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MMC Game Show

Topic closed. 26 replies. Last post 2 years ago by Growler.

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LottoMetro's avatar - Lottery-024.jpg
Happyland
United States
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September 1, 2013
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Posted: November 2, 2014, 3:44 pm - IP Logged

The correct value at infinite tickets is 3.67857 entries per ticket. My number was off, because I had railroads at 15 instead of 16.

I don't actually run a simulation for tickets at infinite tickets, because with any random distribution, if you truly do an infinite number of the events, you will have a perfectly even distribution. This seems counter intuitive, but by the definition of infinity, 1/28th of infinity, is still infinity, and one infinity is not bigger than another infinity.

I adjusted my numbers to correct for the railroad error, and compared them to LottoMetros, and other than the 10 tickets, where my limited number of simulations really shows up, our values are very similar. Obviously, LottoMetro's numbers are more accurate due to more simulations.

TicketsGrengrad Entries Per Ticket 20 SimulationsLottoMetro Entries Per Ticket 100000 SimulationsDifference
100.160.41156.25%
251.011.053.96%
501.551.688.39%
1002.232.21-0.90%
2002.552.633.14%
4002.872.932.09%
1000003.633.630.00%
Infinite/1000000Infinite 3.678571000000 3.6628-0.43%

Since each ticket is an independent event, I think you have to do an independent variable for each draw to represent it most accurately, but I am sure there are other methods that get you within a few percent, that are less calculation intensive.

For 100000 tickets, I generated all the tickets on a 10000x10 page in excel, and then used "=countif(a:j,1)" thru "=countif(a:j,28)" to count the number of instances of each ticket. Doing it the way I did the one for 100 tickets would have been too ugly.

I did not use any simulation software, just running random numbers in Excel multiple times. My simulations #s all came from Excel. I only converted it to a Google Doc to share.

Growler said: "We don't know if the algorithm that chooses the bonus property for each ticket eliminates the property on the actual ticket purchased. That could impact the odds somewhat." 

My bonus group was the same as my property. So, I got the set bonus, and still kept my original property. This combined with others results I have seen posted, implies that community chest is independent of the property you had on your ticket.

The best return on investment is a single ticket.

I bought one ticket, and won't buy another unless the game has a very large # of 1 million dollar prizes.

grengrad:

Thanks for posting the comparison. Nice to know I was right near target the second go around (didn't major in math in college)! Crazy

It does seem counter-intuitive but your explanation makes sense. Correct me if I'm wrong, but you set the sum of tickets for each property to 1/28 and multiplied the 10 lines of 1/28 (ten property groups) by the number of entries per group. Basically an expected value calculation. Alternatively, you can simply add up all the available entries (103) and divide by the number of properties (28). I ended up with 103/28 exact, or 3.67857 approximated (same as you).

Growler:

If you had set aside, say, $20 to play the lottery, how would you spend it?

Scratch-off, hands down (unless there were literally hundreds of MC prizes in MMC and sales were expected low). Probably a $20 one too, or double $10 tickets.

You want the games with the highest payout yet the lowest variance, preferably at the lowest cost (though this is ignorable). The bad thing about draw games is the variance. For the current Mega Millions jackpot you would have to random play 3 to 4 billion times before you had 95% confidence of achieving the return. Obviously you could do it for less (i.e. buying all 258,890,850 combos) but my number was based on a coefficient of variation numeric that assumes random trials.

Believe it or not, Pick3/Pick4 does have better alternative in the realm of scratch-offs, as far as payback for least cost. There is a $1 game in my state with a 10% better payout and 18 times better (lower) variance than Pick 3.  The vast majority of my losing lottery tickets has been on $1-2 draw games, simply because of the odds, which contributes to variance.  In general, the games with the best overall odds provide the best return to player. Not always true but in the few years I have been analyzing games daily, this has proved true for nearly every game and price point. Whether better odds in scratch-offs has something to do with the propensity of the lottery to put higher denomination tickets in smaller packs, usually with a set minimum payout-per-pack guarantee, remains to be seen.

If the chances of winning the jackpot are so slim, why play when the jackpot is so small? Your chances never change, but the potential payoff does.
If a crystal ball showed you the future of the rest of your life, and in that future you will never win a jackpot, would you still play?

2017: 0% (0 tickets)
P&L % = Total Win($)/Total Wager($) - 1

    grengrad's avatar - nw rogue.jpg
    Raleigh
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    Posted: November 2, 2014, 3:49 pm - IP Logged

    Correct!

