Is Playing the Lottery Worth the Risk?

[leroyjenkens]

No, then the odds would be in my favor. The chance gets weighted by the jackpot, so if the cost of the ticket is a dollar and the jackpot is more than a dollar then with 50/50 chance the odds are in my favor.

So you would say that winning $1.01 would be in your favor to spend a dollar on a 50/50 chance?
Well, what if that $1.01 was turned into 300 million? When would the odds be in your favor to spend a dollar? Well, if 50/50 odds are worth the risk of 1 dollar to win 1.01 dollars, then 1/200,000,000 odds should be worth the risk of a dollar to win 300 million dollars.

 

[Jack21222]

And I don't get that "emotional itch" either. To me, it's like buring money for pleasure...I don't see where the pleasure comes from. Yes I understand some people get entertainment out of it, but I absolutely don't get it. But that's no big surprise to me, I'm out of step with a lot of stuff in mainstream culture.

Human brains (along with many other mammals) can easily be taken advantage of by a variable ratio reward schedule. I'm not a neuroscientist so I don't know the exact mechanism behind it, but we go crazy when something rewards us on a variable ratio schedule.

If you've never felt the emotional pull of the variable ratio reward schedule, consider yourself lucky. There's almost a physical feeling of illness to not "press the lever" (or buy the ticket, in this case, or fight a boss in a MMORPG for another example). Buying that lottery ticket relieves that sick feeling and promotes "what-if" daydreaming.

Of course, I can get addicted to things easily. That's why I've never had a sip of alcohol, I'm afraid of getting addicted. As a teenager, I was addicted to a MMORPG. I also believe I have a gambling addiction of sorts, but I do that in moderation.

Again, I don't think it has anything to do with being bad at math, no more than a heroin user is necessarily "bad at biology."

So you would say that winning $1.01 would be in your favor to spend a dollar on a 50/50 chance?
Well, what if that $1.01 was turned into 300 million? When would the odds be in your favor to spend a dollar? Well, if 50/50 odds are worth the risk of 1 dollar to win 1.01 dollars, then 1/200,000,000 odds should be worth the risk of a dollar to win 300 million dollars.

You're not factoring in taxes. The Maryland lottery has a game called Multi-Match whose tickets actually had a positive expected value once the jackpot got above a certain point, but once taxes were factored in, the EV went negative. Yes, I bought a few tickets anyway.

 

[Office_Shredder]

So you would say that winning $1.01 would be in your favor to spend a dollar on a 50/50 chance?
Well, what if that $1.01 was turned into 300 million? When would the odds be in your favor to spend a dollar? Well, if 50/50 odds are worth the risk of 1 dollar to win 1.01 dollars, then 1/200,000,000 odds should be worth the risk of a dollar to win 300 million dollars.

Leroy, when he says the odds are in my favor, he's talking about the expected gain on a ticket vs the cost of the ticket. You're making a mountain out of a molehill that you yourself dug

You're not factoring in taxes. The Maryland lottery has a game called Multi-Match whose tickets actually had a positive expected value once the jackpot got above a certain point, but once taxes were factored in, the EV went negative. Yes, I bought a few tickets anyway.

Clever, but doesn't the state lottery agency have to break even on its own? I thought that was the standard set up.

 

[Jimmy Snyder]

I guess in addition to not buying lottery tickets, you also don't wear a helmet when cycling. Or take a life preserver in a boat. Or install smoke alarms.

Surely there is a difference between increasing risk and reducing risk.

 

[lisab]

Human brains (along with many other mammals) can easily be taken advantage of by a variable ratio reward schedule. I'm not a neuroscientist so I don't know the exact mechanism behind it, but we go crazy when something rewards us on a variable ratio schedule.

If you've never felt the emotional pull of the variable ratio reward schedule, consider yourself lucky. There's almost a physical feeling of illness to not "press the lever" (or buy the ticket, in this case, or fight a boss in a MMORPG for another example). Buying that lottery ticket relieves that sick feeling and promotes "what-if" daydreaming.

Of course, I can get addicted to things easily. That's why I've never had a sip of alcohol, I'm afraid of getting addicted. As a teenager, I was addicted to a MMORPG. I also believe I have a gambling addiction of sorts, but I do that in moderation.

Again, I don't think it has anything to do with being bad at math, no more than a heroin user is necessarily "bad at biology."

Hmm, that brings to mind something I read a long time ago about the 'Pavlov's dog' experiments (conditioned response). You know, the whole ring-a-bell-and-salivate thing. Supposedly, if during the training you ring the bell and occasionally *don't* give the reward, the response is learned quicker than if the reward is given every time. So maybe it's the repeated losing that keeps bringing them back to buy more tickets haha.

I think my strong aversion to any sort of gambling is pretty easily explained...there was a time in my life that I was very poor. I still have my brain somewhat calibrated to that 'value of a dollar' scale, even though my fortunes have changed significantly. So like I said, I can't imagine getting pleasure from playing a game that I'm all but sure to lose.

 

[lisab]

No, it is a sign that people do understand statistics.

This
is a sign of someone who is bad at math.

...thinking that almost zero is basically zero.

OK so when I part with my dollar and get my ticket, my chance of winning is aaaaaalmost zero. Once I look at the numbers, ok then it's exactly zero.

Sounds fun, where can I sign up .

