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Realities of winning the lottery

Topic closed. 22 replies. Last post 10 years ago by RJOh.

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January 23, 2007
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Posted: March 7, 2007, 2:23 am - IP Logged

The odds of winning the record $370+ million Mega Millions jackpot is greater than 170 million to one.

 

It's a big number and it's a hard number to put into perspective. If you play $1 each draw, it is expected that you will have to put up your $1 for 170 million drawings before it is statistically likely for your numbers to hit.

 

But that's based on buying only one ticket at a time. Most people buy many tickets and a lot of people participate in lotto pools to increase their chances of winning.

 

While buying more tickets does increase your chances for hitting the jackpot, it's a difference that really doesn't have an impact.

 

No one person can buy enough tickets to swing the odds in their favor.

 

It would be profitable for someone to buy every possible combination of numbers if the jackpot is over $200 million. However, there are two things to consider. First, if someone else hits the numbers, you will split the pot with them and that would result in a net loss of $70 million on your investment. Secondly, it is logistically impossible for any one person or even a coordinated group of 20,000 to purchase all possible combinations.

 

Lotto pools are also at the mercy of statistical anomalies in order to turn a profit.

 

I did research on this and developed a program that simulates lotto pools. The program generates random quick pick tickets, and compares them against previous winning numbers.

 

The size of the simulated pools ranged from 25 members up to 65,000 members. Each member put up $1 for five draws. Each member invested $5 in an effort to turn a profit.

 

The results were very consistent. The average rate of return (for Mega Millions) was between $.06 and $.08 for every dollar invested, regardless of the size of the pool.

 

One thing was notable in my research; the average rate of return increased slightly as the number of members increased. However, in no case did the members turn a profit at the end of five draws. On a rare occasion, they did turn a profit on a single draw, but the profit was not enough to offset the losses of the other four draws.

 

For this example I will use a 65,000-member lotto pool for five drawings. Each person has put up $5 and the object is to turn a profit by having more than $5 at the end of the fifth draw.

 

Our total investment is $65,000 per drawing or $325,000 total.

 

The way you can visualize this is by imagining me walking up to the guy at the counter and saying, "Yes, I would like 65,000 quick picks for five draws". I hand the guy $325,000 and cross my fingers.

 

Images below show how many winning tickets we have. Below the images is the total $$$ won for that draw.

 

DRAW #1

 

Rate of Return: $.10 (this draw)

Rate of Return: $.02 (overall)

 

DRAW #2

 

Rate of Return: $1.94 (this draw)

Rate of Return: $.40 (overall)

 

DRAW #3

 

Rate of Return: $.25 (this draw)

Rate of Return: $.46 (overall)

 

DRAW #4

 

Rate of Return: $.11 (this draw)

Rate of Return: $.48 (overall)

 

DRAW #5

Rate of Return: $.11 (this draw)

Rate of Return: $.50 (overall)

 

At the end of this lotto pool we won a total of $164,431. We divide that equally between our members and each person gets back fifty cents on their $5 investment. This amount is above the observed average for Mega Millions.

 

There is something that I need to comment on. Some people will say that the winnings are spread too thin when too many people are in a pool. It's true that it will be impossible to win millions or very large sums of money with a pool of this size. But, the rate of return is in-line with lotto pools of any size.

 

Some will then argue that if the pool were small the winnings would be much larger because of the big winning ticket in draw #2. The thing to keep in mind is that getting that winning ticket relied solely on the large pool size. That winning ticket was the 21,935th ticket purchased for that draw. This means that any pool with less than 21,935 members would not have gotten that ticket. The value of that ticket was $120,450. If we divide that by the minimum number of members (21,935), each person would get $5.49. Not exactly a life changing win.

 

If the ticket were the 8th ticket purchased for a ten-person pool, each person would have gotten $12,045. But what are the odds of getting that ticket when buying only ten tickets?

 

Here’s the kicker; we will need more than 2,600 draws before it becomes statistically likely that our 65,000 person lotto pool will hit the jackpot.

 The moral of the story is.... It doesn't matter what you do, to strike it rich in the lottery, you must rely on luck to achieve the allusive "Statistical Anomaly."
    Badger's avatar - adu50016 NorthAmericanBadger.jpg
    Wisconsin
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    Posted: March 7, 2007, 7:44 am - IP Logged

    You have to have some luck no matter what game you play. Even Pick 3 requires guessing the right day the combination you bet will be drawn.