      LottoMetro's avatar - Lottery-024.jpg
      Happyland
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      Posted: November 2, 2014, 5:24 pm - IP Logged

      Getting back to MMC, I spent some time monkeying with my simulator. This seems like it would be better modeled using something like Markov chains with probabilities of a ticket purchase being entered online, being a first-time entry, etc. Unfortunately without access to those numbers such effort would be futile.

      So instead, I set the proportion of entries to purchases as a lognormal distribution with minimum 5%, mean of 50%, and standard deviation of 10%. Similarly I set the proportion of Community Chest entries to tickets entered as a lognormal distribution with minimum 25%, mean of 50%, and standard deviation of 5%. If anyone has better recommendation for values, distributions etc. please let me know. The software can simulate any known distribution and even custom ones.

      Anyway, here are the runs for the eligibility period using the final values we arrived at earlier:

      100,000 tickets sold – min 174,954 entries, max 1,251,617 entries, mean 441,519 entries

      300,000 tickets sold – min 496,792 entries, max 3,760,551 entries, mean 1,324,139 entries

      500,000 tickets sold – min 905,206 entries, max 7,484,084 entries, mean 2,207,066 entries

      1,000,000 tickets sold – min 1,641,286 entries, max 12,547,200 entries, mean 4,414,472 entries

      These numbers differ slightly based on the correlation. Again, each ran for 1,000,000 trials at 99.9% confidence. According to my sensitivity analysis, 92.8% of the variation depends on the number of tickets entered online. The remaining 7.2% of variation is derived from the proportion of first (Community Chest) entries.

      If the chances of winning the jackpot are so slim, why play when the jackpot is so small? Your chances never change, but the potential payoff does.
      If a crystal ball showed you the future of the rest of your life, and in that future you will never win a jackpot, would you still play?

      2017: 0% (0 tickets)
      P&L % = Total Win($)/Total Wager($) - 1

        LottoMetro's avatar - Lottery-024.jpg
        Happyland
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        Posted: November 2, 2014, 6:53 pm - IP Logged

        I went a step further and simulated the above using a utility of $1,000 for getting chosen to go to Vegas and a utility of $50,000 for getting on the show. This is subjective of course, at least until I can crunch the numbers on the expected returns for each of the games on the show.

        For 1 ticket purchased (maximizes return), the total simulated return is:

        100,000 tickets sold – mean 7.92%, min 2.10%, max 22.51%

        300,000 tickets sold – mean 2.64%, min 0.62%, max 7.38%

        500,000 tickets sold – mean 1.59%, min 0.38%, max 4.63%

        1,000,000 tickets sold – mean 0.79%, min 0.16%, max 2.19%

        Note that this excludes returns from the base game. This is not the population ticket return but that for an individual player.

        It is evident that smaller participation states could have an advantage, assuming that nationwide sales are insufficient to support additional winners beyond the minimum 6 per state. This won’t be a realistic assumption in 2015 but at these early stages it could be a good fit (consider it the 'best case' scenario).

        That’s all I have to post for now, maybe will analyze the individual TV show games later this week Smile

        P.S. Now people can breathe a sigh of relief that I will stop pushing this topic to the top of the most active LOL

        If the chances of winning the jackpot are so slim, why play when the jackpot is so small? Your chances never change, but the potential payoff does.
        If a crystal ball showed you the future of the rest of your life, and in that future you will never win a jackpot, would you still play?

        2017: 0% (0 tickets)
        P&L % = Total Win($)/Total Wager($) - 1


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          Posted: November 5, 2014, 10:34 pm - IP Logged

          Hey LottoMetro and anyone else who might be interested:

           Did a little more research on the MMC game show. Some of the tidbits you can find online. In a USA Today story, one state lottery director is calling it a "national premium product" that was a result of the MUSL agreement between states to cross-sell MegaMillions and Powerball tickets. That's an interesting characterization, in the sense that the participating lotteries appear to be targeting a certain consumer.
           
          But the better information on the game show is in Broadcasting & Cable Magazine. Their online site has about half of the article that appears in the magazine, which I was actually able to find a copy of.
           
          The magazine-only portion of the article has some interesting information.
          The main talking points (and of course, this is all subject to change before the first taping):
          The [125] studio members will be divided into groups of 5, with one player called from each group to play a game. That player, according to the article, can win up to $50,000 in a game (different from the promotional video).
          His or her audience group would collectively split the same amount as the contestant wins, amongst themselves. So if the contestant wins the max amount, their section's other contestants would win at least $2000 each.
          This also applies to the end game. If a contestant wins the $1 million, his or her section would split the same amount. So if the article is accurate, 20% of the eligible audience could each win up to $40,000.
          I think this is how you came up with the at least $2.4 million potentially given away, per show.
           
