Welcome Guest
You last visited December 6, 2016, 9:00 am
All times shown are
Eastern Time (GMT-5:00)

# POLL - On The Whole Do The Lotteries Provide Truly Random Numbers?

Topic closed. 104 replies. Last post 6 years ago by Hermanus104.

 Page 5 of 7

From Quick Picks to Winning Numbers, Are We Getting Truly Random Numbers from the Various Lotteries?

 Yes [ 29 ] [29.59%] No [ 52 ] [53.06%] Don't know/Don't care/Doesn't matter to me [ 11 ] [11.22%] Other [ 6 ] [6.12%] Total Valid Votes [ 98 ] Discarded Votes [ 1 ]
Michigan
United States
Member #22395
September 24, 2005
1583 Posts
Offline
 Posted: August 11, 2010, 2:57 pm - IP Logged

Imagine the winning numbers were drawn before sales started and kept secret until sales ended, and the RNG only chose from 20% of the possible combinations. If the winning numbers weren't in that 20% you'd have a valid argument that the ticket was invalid and had no chance of winning. OTOH, if the winning numbers were in that 20% you'd be 5 times as likely to win. As a practical matter we could expect the winning numbers to be in that 20% 1 out of 5 times, and being 5 times as likely to win in 20% of the drawings would balance the 0% chance in the other 80%. There might be instances where there were more winners of parimutuel prizes than expected by probability, but overall the chances of winning would be exactly the same as when the RNG uses all of the possible combinations.

Unfortunately for the hypothetical lawsuit the winning combination doesn't exist until after all of the tickets have been sold. Winning the lottery isn't a case of buying a ticket that matches the winning combination. It's a matter of having them draw a winning combination that matches your ticket. Regardless of what percentage of the combinations might turn up on your QP, once you buy it the chance that the winning combination will match your ticket is determined solely by  the odds of the game. That means that every ticket is valid, and the lottery advertising accurately stated your odds of winning.

You know I hardly ever disagree with your analysis?

When I said the terminal only had 500,000 possibles, I really meant, none of the terminals have 100% of all the numbers available.  The reason might be irrelevant but let's say it is because they couldn't access all possible combinations and produce a ticket in a reasonable time.

So, you think, it is OK to buy a ticket, even though the number has not yet been drawn that does not stand a chance to win - once the number is chosen?  We already know the whole amount of possible numbers - that is not a secret.  It just hasn't been drawn.  Yes, I agree that every ticket should be valid going in - and there is no guarantee that any ticket would have won, had all combinations been available.  But it is also possible that my ticket could have the winning number if the complete combinations were available.  And it is also a fact that the store where I bought the ticket could not sell me the winning ticket under any circumstances because of the limitation of the terminal.

On the scratchoffs, they now tell you when the grand prize has been won.  Not sure if they pull the game and recall all the tickets at that point or not.  BUT if you decide to play a ticket knowing the grand prize has been given out - that is OK.   Previously they did not inform anyone the grand prize had been won and there were lawsuits.  And that was not OK.  The location of the winning scratch-off ticket is unknown to the player.  The location of the winning scratch-off ticket is unknown to the Lottery commision.  For all practical purposes, it is the same as a number that has not been drawn yet.   I at least know it exists.  It may very well not be in the particular store where I bought the ticket - but it exists.  In the MM example, every store should be capable of offering the winning combination.

Michigan
United States
Member #22395
September 24, 2005
1583 Posts
Offline
 Posted: August 11, 2010, 3:42 pm - IP Logged

You know I hardly ever disagree with your analysis?

When I said the terminal only had 500,000 possibles, I really meant, none of the terminals have 100% of all the numbers available.  The reason might be irrelevant but let's say it is because they couldn't access all possible combinations and produce a ticket in a reasonable time.

So, you think, it is OK to buy a ticket, even though the number has not yet been drawn that does not stand a chance to win - once the number is chosen?  We already know the whole amount of possible numbers - that is not a secret.  It just hasn't been drawn.  Yes, I agree that every ticket should be valid going in - and there is no guarantee that any ticket would have won, had all combinations been available.  But it is also possible that my ticket could have the winning number if the complete combinations were available.  And it is also a fact that the store where I bought the ticket could not sell me the winning ticket under any circumstances because of the limitation of the terminal.

