United States Member #160560 November 1, 2014 20 Posts Offline

Posted: November 1, 2014, 10:57 pm - IP Logged

Hello all. I've just joined and I have to say, before last week I couldn't tell you the last time I visited a lottery message board. It's possible I "drove by" years ago, but I couldn't even tell you when. But what got me to sign up and post is Monopoly Millionaires' Club. First, I want to say kudos to LottoMetro. It's clear that s/he (I'll assume it is a "he" unless told otherwise) has access to some great inside, really informative info and can post it to a degree without breaking confidentiality rules. He's a great resource. Any message board on any subject should be happy to have a member/poster like that.

Anyway, I've read all the mostly negative, in some cases vitriolic feedback on the game, and I get it to a degree. I just think it depends on what you want out of the game, which brings me to the point of my post: the game show.

This aspect of the game really piqued my interest. Now, I realize that most posters here have no interest in the game show, or the [relatively] small prize granted if you are chosen to be an audience member. But I am interested in it, and I'm wondering: what are the ballpark odds for getting selected? It is obviously impossible to determine the exact odds, because they are based on multiple factors beyond sales. But I did a little math (in my head only, no spreadsheets!) and I think the odds could be pretty reasonable, especially for those players entered in states with the fewest players. The reason what state you are in matters is: the audience is something akin to both houses of the U.S. Congress: The "Senate" portion would be the 3 players, minimum, from every jurisdiction --- I believe that's 69 of the 125. The remainder, the "House" is based on the individual state's participation rates. So New York, with the most tickets sold, could have 6 or 7 players, or more. But in a state like New Mexico, with a fraction of New York's players, there will be far fewer entries and better odds.

One reason my interest got piqued immediately is I bought two tickets on a lark for the first drawing. Now, I am not a regular lottery player at all. I spend probably a couple hundred dollars a year on tickets, usually when there are huge jackpots. But this was an impulse buy. When I registered in my state (I am in Georgia) my "bonus property set" ended up being the "Blue" set, Park Place and Boardwalk. So I immediately got 20 entries into the random game show drawing. The best possible start. At that point, I started looking online at the rules, etc... and found this website and forum. My assumption was that *everyone* was awarded the "Blue" set as their bonus, but I discovered from here that is not the case.

Then I saw some of LottoMetro's posts about MUSL'S expectations on the game, sales figures, etc. But there has been scant little discussion on the game show aspect, beyond the cool preview video he posted. So here are my thoughts, which I know may be completely off-base:

I'm assuming about a third of the players in any given state will actually register online, enter their properties, and start building a board. That, I suppose, is my biggest guess, and could be much higher -- or lower. Of those who start their board, I'll assume a small percentage (10% or so) would fork over enough money to build up their number of entries to 100 or so. Based on info gleaned from a few participating states' sites (and Georgia's site is mostly lousy, North Carolina's and Iowa's had some of the best info): they are going to draw a minimum of 3 contestants per show for six shows, during the first drawing on December 2. And note: the number of days in the first drawing (tickets can be entered until 11/25) is fewer than for the next two drawings. And, fair to say, sales may not be as high, either. So it seems like if you want to "go for the show" (as opposed for waiting for the million-dollar winners club numbers), better to do it now.

So that's at least 18 names drawn for each state. Here in Georgia I am guessing we'll have a 4th player per show, so 24 here.

Anyway, so how to reach a ballpark figure? This is where I call on LottoMetro's insight or any available analysis.

So in Georgia, I'll assume -- based on early sales figures -- about 20,000 players started building a board, and half of them will continue to play. We'll say, through 11/25, those continuing to play average 20 entries. And those who quit after one time: 8 entries. Let's say I build enough to reach 40 entries. So what would the rough odds be? I'm assuming they'll index the numbers the way LottoMetro stated will happen for the Millionaires' Club winners drawings. But then, how do they draw the anticipated 24 [Georgia] winners? Do they do a unique draw for each spot, eliminating the winners' other entries after that? Or 3 numbers per draw? Or maybe all 24? (in the latter two cases re-drawing if there's a duplicate winner.) My math leads to 280,000 entries.

