 2012, 06:43 PM   #18
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As has been mentioned repeatedly, yes, you're right, any given set of 6 numbers in a fair lottery is equally likely to occur.

What is true, however, is that any set of 6 numbers with a simple pattern is less likely to occur than one of the sets of 6 numbers with no obvious pattern. Obvious might not be the best adjective, but there are far more combinations of the (3, 8, 22, 24, 37, 45) variety (i.e. no obvious pattern) than there are of the (1, 3, 5, 7, 9, 11) variety. There are an awful lot of obvious patterns, to be sure, but there are far more sets that have none.
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Old 30th January 2012, 06:48 PM   #19
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Originally Posted by Skeptic Ginger View Post
There are number wheels that give you slightly better odds playing. So for example you can play 7 numbers in a 6 number game and cover most combinations so that instead of playing with 6 numbers you are essentially playing with 7. But it's expensive just to cover that many combinations so most of the wheels give you 3 or 4 numbers picked if any of the 7 are drawn. The increase in odds is so tiny however, it may not be worth the extra effort.
If the game is fair, there's no way to increase your chances of winning aside from playing more times. Any given ticket is as likely as any other to win. I had to look up "lottery wheels," to be honest, but they just appear to be a mechanism for generating lots of lottery combinations.
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Old 30th January 2012, 07:26 PM   #20
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I've heard that the odds of winning the lottery are about the same whether you buy a ticket or not.
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Old 30th January 2012, 07:33 PM   #21
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Originally Posted by Skeptic Ginger View Post
There are number wheels that give you slightly better odds playing. So for example you can play 7 numbers in a 6 number game and cover most combinations so that instead of playing with 6 numbers you are essentially playing with 7. But it's expensive just to cover that many combinations so most of the wheels give you 3 or 4 numbers picked if any of the 7 are drawn. The increase in odds is so tiny however, it may not be worth the extra effort.
I think I know what you're talking about. Here's one I came up with years ago...

Pick 12 numbers: A B C D E F G H I J K L

Play these games...

Game 1: A B C D E F
Game 2: A B C D G H
Game 3: A B E F G H
Game 4: C D E F G H
Game 5: A B C E G I
Game 6: A B D F G I
Game 7: A B D E H I
Game 8: A B C F H I

If all six numbers fall within the twelve numbers chosen, you're guaranteed a 5-number win.

But I never play this system. The greatly improved odds on the rare occasions all six numbers fall within your chosen twelve are offset by the greatly reduced odds (compared to 8 random games) when they don't, so there's no real advantage.
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Old 30th January 2012, 07:36 PM   #22
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Originally Posted by Skeptic Ginger View Post
There are number wheels that give you slightly better odds playing.
Is a number wheel the same thing as what we call "systems" lotto?

In systems lotto you select more than 6 numbers which is equivalent to playing more lotto tickets.
A system 7 is equivalent to 7 tickets (7C6 = 7)
A system 8 is equivalent to 28 tickets (8C6 = 28)
etc.

You can also play a system 5 where one of the drawn numbers is a given or a system 4 where 2 of the drawn numbers are a given etc.
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Old 30th January 2012, 07:57 PM   #23
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Originally Posted by psionl0 View Post
Is a number wheel the same thing as what we call "systems" lotto?

In systems lotto you select more than 6 numbers which is equivalent to playing more lotto tickets.
A system 7 is equivalent to 7 tickets (7C6 = 7)
A system 8 is equivalent to 28 tickets (8C6 = 28)
etc.

You can also play a system 5 where one of the drawn numbers is a given or a system 4 where 2 of the drawn numbers are a given etc.
not entirely, your system 7 and 8 there guarantee the jackpot if the 6 numbers appear within the 7 or 8, most wheels are designed to give the lower prizes, like guaranteeing 3 or 4 numbers in one line if the 6 drawn numbers are from something like a pool of 18 numbers, and yes, they can also have key numbers included.