    Yet no matter how high the odds, someone will win.  MM had two winners last night, not just one.

    ============

    How can you tell if a politician is lying?

    Answer: His lips are moving.

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      Posted: March 7, 2007, 1:52 pm - IP Logged

      The odds of winning the record $370+ million Mega Millions jackpot is greater than 170 million to one.

       

      It's a big number and it's a hard number to put into perspective. If you play $1 each draw, it is expected that you will have to put up your $1 for 170 million drawings before it is statistically likely for your numbers to hit.

       

      But that's based on buying only one ticket at a time. Most people buy many tickets and a lot of people participate in lotto pools to increase their chances of winning.

       

      While buying more tickets does increase your chances for hitting the jackpot, it's a difference that really doesn't have an impact.

       

      No one person can buy enough tickets to swing the odds in their favor.

       

      It would be profitable for someone to buy every possible combination of numbers if the jackpot is over $200 million. However, there are two things to consider. First, if someone else hits the numbers, you will split the pot with them and that would result in a net loss of $70 million on your investment. Secondly, it is logistically impossible for any one person or even a coordinated group of 20,000 to purchase all possible combinations.

       

      Lotto pools are also at the mercy of statistical anomalies in order to turn a profit.

       

      I did research on this and developed a program that simulates lotto pools. The program generates random quick pick tickets, and compares them against previous winning numbers.

       

      The size of the simulated pools ranged from 25 members up to 65,000 members. Each member put up $1 for five draws. Each member invested $5 in an effort to turn a profit.

       

      The results were very consistent. The average rate of return (for Mega Millions) was between $.06 and $.08 for every dollar invested, regardless of the size of the pool.

       

      One thing was notable in my research; the average rate of return increased slightly as the number of members increased. However, in no case did the members turn a profit at the end of five draws. On a rare occasion, they did turn a profit on a single draw, but the profit was not enough to offset the losses of the other four draws.

       

      For this example I will use a 65,000-member lotto pool for five drawings. Each person has put up $5 and the object is to turn a profit by having more than $5 at the end of the fifth draw.

       

      Our total investment is $65,000 per drawing or $325,000 total.

       

      The way you can visualize this is by imagining me walking up to the guy at the counter and saying, "Yes, I would like 65,000 quick picks for five draws". I hand the guy $325,000 and cross my fingers.

       

      Images below show how many winning tickets we have. Below the images is the total $$$ won for that draw.

       

      DRAW #1

       

      Rate of Return: $.10 (this draw)

      Rate of Return: $.02 (overall)

       

      DRAW #2

       

      Rate of Return: $1.94 (this draw)

      Rate of Return: $.40 (overall)

       

      DRAW #3

       

      Rate of Return: $.25 (this draw)

      Rate of Return: $.46 (overall)

       

      DRAW #4

       

      Rate of Return: $.11 (this draw)

      Rate of Return: $.48 (overall)

       

      DRAW #5

      Rate of Return: $.11 (this draw)

      Rate of Return: $.50 (overall)

       

      At the end of this lotto pool we won a total of $164,431. We divide that equally between our members and each person gets back fifty cents on their $5 investment. This amount is above the observed average for Mega Millions.

       

      There is something that I need to comment on. Some people will say that the winnings are spread too thin when too many people are in a pool. It's true that it will be impossible to win millions or very large sums of money with a pool of this size. But, the rate of return is in-line with lotto pools of any size.

       

      Some will then argue that if the pool were small the winnings would be much larger because of the big winning ticket in draw #2. The thing to keep in mind is that getting that winning ticket relied solely on the large pool size. That winning ticket was the 21,935th ticket purchased for that draw. This means that any pool with less than 21,935 members would not have gotten that ticket. The value of that ticket was $120,450. If we divide that by the minimum number of members (21,935), each person would get $5.49. Not exactly a life changing win.

       

      If the ticket were the 8th ticket purchased for a ten-person pool, each person would have gotten $12,045. But what are the odds of getting that ticket when buying only ten tickets?

       

      Here’s the kicker; we will need more than 2,600 draws before it becomes statistically likely that our 65,000 person lotto pool will hit the jackpot.