Let's say I have 40 entries, well: 280,000/40 = 1 in 7,000. But if they draw all 24 winners in a single draw, then: 7000/24 = 1 in 292, a small but reasonable shot. Now anyone feel free to totally debunk my math! In fact, I expect it! But if it's remotely accurate, I'd be willing to plunk down a few more bucks to build my board. Oh, I forgot to mention, 2 of the first 3 tickets I've bought each won $5, so there has been minimal expense on my part, so far.

No matter what the real odds are for me, they will be better for those in the lowest participating states. In a state like New Mexico, for someone interested in the game show, it may be worth forking over a few hundred dollars to increase entries and see what happens. I also think that the ultimate longevity of MMC could hinge on the game show's success. I suspect it's more important to MUSL's long-term plans than has been discussed here so far.

So that's it, for now! I'll keep an eye on this board for more insight and information.

Happyland United States Member #146344 September 1, 2013 1129 Posts Offline

Posted: November 2, 2014, 12:21 am - IP Logged

Quote: Originally posted by Growler on November 1, 2014

Hello all. I've just joined and I have to say, before last week I couldn't tell you the last time I visited a lottery message board. It's possible I "drove by" years ago, but I couldn't even tell you when. But what got me to sign up and post is Monopoly Millionaires' Club. First, I want to say kudos to LottoMetro. It's clear that s/he (I'll assume it is a "he" unless told otherwise) has access to some great inside, really informative info and can post it to a degree without breaking confidentiality rules. He's a great resource. Any message board on any subject should be happy to have a member/poster like that.

Anyway, I've read all the mostly negative, in some cases vitriolic feedback on the game, and I get it to a degree. I just think it depends on what you want out of the game, which brings me to the point of my post: the game show.

This aspect of the game really piqued my interest. Now, I realize that most posters here have no interest in the game show, or the [relatively] small prize granted if you are chosen to be an audience member. But I am interested in it, and I'm wondering: what are the ballpark odds for getting selected? It is obviously impossible to determine the exact odds, because they are based on multiple factors beyond sales. But I did a little math (in my head only, no spreadsheets!) and I think the odds could be pretty reasonable, especially for those players entered in states with the fewest players. The reason what state you are in matters is: the audience is something akin to both houses of the U.S. Congress: The "Senate" portion would be the 3 players, minimum, from every jurisdiction --- I believe that's 69 of the 125. The remainder, the "House" is based on the individual state's participation rates. So New York, with the most tickets sold, could have 6 or 7 players, or more. But in a state like New Mexico, with a fraction of New York's players, there will be far fewer entries and better odds.

One reason my interest got piqued immediately is I bought two tickets on a lark for the first drawing. Now, I am not a regular lottery player at all. I spend probably a couple hundred dollars a year on tickets, usually when there are huge jackpots. But this was an impulse buy. When I registered in my state (I am in Georgia) my "bonus property set" ended up being the "Blue" set, Park Place and Boardwalk. So I immediately got 20 entries into the random game show drawing. The best possible start. At that point, I started looking online at the rules, etc... and found this website and forum. My assumption was that *everyone* was awarded the "Blue" set as their bonus, but I discovered from here that is not the case.

Then I saw some of LottoMetro's posts about MUSL'S expectations on the game, sales figures, etc. But there has been scant little discussion on the game show aspect, beyond the cool preview video he posted. So here are my thoughts, which I know may be completely off-base:

I'm assuming about a third of the players in any given state will actually register online, enter their properties, and start building a board. That, I suppose, is my biggest guess, and could be much higher -- or lower. Of those who start their board, I'll assume a small percentage (10% or so) would fork over enough money to build up their number of entries to 100 or so. Based on info gleaned from a few participating states' sites (and Georgia's site is mostly lousy, North Carolina's and Iowa's had some of the best info): they are going to draw a minimum of 3 contestants per show for six shows, during the first drawing on December 2. And note: the number of days in the first drawing (tickets can be entered until 11/25) is fewer than for the next two drawings. And, fair to say, sales may not be as high, either. So it seems like if you want to "go for the show" (as opposed for waiting for the million-dollar winners club numbers), better to do it now.