Here's one way of making money off wheeling:

http://www.lotterywheels.com/wheel_list.htm#6
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Old 30th January 2012, 08:11 PM   #24
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Originally Posted by alexi_drago View Post
Here's one way of making money off wheeling:

http://www.lotterywheels.com/wheel_list.htm#6
You mean charging people $29.95 for the software?
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Old 30th January 2012, 08:14 PM   #25
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Originally Posted by Brian-M View Post
You mean charging people $29.95 for the software?
Charging over $500 for a wheel that could probably be made in a $29.95 piece of software.
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Old 30th January 2012, 08:17 PM   #26
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Originally Posted by Undesired Walrus View Post
For years, I've been telling people that it's as likely for you to get the above numbers as something like 35,32,18,16, 28, 21.

People can't seem to believe it. Is this actually the case, or am I making a fool of myself?

I think I might have a theory on why people find this so hard to believe.


Obviously, the odds of drawing any specific set of numbers is identical to drawing any other specific set of numbers and I think people understand this. At the same time, I think people understand that the odds are much lower of drawing a "specific set" than a "random set". (This relates to the birthday paradox). Indeed with a game like Lotto the odds of drawing "any random set" are 1, whereas the odds of drawing a specific set are very very small.

I think where people come undone is that they think of a set with a clear pattern as "specific" but if they randomly select numbers, they think of it in terms of "any random set". Thus think their set has greater chance than a specific set with a recognised pattern. Of course, the moment you have a set, whether selected from a pattern or selected at random, it becomes a specific set, and therefore has equal odds of being drawn. I think a lot of people can't get this distinction through their head (indeed, it's the reason behind the birthday paradox).

It's kind of like people who refer to the statistical probability of an event that already happened and use it to argue that the event didn't happen (i.e. something else happened). This is quite popular with conspiracy theorists.
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Old 30th January 2012, 08:31 PM   #27
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4 years ago this combination came out at loto-québec's 649.

23, 40, 41, 42, 44, 45

http://img339.imageshack.us/img339/5715/loto.jpg

Normaly the prize in the 5/6+ category is shared by 2-3 persons. That week 239 persons had to share the 5/6+ prize.

That proves, I guess, that a lot of people choose consecutive numbers and that this method is worse that choosing random numbers.

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Old 30th January 2012, 08:41 PM   #28
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Originally Posted by Paul2 View Post
I've heard that the odds of winning the lottery are about the same whether you buy a ticket or not.

Not even close...
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Old 30th January 2012, 08:42 PM   #29
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http://www.lotterywheels.com/informa...ling%20system?

Now I get it. A "full wheel" is indeed equivalent to "systems" lotto while an "abbreviated" wheel doesn't include all combinations.
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Old 30th January 2012, 08:47 PM   #30
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Originally Posted by gumboot View Post
I think where people come undone is that they think of a set with a clear pattern as "specific" but if they randomly select numbers, they think of it in terms of "any random set".
It's the same reasoning that people think that the odds of tossing 6 heads in a row is less than tossing 5 heads and 1 tail. This is true if it doesn't matter which toss is the tail.

However, tossing 5 heads followed by 1 tail is the same as tossing 5 heads followed by 1 head.
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Old 30th January 2012, 08:53 PM   #31
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May be I'm missing something but G H I J K L only gives a maximum of 2 correct numbers - not 5 as claimed?


Originally Posted by Brian-M View Post
I think I know what you're talking about. Here's one I came up with years ago...

Pick 12 numbers: A B C D E F G H I J K L

Play these games...

Game 1: A B C D E F
Game 2: A B C D G H
Game 3: A B E F G H
Game 4: C D E F G H
Game 5: A B C E G I
Game 6: A B D F G I
Game 7: A B D E H I
Game 8: A B C F H I

If all six numbers fall within the twelve numbers chosen, you're guaranteed a 5-number win.
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Old 30th January 2012, 08:57 PM   #32
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Originally Posted by Paul2 View Post
I've heard that the odds of winning the lottery are about the same whether you buy a ticket or not.
There is more than one prize. What about the odds of winning 100$, 50$ or 20$ ?
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Old 30th January 2012, 10:06 PM   #33
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Originally Posted by jasonpatterson View Post
As has been mentioned repeatedly, yes, you're right, any given set of 6 numbers in a fair lottery is equally likely to occur.