On the scratchoffs, they now tell you when the grand prize has been won.  Not sure if they pull the game and recall all the tickets at that point or not.  BUT if you decide to play a ticket knowing the grand prize has been given out - that is OK.   Previously they did not inform anyone the grand prize had been won and there were lawsuits.  And that was not OK.  The location of the winning scratch-off ticket is unknown to the player.  The location of the winning scratch-off ticket is unknown to the Lottery commision.  For all practical purposes, it is the same as a number that has not been drawn yet.   I at least know it exists.  It may very well not be in the particular store where I bought the ticket - but it exists.  In the MM example, every store should be capable of offering the winning combination.

I started thinking about what I wrote for scratch-offs.  It seems to me that the lotteries are misstating the full odds of winning a scratch-off grand prize.

If the lottery says the scratch-off grand prize odds are 1 out of a million, isn't that false?

If they issued a million of those tickets, that is correct.  But then you have sort of a different lottery to play.  That grand prize is only sitting in one store.  If there are 10,000 lottery stores, don't you have to add in an additional 10,000 to one?  You can't possibly win if you go to the wrong stores.

Santa Ana
United States
Member #71159
February 20, 2009
651 Posts
Offline
 Posted: August 11, 2010, 11:34 pm - IP Logged

I just contacted the headquarters @ CA Lottery and ask the same question and receive, belive it or not an letter with a weird explaination how they randomly pick the numbers; all I know is CA Lottery is not very good in rotating numbers fast enough--it's driving me to sheer frustration playing the same numbers over and over and not get one or bearly two numbers.  However, I know the minute I stop, that is when they will hit!!

Northern Virginia
United States
Member #83350
December 5, 2009
1315 Posts
Offline
 Posted: August 12, 2010, 4:04 am - IP Logged

My opinion is that some states have draws that are more random than others....................and some states have stats that are more crooked than others.

Here are some stats that do not appear random from Pennsylvania's midday computer draw:

 06/06/2010 1   0   6 Payout 03/15/2009 1   0   6 Payout 02/19/2009 1   0   6 Payout 02/10/2009 1   0   6 Payout 01/28/2009 1   0   6 Payout 09/05/2008 1   0   6 Payout
 02/18/2010 1   6   2 Payout 11/11/2009 1   6   2 Payout 02/24/2009 1   6   2 Payout 01/13/2009 1   6   2 Payout 01/02/2009 1   6   2 Payout 02/20/2008 1   6   2 Payout
 07/31/2004 1   4   6 Payout 06/29/2004 1   4   6 Payout 02/06/2004 1   4   6 Payout 11/01/2003 1   4   6 Payout 09/13/2003 1   4   6 Payout

 11/18/2009 5   5   1 Payout 09/23/2009 5   5   1 Payout 06/25/2009 5   5   1 Payout 03/19/2009 5   5   1 Payout 02/13/2009 5   5   1 Payout

Whether you use a computer or balls to generate numbers, in a set of truly random numbers there are going to be anomalies like these. Virginia uses balls, and they drew "137" five times in just under 200 drawings in 1994, including two days in a row:

04-23-1994 (Sat): 137

05-23-1994 (Mon): 137

05-24-1994 (Tue): 137

08-02-1994 (Tue): 137

11-28-1994 (Mon): 137

In addition, Virginia once produced the same number 4 times in the same month:

11-03-03 (Mon, eve): 618

11-11-03 (Tue, eve): 618

11-19-03 (Wed, day): 618

11-25-03 (Tue, day): 618

Last year in Texas (another ball state), three out of four consecutive evening drawings picked "277":

07-23-2009 (Thu, eve): 277

07-24-2009 (Fri, eve): 277

07-25-2009 (Sat, eve): 604

07-26-2009 (Sun, eve): no draw

07-27-2009 (Mon, eve): 277

One of my favorites is the following from Kentucky (also a ball state)

09-24-2007 (Mon, day): 484

09-25-2007 (Tue, day): 484

09-26-2007 (Wed, eve): 484

Today's winning 3-ball is going to be a number between 000 and 999.

In a lot of states, lotteries benefit education. That makes the REAL winners the only people who can't play!

San Angelo, Texas
United States
Member #1097
January 31, 2003
1394 Posts
Offline
 Posted: August 12, 2010, 10:16 am - IP Logged

I think it would be interesting if a member of LP would explain to the general audience HOW random number generators function.

Personally, I don't think the RNG in the terminal where I buy my QPs scans the total number of combinations available for the
game I'm playing.

The clerk punches the buttons that tell the machine to generate 5 QPs, for example, and Presto, the machine spits out a
ticket with 5 lines.

I've stood behind folks buying 100 QPs. It took some time for the machine to complete the task, but I think thats afunction
of the machine, not the RNG.