So that's at least 18 names drawn for each state. Here in Georgia I am guessing we'll have a 4th player per show, so 24 here.

Anyway, so how to reach a ballpark figure? This is where I call on LottoMetro's insight or any available analysis.

So in Georgia, I'll assume -- based on early sales figures -- about 20,000 players started building a board, and half of them will continue to play. We'll say, through 11/25, those continuing to play average 20 entries. And those who quit after one time: 8 entries. Let's say I build enough to reach 40 entries. So what would the rough odds be? I'm assuming they'll index the numbers the way LottoMetro stated will happen for the Millionaires' Club winners drawings. But then, how do they draw the anticipated 24 [Georgia] winners? Do they do a unique draw for each spot, eliminating the winners' other entries after that? Or 3 numbers per draw? Or maybe all 24? (in the latter two cases re-drawing if there's a duplicate winner.) My math leads to 280,000 entries.

Let's say I have 40 entries, well: 280,000/40 = 1 in 7,000. But if they draw all 24 winners in a single draw, then: 7000/24 = 1 in 292, a small but reasonable shot. Now anyone feel free to totally debunk my math! In fact, I expect it! But if it's remotely accurate, I'd be willing to plunk down a few more bucks to build my board. Oh, I forgot to mention, 2 of the first 3 tickets I've bought each won $5, so there has been minimal expense on my part, so far.

No matter what the real odds are for me, they will be better for those in the lowest participating states. In a state like New Mexico, for someone interested in the game show, it may be worth forking over a few hundred dollars to increase entries and see what happens. I also think that the ultimate longevity of MMC could hinge on the game show's success. I suspect it's more important to MUSL's long-term plans than has been discussed here so far.

So that's it, for now! I'll keep an eye on this board for more insight and information.

It's funny that you posted this. I was just thinking about this yesterday when looking at sales for the game. I actually have not yet "modeled" this as I have been waiting to see how sales performed.

Personally, I think at least 2/3rds of players will enter the online entries. The number of tickets sold is conditional on a) people willing to pay $5, and b) people understanding how to play. Although it is obvious that many players still do not understand how to play, I believe the majority has at least figured out that entering the webcode helps you get on the game show. This is my personal assessment based on sentiment on social media etc. Nevertheless, if I come into any information about submissions rates I may try to drop some hints.

Meanwhile I am trying to figure out the rough odds as well. If I get the time I am going to do a full rundown on this. I suppose I could just ask but they are pretty tight-lipped about these things. It is especially tricky because even if your lottery chooses you to attend the show, it does not mean you get to participate (sure, you get spending money and travel but the real $$$$ is playing on the show). They are not going to tell you who goes on the show until you get to Vegas (lol).

By my estimates Georgia sold about 110,000 tickets for the first 2 draws (if you have info otherwise feel free to share). Most states experienced a decline in sales for the second draw, and this should continue as long as PB and MM jackpots remain high. At minimum, every first ticket entered online gets 2 entries into the show (since Community Chest automatically completes property group, and the lowest one, Med. & Bal., provides 2 entries). So say GA sells 300,000 total in the period and 200,000 of those actually enter online. You're talking at least 400,000 entries (rough here since the # of repeat players/entries unknown...but I'll get there). Each state will actually pick at least 6 players per draw period because there are 2 audiences (shows are taped over 2 days). Based on sales I doubt there will be 18 or 24 winners picked per state for this coming draw.....it's not selected on a per-episode basis. Note: I initially thought it was but upon reading updated documents my understanding is that they shoot 6 episodes over 2 days with 2 different audiences...lottery is just guaranteed that 3 of their players will appear on an episode. Will have to follow up on this!

For simplicity let's say GA chooses the minimum 6 winners (the additional winners by sales is proportional and I doubt anybody except NY, PA, or FL will have more than 6 and honestly they probably won't). So based on the above if you collect 40 entries your best case scenario is odds of around 1 in 1,667 (that's just to go to Vegas, getting on the show will be MUCH harder). This scenario isn't realistic since it assumes everyone except you got Mediterranean and Baltic and then gave up.