       The moral of the story is.... It doesn't matter what you do, to strike it rich in the lottery, you must rely on luck to achieve the allusive "Statistical Anomaly."

      Your basic message that it's very unlikely to turn a profit in the lottery is something that almost every one already knows. Running the model is interesting but the odds and the prize structure already tell us what we can expect. Lotteries usually pay out 50 cents on the dollar, and I expect a lot of people think that's about what they can expect to get back over the long term. The reality is, as you've noted, that even pools that buy an enormous number of tickets are very unlikely to win the jackpot. For megamillions 31.8 cents of each dollar goes to the jackpot. With 50 cents going to the lottery that leaves 18.2 cents for the remaining prizes. 6.3 cents goes to the 2nd place prize, and  that's also a prize that  few pools will ever win, so that's another 6.3 cents  that the vast majority of players will never see again.

      Third  place is also rather unlikely, but  I'll include it with the other low level prizes anyway.  That leaves  11.8 cents out of every $1 that people could reasonably expect to win back. And that's all there is it to it, except for hoping to be that very rare person who wins a big prize and  ends up in the black after they're done playing. Play on your own, or join a pool, and the best you can really expect is to get back just under 12 cents for every dollar you play. A $1 ticket buys you 12 cents, and the chance to dream.

      As far as the numbers you got from your model, you've got some errors. If your imaginary pool spent $325,000 and won $164,431 each person would get $2.53 back. That's a return of just over 50 cents on each dollar, not the full $5 investment, but the $164,431 figure is wrong. With one 5+ 0 win they would have gotten $250,000. The other prizes in that drawing are  fairly consistent with the other drawings, so I'll  figure the real return on that drawing would have been about $130,000 higher, for a total return of  $294,431. That's $4.53 for each $5, or  just over 90 cents on the dollar.  Subtracting the very lucky 5+0 win, your pool would have won $44,431, for a return of about 13.7 cents on each dollar. That's still a bit better than expected because of the $10,000 for the 4+1 win. Your pool got very luck winning the 4+1 that was only 50% likely and the 5+0 that had about an 8% chance.

        four4me's avatar - gate1
        MD
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        Posted: March 7, 2007, 2:01 pm - IP Logged

        last night on WJZTV some mathematician said if you include the bonus ball in all the possible combinations you could play to win... you would need 25 billion lines.

        in other words there are 25 billion combinations for the mega million drawing. This is the first time i ever heard that or maybe this info was posted before.

        Big John says. You don't hit the number. The number hits you!!!!

                       I'm not Big John, I'm Four4me, Big John's a friend.
          RJOh's avatar - chipmunk
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          Posted: March 7, 2007, 2:10 pm - IP Logged

          last night on WJZTV some mathematician said if you include the bonus ball in all the possible combinations you could play to win... you would need 25 billion lines.

          in other words there are 25 billion combinations for the mega million drawing. This is the first time i ever heard that or maybe this info was posted before.

          The possible combinations in a 5/56 + 1/46 game are 175,711,536, if that mathematician thinks there 're more then he needs to go on that new Fox show "Are you smarter than a fifth grader?".

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

            four4me's avatar - gate1
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            Posted: March 7, 2007, 2:40 pm - IP Logged

            The possible combinations in a 5/56 + 1/46 game are 175,711,536, if that mathematician thinks there 're more then he needs to go on that new Fox show "Are you smarter than a fifth grader?".

            Beats me RJOH i thought the same thing too. No one around him questioned his topic they just agreed with him. I tried to find the pod cast but i couldn't. I will look again today. If i find it i will post the link.

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              Posted: March 7, 2007, 3:21 pm - IP Logged

              Your basic message that it's very unlikely to turn a profit in the lottery is something that almost every one already knows. Running the model is interesting but the odds and the prize structure already tell us what we can expect. Lotteries usually pay out 50 cents on the dollar, and I expect a lot of people think that's about what they can expect to get back over the long term. The reality is, as you've noted, that even pools that buy an enormous number of tickets are very unlikely to win the jackpot. For megamillions 31.8 cents of each dollar goes to the jackpot. With 50 cents going to the lottery that leaves 18.2 cents for the remaining prizes. 6.3 cents goes to the 2nd place prize, and  that's also a prize that  few pools will ever win, so that's another 6.3 cents  that the vast majority of players will never see again.