What is true, however, is that any set of 6 numbers with a simple pattern is less likely to occur than one of the sets of 6 numbers with no obvious pattern. Obvious might not be the best adjective, but there are far more combinations of the (3, 8, 22, 24, 37, 45) variety (i.e. no obvious pattern) than there are of the (1, 3, 5, 7, 9, 11) variety. There are an awful lot of obvious patterns, to be sure, but there are far more sets that have none.
No.
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Old 30th January 2012, 10:07 PM   #34
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Originally Posted by jasonpatterson View Post
If the game is fair, there's no way to increase your chances of winning aside from playing more times. Any given ticket is as likely as any other to win. I had to look up "lottery wheels," to be honest, but they just appear to be a mechanism for generating lots of lottery combinations.
No.

You don't seem to understand probability.
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Old 30th January 2012, 10:08 PM   #35
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Originally Posted by Paul2 View Post
I've heard that the odds of winning the lottery are about the same whether you buy a ticket or not.
If you round off.
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Old 30th January 2012, 10:16 PM   #36
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Originally Posted by Brian-M View Post
I think I know what you're talking about. Here's one I came up with years ago...

Pick 12 numbers: A B C D E F G H I J K L

Play these games...

Game 1: A B C D E F
Game 2: A B C D G H
Game 3: A B E F G H
Game 4: C D E F G H
Game 5: A B C E G I
Game 6: A B D F G I
Game 7: A B D E H I
Game 8: A B C F H I

If all six numbers fall within the twelve numbers chosen, you're guaranteed a 5-number win.

But I never play this system. The greatly improved odds on the rare occasions all six numbers fall within your chosen twelve are offset by the greatly reduced odds (compared to 8 random games) when they don't, so there's no real advantage.
(Are you sure about your wheel? Because getting 5 numbers in 8 games of 12 numbers seems much better odds than I recall. We have a 6 number game and I believe one can play 7 numbers and guarantee 4 with 4 plays. But never mind that question, I'll take your word for it for this discussion that your wheel is correct.)

Anyway, let's think about this. In each of the 8 games you have an equal chance of winning be it 5 numbers or 6.

So that would suggest you have the same odds as a quick pick. But you are playing 12 numbers rather than 6 numbers. I do believe that gives one better odds.
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Old 30th January 2012, 10:19 PM   #37
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Originally Posted by Brian-M View Post
You mean charging people $29.95 for the software?
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Old 30th January 2012, 10:21 PM   #38
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Originally Posted by Matty1973 View Post
May be I'm missing something but G H I J K L only gives a maximum of 2 correct numbers - not 5 as claimed?
I think you are right.
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Old 30th January 2012, 10:29 PM   #39
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Originally Posted by Brian-M View Post
I think I know what you're talking about. Here's one I came up with years ago...

Pick 12 numbers: A B C D E F G H I J K L

Play these games...

Game 1: A B C D E F
Game 2: A B C D G H
Game 3: A B E F G H
Game 4: C D E F G H
Game 5: A B C E G I
Game 6: A B D F G I
Game 7: A B D E H I
Game 8: A B C F H I

If all six numbers fall within the twelve numbers chosen, you're guaranteed a 5-number win.
I don't think that can be right.

There are 792 combinations of 5 choices represented by the 12 numbers.

Each Game you pick covers only 6 combinations of 5 choices, giving you at most 48 choices for the eight games.

Unless I've missed something here, you can cover eight numbers with ten games, or seven numbers with four games. You can't cover twelve numbers with eight games.

EDIT: I realized my mistake. Of the 792 combinations, six of them will be represented in the lotto draw. So you only need to cover, optimally, 132 combinations, which means you can do it picking just 22 games.
Similarly, you can theoretically cover ten numbers with eight games. That factor of 6 really makes a difference.

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Old 31st January 2012, 04:54 AM   #40
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Originally Posted by Matty1973 View Post
May be I'm missing something but G H I J K L only gives a maximum of 2 correct numbers - not 5 as claimed?
Sorry, I got a 9 number system mixed up with a 12 number system - the absence of J, K and L in the games should have tipped me off to the mistake. I should have written...

Pick 9 numbers: A B C D E F G H I

Play these games...

Game 1: A B C D E F
Game 2: A B C D G H
Game 3: A B E F G H
Game 4: C D E F G H
Game 5: A B C E G I
Game 6: A B D F G I
Game 7: A B D E H I
Game 8: A B C F H I

If all six numbers fall within the nine numbers chosen, you're guaranteed a 5-number win.
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