I haven't addressed much of what you've asked (yet) but give me some time and I will figure it out

Bottom line for now is that players in lower participation jurisdictions likely have an advantage due to the fact that a minimum number of winners will be chosen. You could even go as far as digging up your lottery's demographic reports to determine the % of playing participation who is elderly and likely wouldn't bother with the online element. That would help narrow down an estimate on the number of entries. You are also correct in speculating that now is the best time to enter. When sales are low and before the other states join (2015), there will be better odds of actually getting to play on the show.

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?

Happyland United States Member #146344 September 1, 2013 1129 Posts Offline

Posted: November 2, 2014, 1:47 am - IP Logged

To start off, I did some quick calculations and now I understand why they included the Community Chest for new accounts.

I would wager if you get even 40 entries you will be VERY lucky (unless of course you buy many tickets).

Here's why:

In order to complete a property set you have to have entered codes for each property in the set. Because the property is QP, every ticket is independent. This means that your odds of getting any one property are 1 in 28 (unless the terminal is biased). As you know, each property set has a different number of properties and also provides a different number of entries. This affects the expected number of entries per ticket entered.

So for say, Park Place and Boardwalk, which requires 2 properties, your odds of completing the set are (1/28)^2 or 1 in 784. Note that this does not apply to the Community Chest which everyone gets. The odds of completing any set with that are 1 in 10, since there are only 10 property sets and you get the entire set. Anyway, as you can imagine, in reality it is very difficult to complete a property set due to the random draw nature of the property element.

By multiplying the probability of completing each set by their respective number of entries, we can get a good expected value which can be multiplied by the number of tickets entered to get an estimate on the number of total entries. If my math and methodology is correct, this comes out to be about 1 entry per 23 tickets (23.0692 to be precise). And again, this does not factor in the Community Chest. The expected number of entries per initial ticket for that is 10.3. With this in mind, if you estimate that 80,000 of the 200,000 total tickets (40%) are first-time entries then the number of total game show entries should be about (80,000*10.3)+(200,000/23) = 832,696. Really, it comes down to how many tickets are new players. If you think there are only 10,000 players and they just repeat play, then it could be just 112,000 entries. Without access to more demographic information or actual lottery data this estimation is highly speculative.

Based on all the above, you can expect to buy about 685 tickets, Chest-included, before you tally up 40 entries (again assuming my math/methodology is correct). It sounds awful but remember the payout for the game show is set at less than 5% of sales. So they're not going to make it easy!

I will have much more where this came from but this is just to give you something to ponder. You are definitely ahead by having 20 entries from the start!

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?

Raleigh United States Member #49057 January 17, 2007 172 Posts Offline

Posted: November 2, 2014, 3:29 am - IP Logged

LottoMetro, I really respect your posts. That said, your math for calculating entries is incorrect, because it doesn't take into account that the more tickets you have bought the more likely you are to be completing a set with each additional ticket. The following is only based on entering the property off your ticket, and does not include community chest.

I created a spreadsheet to model the random distribution of ticket purchases for properties. The more tickets you buy, the more entries per ticket you get, and the less variance you have in the distribution.

An example of the math for the 100 ticket spreadsheet can be found at: https://docs.google.com/spreadsheets/d/1OVVRKFexhTkjbrJe4_9v6kkOBBuObjnFf440GU85swc/edit?usp=sharing

I did 20 simulations with purchasing varying numbers of tickets: In 20 simulations of purchasing 10 tickets, the average yield was 3.2 entries, for 0.16 entries per ticket. Best run was 20, worst was 0.(Most were 0) In 20 simulations of purchasing 25 tickets, the average yield was 25 entries, for 1.25 entries per ticket. Best run was 49, worst was 0. In 20 simulations of purchasing 50 tickets, the average yield was 76.95 entries, for 1.539 entries per ticket. Best run was 117, worst was 26. In 20 simulations of purchasing 100 tickets, the average yield was 220.9 entries, for 2.209 entries per ticket. Best run was 261, worst was 135. In 20 simulations of purchasing 200 tickets, the average yield was 504.95 entries, for 2.525 entries per ticket. Best run was 565, worst was 444. In 20 simulations of purchasing 400 tickets, the average yield was 1136.6 entries, for 2.842 entries per ticket. Best run was 1333, worst was 994. In 2 simulations of purchasing 100000 tickets, the average yield was 359646 entries, for 3.596 entries per ticket.