We had a situation here in Texas years ago where a player complained about getting the same numbers on two lines on the
same ticket. Lottery folks more or less said that exact duplicates are possible because the RNG 'doesn't know where it's been
or where it's going, so to speak.

Te RNG resets after each line, meaning anything is possible. No record of the combinations sold is available at the terminal.

I believe the combinations sold are logged at lottery headquarters, but that's a one way street. That is, the terminals can't
scan the 'sold files' to avoid selling a combination more than once. This allows the lottery to quickly determine if a winning combination
has been sold.

In Texas, the lottery can determine whether or not there is a winner within a small time frame. In order to do this, they must
have access to a central file of combinations in play for a specific drawing.

Atlanta, GA
United States
Member #1265
March 13, 2003
3333 Posts
Offline
 Posted: August 12, 2010, 11:02 am - IP Logged

Random Number Generator = Rigged Number Generator(S)

With computers they can analyze all wagers and payout however they please.  They do this with computerized Keno.   They can do what ever they want with outcomes.

YOU MUST PLAY GAMES WITH BALLS!  BALLS ARE FREE OF SOFTWARE!  ALL BALLS FOREVER!

About the only factor that influences ball drop draws is 'number affiinities' which is an anomaly even the best of 'em haven't been able to figure out why it happens.  Number affinities is when certain numbers seem to be drawn with other numbers more frequently for a given time.

Good luck to everyone!

Texas city,tx
United States
Member #50125
February 26, 2007
201 Posts
Offline
 Posted: August 23, 2010, 11:04 pm - IP Logged

no.

United States
Member #83701
December 13, 2009
225 Posts
Offline
 Posted: August 24, 2010, 12:53 pm - IP Logged

Missouri Lottery gives inside view of computerized drawings.  10:54 am - The Missouri Lottery takes viewers on a tour of their computerized drawing facilities and procedures.

Hello:  I don't believe it's random, check this out.

Feb. 14th, 2010  485

Feb. 19th, 2010 584

Feb.20th, 2010 548

All within 7 days,  14 draws.

Feb. 22, 2010 555

Is that random or programmed?

You can watch that video again.

lmaoooooooooooooooooooooooooooooooooooooo

Good Luck.

Very unsatisfactory.   Physical security, background checks, auditing and monitoring, that's a given.   But what are the RNG algorithms?   Are they Merseille Twisters.   It looks like a Windows platform so is it the CryptGenRandom libraries?   Microsoft has a history of using lawyers to define their code as satisfactory instead of actually writing good code, saying that the software has been verified means very little, who verified it? How was it verified?   All Quasirandom algorithms are far more distribution focused then random sequences from physical sources and for computer modeling that's a plus but the fact remains, it's different and potentially predictable.

They need to open source the software.

United States
Member #47420
November 4, 2006
3930 Posts
Offline
 Posted: August 24, 2010, 2:14 pm - IP Logged

Right now the poll shows 58.3% don't believe the numbers are true and fair..These people should not be playing the lottery if they don't trust it..Buy your ticket win or lose and stop complaining about it..Find some other form of gambling if you "need" to gamble..

United States
Member #83701
December 13, 2009
225 Posts
Offline
 Posted: August 24, 2010, 2:25 pm - IP Logged

I think it would be interesting if a member of LP would explain to the general audience HOW random number generators function.

Personally, I don't think the RNG in the terminal where I buy my QPs scans the total number of combinations available for the
game I'm playing.

The clerk punches the buttons that tell the machine to generate 5 QPs, for example, and Presto, the machine spits out a
ticket with 5 lines.

I've stood behind folks buying 100 QPs. It took some time for the machine to complete the task, but I think thats afunction
of the machine, not the RNG.

We had a situation here in Texas years ago where a player complained about getting the same numbers on two lines on the
same ticket. Lottery folks more or less said that exact duplicates are possible because the RNG 'doesn't know where it's been
or where it's going, so to speak.

Te RNG resets after each line, meaning anything is possible. No record of the combinations sold is available at the terminal.

I believe the combinations sold are logged at lottery headquarters, but that's a one way street. That is, the terminals can't
scan the 'sold files' to avoid selling a combination more than once. This allows the lottery to quickly determine if a winning combination
has been sold.

In Texas, the lottery can determine whether or not there is a winner within a small time frame. In order to do this, they must
have access to a central file of combinations in play for a specific drawing.