          The article mentions the local, state insert games, but does not go into detail about those.
           
          The show can air in 95% of U.S. television markets, and has been cleared to run in 95% of those. The reason it cannot air "nationally" is due to the six states that don't have lotteries. It will air in weekend prime access starting in February.
           
          A different story I found online stated there will be at least 63 shows over the first 83 weeks it airs. Take of that what you will.
           
          All I'll say is that anyone buying a ticket should at least enter their code and get the Community Chest bonus to get into the drawing. If (the big "if," of course) you get chosen to go to Vegas, the odds of winning some good cash may be better than you think.
           
          Oh, I did look at the MMC FB page. The questions and comments there are pretty funny! One guy says he's got 362 entries into the drawing! LOL! I doubt it, but if he's telling the truth I can't imagine how much he spent to get to that level.
           
           

           
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            Happyland
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            Posted: November 5, 2014, 11:20 pm - IP Logged

            Hey LottoMetro and anyone else who might be interested:

             Did a little more research on the MMC game show. Some of the tidbits you can find online. In a USA Today story, one state lottery director is calling it a "national premium product" that was a result of the MUSL agreement between states to cross-sell MegaMillions and Powerball tickets. That's an interesting characterization, in the sense that the participating lotteries appear to be targeting a certain consumer.
             
            But the better information on the game show is in Broadcasting & Cable Magazine. Their online site has about half of the article that appears in the magazine, which I was actually able to find a copy of.
             
            The magazine-only portion of the article has some interesting information.
            The main talking points (and of course, this is all subject to change before the first taping):
            The [125] studio members will be divided into groups of 5, with one player called from each group to play a game. That player, according to the article, can win up to $50,000 in a game (different from the promotional video).
            His or her audience group would collectively split the same amount as the contestant wins, amongst themselves. So if the contestant wins the max amount, their section's other contestants would win at least $2000 each.
            This also applies to the end game. If a contestant wins the $1 million, his or her section would split the same amount. So if the article is accurate, 20% of the eligible audience could each win up to $40,000.
            I think this is how you came up with the at least $2.4 million potentially given away, per show.
             
            The article mentions the local, state insert games, but does not go into detail about those.
             
            The show can air in 95% of U.S. television markets, and has been cleared to run in 95% of those. The reason it cannot air "nationally" is due to the six states that don't have lotteries. It will air in weekend prime access starting in February.
             
            A different story I found online stated there will be at least 63 shows over the first 83 weeks it airs. Take of that what you will.
             
            All I'll say is that anyone buying a ticket should at least enter their code and get the Community Chest bonus to get into the drawing. If (the big "if," of course) you get chosen to go to Vegas, the odds of winning some good cash may be better than you think.
             
            Oh, I did look at the MMC FB page. The questions and comments there are pretty funny! One guy says he's got 362 entries into the drawing! LOL! I doubt it, but if he's telling the truth I can't imagine how much he spent to get to that level.
             
             

             

            Word of caution about reading outside (i.e. publication) sources.....back during the summer, the lottery "standard" magazine published that the game would have a jackpot capped at $50 million. In all fairness, that was the original plan, but it changed, so the publication ended up looking a little foolish for jumping the gun.

            Anyway, thanks for sharing what you've heard.

            According to finalized internal documents, 3 players (not one) will be chosen from each of the 5 groups. It is possible this covers all the episodes that they will shoot in the day, or I am misunderstanding (doc sounds like it was written by a lawyer lol). Will have to get back to you on that. I do know that 3 of the (minimum 6) chosen local winners will appear on their separate show.

            63 episodes is correct; the first 48 episodes will be taped in 2015 with the remainder in 2016. Right now they have "TBD" dates for the 11th drawing deadline (last 3 episodes, summer 2016), so I assume that this is around when they plan to re-evaluate the game etc.

            Regarding the claim about 362 entries, I saw that too. I suppose anything is possible, or maybe the player misunderstood what completing a set means. However, I am starting to think that the online participation rate could be closer to 80-90%. I am hearing more about the webcode element than even the MC prizes.

            I've been a little busy this week, but hopefully I will be able to elaborate on some of what you mentioned in the near future. The amount of information regarding the game show exceeds that of the base game by multiples, so it takes a lot longer for me to read and process. Smile

            If the chances of winning the jackpot are so slim, why play when the jackpot is so small? Your chances never change, but the potential payoff does.
            If a crystal ball showed you the future of the rest of your life, and in that future you will never win a jackpot, would you still play?