Happyland United States Member #146344 September 1, 2013 1129 Posts Offline

Posted: November 2, 2014, 4:15 am - IP Logged

Grengrad:

You’re probably right…I crunched that off the top of my head because I’m not on the PC that has my sim software (I might run some sims and post charts later). Where I made a mistake was being hasty and as you said, not considering that the player does not discard old tickets/properties (as you would in a truly independent event), but use them in conjunction of making a set.

I’ve spent some time reviewing some internal documents which weren’t finalized until about a week and a half ago (believe me, the amount of information that lotteries disperse to the public is a mere fraction of what goes on every day). There are a couple of things that I should mention first:

The game show drawings will not be conducted by MUSL, so it isn’t quite like the MMC prize drawing. However, the company doing it is equally reputable with proper draw procedures. Going to have to trust me on that one

There will potentially be opportunities for players watching the show to enter codes to earn additional properties. All the more reason to enter in drawings that occur before the shows are aired, because as the shows are aired there will be more and more entries (in addition to further attention to the game).

Okay, now for some details to address earlier questions. Entries will be selected via simple random draw— if duplicate winners are picked then all but the first entry are obviously discarded. So it doesn’t matter if you have 80 entries, this will not put you higher in ‘rank’ than someone with 2 (but it will give you better chances of being selected). Along with the primary selections they will also choose a few alternates, like in all contests, just in case one of the winners backs out or whatever.

Two distinct sets of at least 3 winners will be selected for each jurisdiction. I say distinct because neither group will likely even see the other, since as mentioned earlier they will be attending the shows during 2 different days. After all the sets of jurisdiction winners have been compiled, they will be divided into 5 groups. Now, I will withhold further detail here for brevity and respect to the game show concept. But I will say that for each of the 5 groups, only 3 players will be randomly selected representing each audience. So in total, out of the nationwide pool, there will be 30 winners who actually go on the show. As you may realize, having more winners from your state basically increases the proportion of winners playing on the show. This is fair since those who sell more tickets obviously deserve more airtime, and it doesn’t hurt the little guys because they are guaranteed to be represented too (also where the local ‘mini-games’ come into play, and I am seeking more details on that).

Anyway, every player has an equal chance of getting to appear on the show. The fact you are divided into 5 groups doesn’t really matter. Using the minimum 6 total (3 each audience) for 23 jurisdictions, the odds of being selected are 15/69 (each) or 30/138 (total), which is about 1 in 4.6. This of course is conditional on you being chosen to even go to Vegas. And it doesn’t even scrape the surface on the odds of actually winning anything while on the show! P.S. While the top prize of $1 million is only available to one player, everyone else keeps their winnings too. I think $2.4 or $2.8 million in total will be available.

So given the odds of 1 in 4.6 to be on the show after being sent to Vegas, we can simply multiply this by the player’s odds of being selected out of the pool of their lottery’s entries. In my first response I gave a very optimistic number for Georgia, so for the sake of realism let’s just say there will be 500,000 entries.

(EDIT: Based on my mistake in the first post, this is likely underestimated.)

Odds of going to Vegas: 500,000/6 winners/20 entries = 1 in 4,166.67

Odds of going to Vegas AND getting on the show: 4,166.67*4.6 = 1 in 19,166.67

Honestly, not as bad as it could be, or should I say as it will be once the other states join the game (for example, having 30 states with minimum attendees would push the odds of appearance to 1 in 6). Keep in mind this is conservative, but it is likely that more than 6 winners will come from either or all of NY, FL, or PA (maybe TX). And this will dilute your chances, just like higher sales hurts your chances of winning a MMC prize. For the show they’re aiming for 1 participant for every 1.2 million in population.