              Third  place is also rather unlikely, but  I'll include it with the other low level prizes anyway.  That leaves  11.8 cents out of every $1 that people could reasonably expect to win back. And that's all there is it to it, except for hoping to be that very rare person who wins a big prize and  ends up in the black after they're done playing. Play on your own, or join a pool, and the best you can really expect is to get back just under 12 cents for every dollar you play. A $1 ticket buys you 12 cents, and the chance to dream.

              As far as the numbers you got from your model, you've got some errors. If your imaginary pool spent $325,000 and won $164,431 each person would get $2.53 back. That's a return of just over 50 cents on each dollar, not the full $5 investment, but the $164,431 figure is wrong. With one 5+ 0 win they would have gotten $250,000. The other prizes in that drawing are  fairly consistent with the other drawings, so I'll  figure the real return on that drawing would have been about $130,000 higher, for a total return of  $294,431. That's $4.53 for each $5, or  just over 90 cents on the dollar.  Subtracting the very lucky 5+0 win, your pool would have won $44,431, for a return of about 13.7 cents on each dollar. That's still a bit better than expected because of the $10,000 for the 4+1 win. Your pool got very luck winning the 4+1 that was only 50% likely and the 5+0 that had about an 8% chance.

              Thanks for your comments. I did make a mistake in saying that each person gets back only $.50. That should be $2.52.

              What I failed to clarify in my message is that I am basing my simulations on California results where all payouts are paramutual.

              The real life payout for the 5+0 ticket in California was $160,600 to three winning tickets. To make my simulation as real as possible, I used the following math:

              (160,600 * 3) / 4

              This comes out to 120,450 which I used as the winning total for that ticket.

              Recently I ran a series of simulated lottery pools ranging in size from 25 members to 65,000 members. Each pool ran for twenty draws using the same numbers. Actual past winning numbers were used as simulated draw results.

              I ran simulations for Mega Millions and Californias SuperLotto Plaus. Here are the summaries showing combined results from all simulated pools.

              Mega Millions

               

              SuperLotto Plus

                SirMetro's avatar - center
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                Posted: March 8, 2007, 11:59 am - IP Logged

                In your opening line, you note that "The odds of winning the record $370+ million Mega Millions jackpot is greater than 170 million to one."

                To perhaps put it in better perspective, the amount of the pot doesn't really matter. One's odds of winning ANY MegaMillion jackpot will be in excess of 170 million to one.

                The only time anyone wants to face or admit that reality is when the jack pot is super-sized. The odds doesn't change just because of the size of the jackpot, only the value changes.

                The only reason the Mathematicians want to point out the seemingly impossible odds is becuase it's easier to do that then it is to actually devise a method of selecting the winning numbers.

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                  Posted: March 8, 2007, 12:42 pm - IP Logged

                  lady luck  and a six full number wheel  isnt the worst way  big deal 12 bucks a week with 2 extra numbers per week  play em as you see em  as clint would say  DO YOU FEEL LUCKY Big Smile

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                    Posted: March 8, 2007, 3:07 pm - IP Logged

                    I wrote this message for another message forum. I added the $370 million jackpot just to make it current. I think everyone here at lotterypost already knows that "The odds of winning the record $370+ million Mega Millions jackpot is greater than 170 million to one" and "The odds of winning the record $370+ million Mega Millions jackpot is greater than 170 million to one", have the same level of truth.

                    "The only reason the Mathematicians want to point out the seemingly impossible odds is becuase it's easier to do that then it is to actually devise a method of selecting the winning numbers."

                    That's not the only reason. But I will say that finding ways to point out the crazy odds may or may not be easier than developing a method to select winning numbers.

                    People can spend years developing a system to help them pick the winning numbers. Once the winning numbers hit, then their system has validated itself. In this case, it is true that pointing out the odds is easier than spending years to get those winning numbers.

                    Then, there's the guy who walks up and buys a pick quick ticket. If his numbers hit, then his method of selecting winning numbers has been validated. In this case, the method of selecting winning numbers is easier than taking the time to point out the crazy odds.

                    In time, the laws of probability will show that both methods of selecting winning numbers have the same winning percent level.