An RNG is a number sequence.   The very earliest versions were just counters.   If you remember the 70's, you may have remembered early handheld electronic games where a number would be flashing very quickly till you hit a button and then it would freeze on the result, you saw this in handheld dice games and Blackjack games.   There the RNG there is simply counting.

A common RNG sequence is to take the seed, multiply it by a very large number and then add a very large number to it, this is called the Linear Congruential  Generator.   The LCG is what's usually used in the operating system and the compilers so if the programmer just makes a random() call, this is what it is.   There's a good chance that the RNG used is a LCG with the multiplier being 214013 and the additive value being  2531011 if Microsoft Visual C, or C++ was used for the program.   This actually provides very good results but isn't considered acceptable for cryptography.   THe LCG exhibits several defects and aligns numbers predictably along certain planes.  If it is used for the lottery, it would be possible to exploit the lottery.

You see the idea of a large number a lot, the concept of a large number and often it's the product of two large prime numbers often referred to as p and q hence the large number M=pq.   Why prime numbers, the idea is that it takes time for people to find a large prime number so the assumption is that it would take time for people to figure out which it is.   The Blum Blum Shub generator is x(n+1)=x(n)^2 mod M where M=pq.   The Blum Blum is not suitable for simulations but is suitable for cryptography because it is slow and computationally intensive.   The Fibonacci algorithm has been called Nature's random number generator, it is x(n) = x(n-1) + x(n-2); variations of this was used by Thinking Machines for it's computers since those computers were often used for modeling natural systems.

All sequences have a starting point and an internal state.   The internal state is called a seed and selecting the starting point is seeding the entropy.   They attempt to seed from factors that are accepted as unpredictable by the program.   The Microsoft CryptGenRandom which is the most likely suspect for the RNG used, seeds from the process number, the thread number, a hash of the user environment such as user name, machine name, the tick count, current time etc. but it doesn't seed very often.   All of those factors are external factors and could be manipulated in some fashion.   The CryptGenRandom libraries also uses the RC4 hash for the sequence which can be run backwards as well as forwards so all that is needed is to determine the internal state at any point in time then you can run it forwards or backwards till you are in sync.   The Hebrew University developed an attack called Cryptanalysis which is a tool for doing just that but you have to somehow tap the internal state, with Microsoft, the code runs in user space so a simple trojan horse could grab the state quite easily.   It's likely that the lotteries use the CryptGenRandom libraries to get around weaknesses with the LCG as that would be what Microsoft would tell them to do but then it should be possible to use historical data to predict future outcomes provided enough historical data existed between entropy seeding.  Such a RNG exploit would be most advantageous for Keno where the program may be kept running through the entire day, preferably non-stop as might be the case in a Casino.   One such exploit was used by a Casino insider in Vegas but he actually stole the software that was used and then worked out equations to try and sync the sequences (brute force would take too long).   If one knew how the symbols of a scratchoff was determined by an RNG then this approach might work on scratchers like Bingo games where many of the symbols are visible prior to scratching.

In the video, you see the girl closing programs for various draws so it's possible that they reseed from entropy (i.e.: restart the program) for each draw but not for the testing that  they showed which actually makes the Chi Square testing results irrelevant except within a given draw.

One aspect about seeding from multiple sources of entropy is that as the number of sources approach infinity, the distribution approaches a normal distribution (aka a bell curve).   The more sources of entropy, the smaller the standard deviation (the narrower the bell curve).   Usually some kind of hash or scrambler is needed to deal with this tendency.

The absolute best RNG's are called Quasirandom sequences and are not mathematically defined but arbitrarily predefined sequences either recorded from nature or initially generated with a RNG and then manually tweaked to address the defects.   An example of this would be a diplomatic encryption pad which is the same length as the message.   Such pads are hand carried to our embassies and consulates.   Modems use a very short predefined sequence called a scrambler to remove the periodicity of the english language expressed in ASCII, this is common in all telecommunications.   The scrambler is to "whiten" the spectrum.

If I had to guess, the Quickpicks are by a low quality RNG such as the LCG but the draws would likely be from a MicroSoft blessed RNG like CryptGenRandom.   The seeding from entropy may make the draws subject to certain attractors which I've observed when seeding Fibonacci sequences from the system's LCG sequence.   The chi square testing that they do would not detect this tendency but would satisfy legal requirements for randomness.   Of course, I've only put a cursory effort into my programs, if I was paid, I would be far more thorough (gone are the hacker days where pizza and Coke Classic were the prime motivators).