I have not yet analyzed the individual setups that occur on the game show, but this could potentially have a nice payoff considering the 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?

Raleigh United States Member #49057 January 17, 2007 172 Posts Offline

Posted: November 2, 2014, 4:16 am - IP Logged

Using the math above, existing ticket history for Georgia, projecting future tickets as similar to the most recent drawing, assuming 70% of tickets are entered online, that community chest is worth 10.2 entries, and that most people buy 10 tickets (even though it would probably be far less), we see that entries from regular purchases are not really a threat at all, but lots and lots of entries will be generated by first time players.

Buying 200 tickets for $1000 to get 505 entries, would give you a (505/(608524+32637)) or 1 in 1270.

Divide that by 6 drawings, and you have 1 in 212 of going to Vegas.

Multiply that by 4.6, and you have 1 in 975 chance of getting on the show.

Happyland United States Member #146344 September 1, 2013 1129 Posts Offline

Posted: November 2, 2014, 6:18 am - IP Logged

grengrad:

A couple of things I noticed in your spreadsheet: 1) Your values for the railroads are incorrect....the set awards 16 entries, not 15. 2) The function you used, RANDBETWEEN produces continuous values. The distribution in the lottery is discrete. Not a big deal à la central limit theorem.

P.S. What simulation application did you use? Or did you just run it through Excel like the example spreadsheet?

IMO 20 simulations is a little too few especially at lower purchase rates. Unfortunately software has its limitations.

With that being said, I ran your scenarios @ 1 million simulations each (99.9% confidence). Perhaps excessive but gotta love the law of large numbers

My results were pretty similar: 10 tickets - mean of 4.13 entries (0.413/ticket), max of 65 (6.5/ticket), and probability of 1 or more entries was 36.11% 25 tickets - mean of 26.29 entries (1.05/ticket), max of 127 (5.08/ticket), and probability of 1 or more entries was 96.92% 50 tickets - mean of 83.78 entries (1.68/ticket), max of 214 (4.28/ticket), and probability of 1 or more entries was virtually 100% (same beyond) 100 tickets - mean of 221.40 entries (2.21/ticket), max of 386 (3.86/ticket), min of 57 (0.57/ticket) 200 tickets - mean of 524.89 entries (2.625/ticket), max of 750 (3.75/ticket), min of 250 (1.25/ticket) 400 tickets - mean of 1,170.39 entries (2.926/ticket), max of 1,541 (3.85/ticket), min of 810 (2.03/ticket) 100000 tickets to Infinity - in progress, but trusting your values as they seem comparable*

According to the sim, buying 20 tickets has a 42.64% probability of earning at least 20 entries.

I agree, the most entries will come from Community Chest first-timers. Imagine that, they get you hooked via free entries so you will play more!

Thanks for your contributions btw.

*Have not yet figured out how to model successive tickets without creating a variable for each one (used your setup as example). Any insight would be welcomed i.e. how you arrived at your infinity value.

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?

United States Member #160560 November 1, 2014 20 Posts Offline

Posted: November 2, 2014, 7:50 am - IP Logged

LottoMetro and Grengrad,

Thank-you both for your feedback!

LottoMetro, that point you made about getting a player hooked via free entries is exactly why I came to this message board: to see if everyone playing was getting the max points possible at first.

Buy it seems like trying to get on the show is not really worth pursuing beyond a lark, even though I certainly did get a good start with the Boardwalk-Park Place pairings.

Anyway, the math is dizzying.

I'll only add a few points:

Certainly random luck means that a few players will be able to accumulate a good deal of entries with just a few tickets purchased. And of course there's always a chance of winning smaller amounts of cash in the main game and rolling it over to those.

I'd say not all properties are equal, in terms of figuring out the odds of accumulating entries. Aside from the obvious Boardwalk/Park Place pairing, you're probably best off getting a utility, because you need only the two to complete the group get more entries. Also, they are tied with the Green group for the 2nd highest value, per property.

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.

In my premise, I purposely did not account for the actual odds of making it onto the actual game, because I realize only 5 or so of the 125 contestants per show will get called to the floor.