            2017: 0% (0 tickets)
            P&L % = Total Win($)/Total Wager($) - 1

              Taurus$'s avatar - Lottery-043.jpg
              Ft. Washington, MD
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              Posted: November 6, 2014, 12:34 am - IP Logged

              Lotto Metro,hey i have been looking at your calculations and  Growlers theory of getting on the game show is where the the real challenge is for now. You both are correct about this and i saw this also. But guess what i have only gone thru the first two drawings and already have accumulated 36 entries on no more than 19 tickets and another 12 for the current upcoming drawing i could past the 40 entries you stated on less than the 600 tickets you figured out. I am in maryland so it seems interesting how this is all playing out. I am gunning for that show knowing full well it is going to be <snip> hard to make it. I tried to get on other game shows too and it ain't easy. MMC is no different but worth taking a shot at. Wink I am no math man, but i can see this game is worth a try. 

              This post has been automatically changed by the Lottery Post computer system to remove inappropriate content and/or spam.

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                Happyland
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                Posted: November 6, 2014, 12:52 am - IP Logged

                Lotto Metro,hey i have been looking at your calculations and  Growlers theory of getting on the game show is where the the real challenge is for now. You both are correct about this and i saw this also. But guess what i have only gone thru the first two drawings and already have accumulated 36 entries on no more than 19 tickets and another 12 for the current upcoming drawing i could past the 40 entries you stated on less than the 600 tickets you figured out. I am in maryland so it seems interesting how this is all playing out. I am gunning for that show knowing full well it is going to be <snip> hard to make it. I tried to get on other game shows too and it ain't easy. MMC is no different but worth taking a shot at. Wink I am no math man, but i can see this game is worth a try. 

                This post has been automatically changed by the Lottery Post computer system to remove inappropriate content and/or spam.

                i could past the 40 entries you stated on less than the 600 tickets you figured out

                Taurus, just wanted to reiterate that I made a mistake in my initial calculations....you will want to read grengrad's posts and mine thereafter. It is not quite as difficult to rack up many entries as originally believed, so the 600ish ticket figure was derived in error.

                You're right, it's certainly worth the shot, and even if you don't get on the show at least you have fun trying for it!

                For Maryland, I estimate about 400,000-500,000 tickets will be sold for the eligibility period for the first drawing. Assuming 85% enter online and 50% are first-time entries, you can expect between 3,310,714 and 4,138,393 online entries to be competing with (see below for formula to do your own estimate). If you wanted to figure your rough odds, you could take the average (3,724,554) and divide it by the winner picks then by your entries to find the odds.

                -----------------------------------------------------------

                t = total tickets sold (all drawings in period, your state)

                o = % of tickets sold entered online

                f = % of tickets sold entered online that are first-entries

                picks = number of winners your lottery will choose (minimum 2 sets of 3; remainder determined by sales)

                Total entries = ((103/28) * t * o) + (10.3 * t * f))

                Odds = Total entries / picks / your entries

                If the chances of winning the jackpot are so slim, why play when the jackpot is so small? Your chances never change, but the potential payoff does.
                If a crystal ball showed you the future of the rest of your life, and in that future you will never win a jackpot, would you still play?

                2017: 0% (0 tickets)
                P&L % = Total Win($)/Total Wager($) - 1


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                  Posted: November 6, 2014, 1:17 am - IP Logged

                  And LottoMetro, I just wanted to restate to you ('cause I am not sure you ever acknowledged it) that every ticket purchased gets two properties (in addition to the Community Chest bonus on the first entry). Grengrad said: just divide the stated odds in half, given that fact.

                  I don't know if you're able to get access to any state lottery's numbers on who's entered/number of entries, etc.. so we may never know for sure. 85% sounds high to me. I think the people posting on FB, just by the fact they're going there for info and answers, means that they will enter online. Not sure about players who decide to try it one time, realize there are no $1 million winners when no one wins the big jackpot, and then give up.

                    LottoMetro's avatar - Lottery-024.jpg
                    Happyland
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                    Posted: November 6, 2014, 1:28 am - IP Logged

                    And LottoMetro, I just wanted to restate to you ('cause I am not sure you ever acknowledged it) that every ticket purchased gets two properties (in addition to the Community Chest bonus on the first entry). Grengrad said: just divide the stated odds in half, given that fact.

                    I don't know if you're able to get access to any state lottery's numbers on who's entered/number of entries, etc.. so we may never know for sure. 85% sounds high to me. I think the people posting on FB, just by the fact they're going there for info and answers, means that they will enter online. Not sure about players who decide to try it one time, realize there are no $1 million winners when no one wins the big jackpot, and then give up.