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                      Posted: March 8, 2007, 7:44 pm - IP Logged

                      last night on WJZTV some mathematician said if you include the bonus ball in all the possible combinations you could play to win... you would need 25 billion lines.

                      in other words there are 25 billion combinations for the mega million drawing. This is the first time i ever heard that or maybe this info was posted before.

                      I'd certainly be curious to  see the clip. There are stupid mathematicians, just like there are stupid people in any other field, and we all occasionally disconnect our mouths from our brains and say something we should know is off the wall. The bit about 25 billion is definitely off the wall as you describe it, so I'm curious if the mathematician was really answering some other question, or if there's somthing in the clip that would give us a clue where that number really comes from.Working backwards, 25 billion divided by MM odds is about 142, and I don't see any significance to that number. The actual math is fairly simple and certainly doesn't require any advanced  education in math.

                      Any chance he might have been talking about the guy in Minnesota (?) who recently won a smaller lottery twice? Those odds were about 25 billion to 1 asuming he had 1 ticket for just those two days. 

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                        Posted: March 9, 2007, 1:50 am - IP Logged

                        I wrote this message for another message forum. I added the $370 million jackpot just to make it current. I think everyone here at lotterypost already knows that "The odds of winning the record $370+ million Mega Millions jackpot is greater than 170 million to one" and "The odds of winning the record $370+ million Mega Millions jackpot is greater than 170 million to one", have the same level of truth.

                        "The only reason the Mathematicians want to point out the seemingly impossible odds is becuase it's easier to do that then it is to actually devise a method of selecting the winning numbers."

                        That's not the only reason. But I will say that finding ways to point out the crazy odds may or may not be easier than developing a method to select winning numbers.

                        People can spend years developing a system to help them pick the winning numbers. Once the winning numbers hit, then their system has validated itself. In this case, it is true that pointing out the odds is easier than spending years to get those winning numbers.

                        Then, there's the guy who walks up and buys a pick quick ticket. If his numbers hit, then his method of selecting winning numbers has been validated. In this case, the method of selecting winning numbers is easier than taking the time to point out the crazy odds.

                        In time, the laws of probability will show that both methods of selecting winning numbers have the same winning percent level.

                        You posted something I actually agree with 100%.

                        Nicely done. 

                          Thoth's avatar - binary
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                          Posted: March 9, 2007, 10:52 am - IP Logged

                          FatLane: "It's a big number and it's a hard number to put into perspective. If you play $1 each draw, it is expected that you will have to put up your $1 for 170 million drawings before it is statistically likely for your numbers to hit."

                           

                          Interesting post, but according to probability, even if you play your $1 for the full course of 175,711,536 games (the exact odds & # of combos), you only stand a 63.21% chance of winning the jackpot.  Playing the $1 for twice that amount of games (351,423,072) still only gives you an 86.47% chance of winning.  It shouldn't matter if it is the same number or a new number being played each draw.

                           

                          Another interesting observation...a 65,000 member pool each spending $1 per drawing only has a .1848% chance of winning the jackpot within 5 draws.  If that same pool plays for 1874 consecutive drawings, they will still only have a 50% chance of winning the jackpot within that time frame...and they will be spending $121,810,000 to attain it.  If they hit, they better hope its during one of those really big jackpots lol

                           

                             

                          ~Probability=Odds in Motion~

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                            Posted: March 9, 2007, 11:18 am - IP Logged

                            "if you play your $1 for the full course of 175,711,536 games (the exact odds & # of combos), you only stand a 63.21% chance of winning the jackpot."

                            That's why you should always buy more than1 ticket at a time.  If you buy half of the possible combinations for two drawings you'll risk the same amount of money, but your probability of winning a jackpot goes up to 75% and there's a 25% chance of winning both.

                              Thoth's avatar - binary
                              Findlay, Ohio
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                              Posted: March 9, 2007, 11:56 am - IP Logged

                              "if you play your $1 for the full course of 175,711,536 games (the exact odds & # of combos), you only stand a 63.21% chance of winning the jackpot."

                              That's why you should always buy more than1 ticket at a time.  If you buy half of the possible combinations for two drawings you'll risk the same amount of money, but your probability of winning a jackpot goes up to 75% and there's a 25% chance of winning both.

                              Very True...

                              ~Probability=Odds in Motion~