But, if the promotional video is accurate, and each state has their own mini-game, then the odds are much better of getting called for that one: for most states, 1 in 3! Or if another person from your state gets into the main game, maybe 1 in 2!

Oh, and LottoMetro: I looked at the Georgia winners list for the 2nd drawing. I think your numbers are pretty accurate. And since the odds of winning (in the main game) on any ticket are just a shade over 1 in 10, it's easy to look at the numbers and determine if the computer-generated property is truly random, and it is. By looking at the list of all winners vs. winners who also matched the winning property, the ratio is, indeed, right at 1 in 28! So the computer is spitting them out almost exactly based on the odds.

I am still thinking that players in the smallest states who got a good start with their Community Chest bonus and maybe get a few more groups completed will have a decent chance of getting chosen in the first drawing.

I'll continue to keep an eye out here. I appreciate your effort in trying to figure all this out. Win or lose, I find the math behind it fascinating -- and MMC certainly has some different twists to it than what we've see before.

Happyland United States Member #146344 September 1, 2013 1129 Posts Offline

Posted: November 2, 2014, 9:34 am - IP Logged

Quote: Originally posted by Growler on November 2, 2014

LottoMetro and Grengrad,

Thank-you both for your feedback!

LottoMetro, that point you made about getting a player hooked via free entries is exactly why I came to this message board: to see if everyone playing was getting the max points possible at first.

Buy it seems like trying to get on the show is not really worth pursuing beyond a lark, even though I certainly did get a good start with the Boardwalk-Park Place pairings.

Anyway, the math is dizzying.

I'll only add a few points:

Certainly random luck means that a few players will be able to accumulate a good deal of entries with just a few tickets purchased. And of course there's always a chance of winning smaller amounts of cash in the main game and rolling it over to those.

I'd say not all properties are equal, in terms of figuring out the odds of accumulating entries. Aside from the obvious Boardwalk/Park Place pairing, you're probably best off getting a utility, because you need only the two to complete the group get more entries. Also, they are tied with the Green group for the 2nd highest value, per property.

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.

In my premise, I purposely did not account for the actual odds of making it onto the actual game, because I realize only 5 or so of the 125 contestants per show will get called to the floor.

But, if the promotional video is accurate, and each state has their own mini-game, then the odds are much better of getting called for that one: for most states, 1 in 3! Or if another person from your state gets into the main game, maybe 1 in 2!

Oh, and LottoMetro: I looked at the Georgia winners list for the 2nd drawing. I think your numbers are pretty accurate. And since the odds of winning (in the main game) on any ticket are just a shade over 1 in 10, it's easy to look at the numbers and determine if the computer-generated property is truly random, and it is. By looking at the list of all winners vs. winners who also matched the winning property, the ratio is, indeed, right at 1 in 28! So the computer is spitting them out almost exactly based on the odds.

I am still thinking that players in the smallest states who got a good start with their Community Chest bonus and maybe get a few more groups completed will have a decent chance of getting chosen in the first drawing.

I'll continue to keep an eye out here. I appreciate your effort in trying to figure all this out. Win or lose, I find the math behind it fascinating -- and MMC certainly has some different twists to it than what we've see before.

Glad I have been of help, though sometimes mistaken or misinforming

On a side note, I ended up using another application for the big scenario and these are my results for mean entries per ticket (assuming I programmed it correctly):

Doesn't matter much, but just thought I would include it as the results pretty much confirm around what grengrad computed.

This is probably the first lottery game I have actually had to use simulations for. I mean, I've used them before to check game skew etc. but never to compute the expected value of a game element or otherwise. Still, it's pretty interesting to do and look at. There is a ton of math analysis on casino games but not much on lotto games except the traditional 6/49 type. I am fortunate to have massive computing power and software that can do these things almost instantly. If you think this math is dizzy, you haven't even seen the calcs for the game show stuff! It's fairly complex but I'm sure somebody will eventually compute it down to the last dollar.