United States
Member #83701
December 13, 2009
225 Posts
Offline
 Posted: August 24, 2010, 2:44 pm - IP Logged

I started thinking about what I wrote for scratch-offs.  It seems to me that the lotteries are misstating the full odds of winning a scratch-off grand prize.

If the lottery says the scratch-off grand prize odds are 1 out of a million, isn't that false?

If they issued a million of those tickets, that is correct.  But then you have sort of a different lottery to play.  That grand prize is only sitting in one store.  If there are 10,000 lottery stores, don't you have to add in an additional 10,000 to one?  You can't possibly win if you go to the wrong stores.

Yes, this is why I like what Texas does with their Scratchoff's.   They publish the number of claimed prizes as well as the number of prizes printed in each category and the total number of prizes printed updated on a daily basis.   A game that may have been initially 1 in a million for the top prize will often be 1 in 650,000 before another top prize is claimed.

Now, I would like to be able to get the addresses of the stores where the winning tickets were purchased, that should define the delivery routes most likely to have the larger prizes as mechanical shuffling have been proven to not be very random.   There should be a stark difference in the distribution of high valued winning tickets and the distribution of low valued winning tickets.   Mind you with computerized inkjet printing, they may no longer need to mechanically shuffle the hot packs with the cold before delivery in which case you wouldn't be able to identify any hot routes.

If you do the math, because the million tickets are divided into the 10,000 stores the odds when you factor in the stores work out back to a million because each store only has 1/10,000 of a million tickets.   It cancels itself out. It looks something like 1/10,000 * 1/(1,000,000/10,000) + 9,999/10,000 * 0/(1,000,000/10,000).   But you're right, you can't win if you go to the wrong stores.   Lucky stores count with scratchers but not with pick games.

United States
Member #83701
December 13, 2009
225 Posts
Offline
 Posted: August 24, 2010, 2:56 pm - IP Logged

Right now the poll shows 58.3% don't believe the numbers are true and fair..These people should not be playing the lottery if they don't trust it..Buy your ticket win or lose and stop complaining about it..Find some other form of gambling if you "need" to gamble..

Some people will be buying because they believe that it isn't random and they know how to predict the next set of numbers and hence it can be unfair to their advantage.

Some people will be buying because they think that it is random and that it is therefore fair.

Some people will be buying because they think that it isn't random but it isn't systematically predictable and hence is fair.

Some people will buy it for the fun of it.

United States
Member #83701
December 13, 2009
225 Posts
Offline
 Posted: August 24, 2010, 3:11 pm - IP Logged

You can sue anybody for any thing. Fill out the papers and pay the fee, and the process starts.

The real question is will the suit be dismissed quickly or will it continue? What *exactly* would you sue the lottery for? "Not being able to generate every possible combination" isn't a cause of action in itself. OTOH, if the lottery claims that the RNG generates random combinations and it doesn't* there might be a cause of action. If they know it can't generate them all they may be committing fraud if the court believes they claimed it was possible. If they don't know, or if any given RNG is malfunctioning they might be found negligent.

The next question is what damage you suffered and how much they owe you as compensation, and that's the problematic part. Whatever the deal is with the RNG, when it spits out the ticket there is no winning number for it to match. Once the winning numbers are selected there's a chance it will match the numbers on your ticket regardless of how few of the possible combinations the RNG could have given you. You'll never be able to prove that you would have won something if the RNG could have generated combinations from a larger pool, so your maximum loss is limited to the cost of the ticket(s) you bought.

About the only realistic possibility I see would be if you shared a parimutuel prize with an unexpectedly large number of winners because a significant percentage of the RNG's only generated a limited set of the possible combinations. In that case probability would demonstrate the amount of the damage. You'd still have to prove that the lottery had failed to meet some obligation to you. In the past, NY advertised benefits of playing QP's. I believe one of th eclaimed benefits was that  the comb9inations played would be more random (no concentration of birthday numbers, for example) and that jackpots would be less likely to be shared. If they made that promise and failed to deliver you might have a good case. Note that you would have to prove the RNGs were defective, not just that there were more winners than suggested by probability.

*Note that the numbers aren't ever truly random, in that they are limited to those that are used in the game. Obviously the RNG shouldn't randomly spit out numbers that aren't in the matrix. If an RNG was programmed so that it could only generate 20% of the possible combiantions it could still generate randomly from within that 20%. What is an advertiser actually promising you if they simply say you'll get a combination that is random?

If I was to sue, I would argue that Buying a ticket with a certain number of lines was buying a certain number of chances at various prizes.   If the numbers that the machine chose were identical or overlapped then I would not have received as many chances for my money as I would've had they be different.