                    Yes, sorry, that slipped my mind. I was so focused on the calculations it didn't click the first time you mentioned it Embarassed

                    Adjusted formula (also simplified t, ran out of edit time in last post):

                    Total entries = t*((103/14)*o+10.3*f)

                    That's 5,701,786 for 500,000 tickets sold and using the percentages from earlier.

                    Wait, you ask, why is the total number of entries worse? Since 2 properties are awarded per ticket, it actually means the expected yield per ticket is twice as high.

                    So unless I am missing something, you do not divide the odds in half. You multiply them. So you would need 80 entries to have the power of 40. Now that I think about it, this invalidates my simulations I posted a few posts back. Completely forgot to include this factor. Oh well. Sleepy

                    85% may sound high but that is 75,000 tickets not played online for MD. My gut feeling is most people wouldn't be playing the game unless they understood it. And entering the webcode is a big part of it. All it takes is entering once and you understand. I think it's better to overestimate than underestimate and get too hopeful.

                    It bugs me that I don't have access to real-time sales and especially, entries with this game LOL

                    Lots of uncertainty which requires simulations that are only as good as your guesses. Most of the time my estimates are spot-on but that is because I have access to more data. There are many variables here and the door is closed on the data (at least until after the fact, and that will probably require FoI request).

                    Without more data all you could do is make a "worst case" (high %) and "best case" (low %), take the average, and that will give you rough odds.

                    If the chances of winning the jackpot are so slim, why play when the jackpot is so small? Your chances never change, but the potential payoff does.
                    If a crystal ball showed you the future of the rest of your life, and in that future you will never win a jackpot, would you still play?

                    2017: 0% (0 tickets)
                    P&L % = Total Win($)/Total Wager($) - 1

                      LottoMetro's avatar - Lottery-024.jpg
                      Happyland
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                      Posted: November 6, 2014, 2:24 am - IP Logged

                      Ugh screwed up again! Ignore the formula(s) above, because it does not include the fact that the percentage f is a proportion of the online percentage o.

                      Use this one instead (same variables):

                      Total entries = t*o*(103/14+10.3*f)

                      According to my calculations, if the lottery awards 6 winners and you have 40 entries, then based on 50% first-time entries and 500,000 tickets mentioned earlier, your lottery would have to have an online participation rate of a paltry 3.84% for your odds of going to Vegas to be 1 in 1,000 (Pick3 straight equivalent). Even if the first-time entry rate was 25%, the participation would have to be 4.83%. If the gentleman with 362 entries lived in MD he would need 25% first-timers and 43.74% online participation to have Pick3 odds of going to Vegas (50% first-timers would worsen the required online rate by 9%).

                      It follows that for 85% online participation with 50% first entries, you would need 886 entries to match Pick3 odds. That dips to 521ish if you say 50% on both.

                      I think we can surmise from this that the odds actually aren't as great as you would expect, even with low participation.

                      If the chances of winning the jackpot are so slim, why play when the jackpot is so small? Your chances never change, but the potential payoff does.
                      If a crystal ball showed you the future of the rest of your life, and in that future you will never win a jackpot, would you still play?

                      2017: 0% (0 tickets)
                      P&L % = Total Win($)/Total Wager($) - 1


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                        Posted: November 6, 2014, 2:43 am - IP Logged

                        Ugh screwed up again! Ignore the formula(s) above, because it does not include the fact that the percentage f is a proportion of the online percentage o.

                        Use this one instead (same variables):

                        Total entries = t*o*(103/14+10.3*f)

                        According to my calculations, if the lottery awards 6 winners and you have 40 entries, then based on 50% first-time entries and 500,000 tickets mentioned earlier, your lottery would have to have an online participation rate of a paltry 3.84% for your odds of going to Vegas to be 1 in 1,000 (Pick3 straight equivalent). Even if the first-time entry rate was 25%, the participation would have to be 4.83%. If the gentleman with 362 entries lived in MD he would need 25% first-timers and 43.74% online participation to have Pick3 odds of going to Vegas (50% first-timers would worsen the required online rate by 9%).

                        It follows that for 85% online participation with 50% first entries, you would need 886 entries to match Pick3 odds. That dips to 521ish if you say 50% on both.

                        I think we can surmise from this that the odds actually aren't as great as you would expect, even with low participation.

                        The situation is beyond grim! Shocked

                        But I sincerely hope someone on this forum gets chosen to be on the show and reports back to us about it. You also may come across some inside info from a lottery down the line. I may buy one more ticket for next week (I know, famous last words) and stand down, with a $15 max "investment." But the speculation and these exchanges here have already made the cost worth it, to me.