From a utility perspective you should buy as few tickets as possible while the odds are not in favor. With that in mind, it is probably economically better to just buy 1 ticket since that gives you a 1 in 10 chance of getting 20 entries (60% chance of 10 or more). Buying more than 1 ticket obviously gives you chances at more entries, but the ratio of tickets to entries is 1:1 or worse and these improved chances come at a cost of $5 a pop with poor base game value. I may buy 1 on the last day of eligibility, just so I can get my free entries into the first round. This will depend on the MMC jackpot and available prizes at the time, of course.

Yes, if you look at the entire history of Powerball and Mega Millions prizes, other than occasional periods where player bias bleeds through (i.e. birthday digits), the number of prizes matches up with the odds and hence the sales match up with the overall odds. I use the same technique with scratch-offs and after comparing the estimated sales with actual internal reports the difference is typically negligible. This is especially applicable to MMC because the property is quick-pick only, which should smooth out the jumps caused by player selection bias and make for a more accurate result.

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?

Raleigh United States Member #49057 January 17, 2007 172 Posts Offline

Posted: November 2, 2014, 10:25 am - 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.

Tickets

Grengrad Entries Per Ticket 20 Simulations

LottoMetro Entries Per Ticket 100000 Simulations

Difference

10

0.16

0.41

156.25%

25

1.01

1.05

3.96%

50

1.55

1.68

8.39%

100

2.23

2.21

-0.90%

200

2.55

2.63

3.14%

400

2.87

2.93

2.09%

100000

3.63

3.63

0.00%

Infinite/1000000

Infinite 3.67857

1000000 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.

United States Member #160560 November 1, 2014 20 Posts Offline

Posted: November 2, 2014, 2:10 pm - IP Logged

Thanks again to both of you.

I just wanted to clarify one thing:

Grengrad said:

"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."

That part, I had always assumed. I meant the bonus property you get with every purchased ticket (independent of the Community Chest property set on the first such ticket). I assume both of your calculations counted *two* [random] properties for every ticket purchased.

In the end, you are both right, of course, in terms of how many tickets to buy (one) to maximize your risk vs. reward.

But it begs the larger question:

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

The best payback per dollar spent vs. odds of winning is the Pick 3/Pick 4's. But they don't offer the huge paydays of the lotto-type games and probably don't appeal as much to the casual player.

Some people will just buy all MegaMillions or Powerball tickets (especially this week) and hope beyond hope for the huge jackpot hit.

Others may buy a $20 scratcher and if they're lucky enough, with probably get their money back (or a few extra dollars). In Georgia, for most of those $20 instant tickets, two out of three are instant losers.

I think MMC is meant to appeal to people who want more than just matching numbers to the Powerball/Mega Millions draws. Time will tell if their multi-faceted approach works. LottoMetro's tidbit that they will offer more chances to enter properties during the TV show is interesting. I think they should have started out by putting in ongoing Community Chest-type bonuses when you enter your tickets (maybe, say, 1 in 100 gets another complete property set) to keep in interesting. Maybe they'll do that, eventually.

As for me, well I rolled over my second $5 winner today. Did not even look at the ticket yet. Oh, the clerk said he bought one last Friday, it was a loser and he wasn't going to enter it online (not that what one person does matters). In the end I'll have spent $10 and que sera sera. I won't be holding my breath for the happy email, either. ;)

Raleigh United States Member #49057 January 17, 2007 172 Posts Offline

Posted: November 2, 2014, 2:28 pm - IP Logged

Actually, our calculations are based on one property per ticket.

To correct for 2 properties per ticket you would just divide the tickets required in half.

For me, in NC, Cash 5 gets in the 600k-900k range every few months, with 1 in 575000ish odds. This yields an expected value over 100% of the ticket price. This and office pools for $300 million plus jackpots are where I put my lotto money.

Michigan United States Member #139344 February 20, 2013 1142 Posts Offline

Posted: November 2, 2014, 3:30 pm - IP Logged

This was interesting under the FAQ's:

Q: Will trip drawing entries be retained for future drawings if they do not get picked?

A: No. Trip drawing entries are only eligible for the next drawing after they have been awarded. All entries are purged after each drawing.

So I am reading this as after the 1st drawing date of 12/02/2014, they will purge all previous entries and you need to start over for the 2nd chance drawings.