For example,  imagine a pick 6 game where the lowest value subsidiary prize was awarded for a 3/6 match.   The two tickets 1-2-3-4-5-6- and 1-2-3-4-5-7 would represent 30 chances at that lowest value prize while the two tickets 1-2-3-4-5-6 and 7-8-9-10-11-12 would represent 40 chances at that lowest value prize.   Shouldn't the first two tickets cost only 75% that of the second two tickets?

Am I wagering the numbers or am I buying chances.   If I bought personal picks then clearly I'm wagering the numbers I believe would be drawn but if I'm buying QuickPicks then I'm obviously am after the chances to win and don't care about the numbers hence QuickPicks should have the option to not repeat and not overlap on a given ticket with multiple lines.   If the lottery commision sold me two lines on a ticket by QP that were 1-2-3-4-5-6 and 1-2-3-7-8-9, they are shortchanging me because both tickets would have the 1-2-3 combination but if they were 1-2-3-4-5-6 and 1-2-7-8-9-10 then there would be no 3 number overlap and hence I would get all the chances I could've possibly bought with my money.

United States
Member #83701
December 13, 2009
225 Posts
Offline
 Posted: August 24, 2010, 3:23 pm - IP Logged

I think it would be interesting if a member of LP would explain to the general audience HOW random number generators function.

Personally, I don't think the RNG in the terminal where I buy my QPs scans the total number of combinations available for the
game I'm playing.

The clerk punches the buttons that tell the machine to generate 5 QPs, for example, and Presto, the machine spits out a
ticket with 5 lines.

I've stood behind folks buying 100 QPs. It took some time for the machine to complete the task, but I think thats afunction
of the machine, not the RNG.

We had a situation here in Texas years ago where a player complained about getting the same numbers on two lines on the
same ticket. Lottery folks more or less said that exact duplicates are possible because the RNG 'doesn't know where it's been
or where it's going, so to speak.

Te RNG resets after each line, meaning anything is possible. No record of the combinations sold is available at the terminal.

I believe the combinations sold are logged at lottery headquarters, but that's a one way street. That is, the terminals can't
scan the 'sold files' to avoid selling a combination more than once. This allows the lottery to quickly determine if a winning combination
has been sold.

In Texas, the lottery can determine whether or not there is a winner within a small time frame. In order to do this, they must
have access to a central file of combinations in play for a specific drawing.

In Texas, they shutdown the Statewide network between midnight and 6 am every night in order to be able to do things like this.   You can't even cash in a ten dollar scratcher after midnight unless you find a retailer willing to take a risk and validate in the morning.   Really puts a damper on a winning streak.

mid-Ohio
United States
Member #9
March 24, 2001
19825 Posts
Offline
 Posted: August 24, 2010, 4:53 pm - IP Logged

If I was to sue, I would argue that Buying a ticket with a certain number of lines was buying a certain number of chances at various prizes.   If the numbers that the machine chose were identical or overlapped then I would not have received as many chances for my money as I would've had they be different.

For example,  imagine a pick 6 game where the lowest value subsidiary prize was awarded for a 3/6 match.   The two tickets 1-2-3-4-5-6- and 1-2-3-4-5-7 would represent 30 chances at that lowest value prize while the two tickets 1-2-3-4-5-6 and 7-8-9-10-11-12 would represent 40 chances at that lowest value prize.   Shouldn't the first two tickets cost only 75% that of the second two tickets?

Am I wagering the numbers or am I buying chances.   If I bought personal picks then clearly I'm wagering the numbers I believe would be drawn but if I'm buying QuickPicks then I'm obviously am after the chances to win and don't care about the numbers hence QuickPicks should have the option to not repeat and not overlap on a given ticket with multiple lines.   If the lottery commision sold me two lines on a ticket by QP that were 1-2-3-4-5-6 and 1-2-3-7-8-9, they are shortchanging me because both tickets would have the 1-2-3 combination but if they were 1-2-3-4-5-6 and 1-2-7-8-9-10 then there would be no 3 number overlap and hence I would get all the chances I could've possibly bought with my money.

Sounds like you want the terminals to have programs that allow you to select parameters for the combinations it generates for you.  If that was an option then the combinations generated wouldn't be random.  You are allowed to generate combinations offline any way you want and fill out a play slip with them which allows you to pick combinations with any parameters you chose, when select to have the terminal pick them you give up those options.

* you don't need to buy more tickets, just buy a winning ticket *

 Page 5 of 7