 

[BobG]

To all you folks who think that "almost zero" might as well be "zero":

I guess in addition to not buying lottery tickets, you also don't wear a helmet when cycling. Or take a life preserver in a boat. Or install smoke alarms.

Hm. I wonder if there is an acceptable cost to (ensure/avoid) a circumstance - even though, for the majority of us, it will never come to pass in our lifetime. But we pay the cost anyway because the (benefit/detriment) is so great that we decide the cost is worth it...

Surely there is a difference between increasing risk and reducing risk.

Moneywise, it's the same. In a class I teach, I always get asked why we don't deorbit all satellites after we're done with them. It takes the same amount of energy to deorbit a satellite as it did to put it into orbit in the first place. Only the sign has changed. The only difference is you fire the thrusters in the opposite direction.

Granted, it's hard to put an arbitrary value on a human life. I consider my own life to be very valuable, so helmets and life preservers are a good investment.

I imagine my ex would buy me a helmet and a life preserver (I pay her alimony). I'd probably decide she could buy her own if she wanted one (I pay her alimony). Everyone values a particular person's life differently based on their own criteria.

But insurance is always a bad deal mathematically. The average person always pays out more in premiums than they collect - especially if they focus on the cost of the premiums more than the clauses about receiving benefits. None the less, buying things like car insurance, home insurance, health insurance, etc is usually a smart choice.

But people do tend to put more emphasis on avoiding risk than on achieving gain.

 

[DaveC426913]

Surely there is a difference between increasing risk and reducing risk.

The way I worded it, you can see that it's the same argument.

We pay a small amount of money, knowing that, despite the high likelihood of the event not occurring, it is still worth it, just in case it does occur.

The vast majority of us will ride our bikes every day for the rest of our lives, and never find the helmet making itself useful. Yet we pay the money. Same with life jackets and smoke detectors.

Why?

Because "almost zero" is most definitely not the same as "zero" when the stakes are high.

 

[DaveC426913]

OK so when I part with my dollar and get my ticket, my chance of winning is aaaaaalmost zero. Once I look at the numbers, ok then it's exactly zero.

Sounds fun, where can I sign up .

See my comment about bicycle helmets, life jackets and smoke alarms.

 

[Jimmy Snyder]

But insurance is always a bad deal mathematically.

The point of insurance is not to maximize profit. It is to minimize risk.

 

[Office_Shredder]

All these calculations early in the thread for how much money you really waste on a lottery ticket don't take into account that some of the money spent on lottery tickets goes back into making the prize pool larger. I pick Maryland here only because I found this first on their website

http://www.mdlottery.com/benefits.html

60.3% of the money brought in by revenue was spent on prizes to players, so you're really losing 40 cents on each ticket that you buy on average

New Jersey lottery:
http://www.state.nj.us/lottery/money/4-0_where_money_goes.htm

57% goes back as prizes, so again we see you only lose about 40 cents on each ticket you buy.

The point of insurance is not to maximize profit. It is to minimize risk.

All the arguments against the lottery is that on average you lose money buying a ticket. On average, you lose money buying insurance. So either you accept insurance is a raw deal, or you accept that the single argument: "it doesn't earn you money on average" is a bad one.

Insurance exists because large swings in our money supply hurt a lot more than small ones. Why can't lottery tickets work the same way? A small change in my money supply is not noticeable; a large one is

 

[Jimmy Snyder]

All the arguments against the lottery is that on average you lose money buying a ticket. On average, you lose money buying insurance.

When you buy insurance, you reduce risk that exists. When you gamble, you create risk where there was none.

 

[Danger]

Human brains (along with many other mammals) can easily be taken advantage of by a variable ratio reward schedule. I'm not a neuroscientist so I don't know the exact mechanism behind it, but we go crazy when something rewards us on a variable ratio schedule.

If you've never felt the emotional pull of the variable ratio reward schedule, consider yourself lucky. There's almost a physical feeling of illness to not "press the lever" (or buy the ticket, in this case, or fight a boss in a MMORPG for another example). Buying that lottery ticket relieves that sick feeling and promotes "what-if" daydreaming.

Of course, I can get addicted to things easily. That's why I've never had a sip of alcohol, I'm afraid of getting addicted. As a teenager, I was addicted to a MMORPG. I also believe I have a gambling addiction of sorts, but I do that in moderation.

Again, I don't think it has anything to do with being bad at math, no more than a heroin user is necessarily "bad at biology."
You're not factoring in taxes. The Maryland lottery has a game called Multi-Match whose tickets actually had a positive expected value once the jackpot got above a certain point, but once taxes were factored in, the EV went negative. Yes, I bought a few tickets anyway.

Very nice post, Shredder. I'm an alcoholic, and can't seem to quit smoking even though said smoking allows me only a few months to live. Gambling is governed by the same section of the brain (the "addiction centre" in the hippocampus, hypothalamus, amygdala, or whatever; sorry, but I'm not a neuroscientist either) as my problems are. What non-gamblers and recreational gamblers don't seem to understand is that an addicted gambler gets a blast of endorphins while placing a wager. The thrill is not in winning; it's in placing the bet and awaiting the outcome.
As for the tax thing... (There are no smilies to express my feelings... )
All lotteries that I know of in Canada are tax-free in that the winner(s) aren't susceptible to income tax resultant of the lottery. What nobody seems to understand is that the lottery itself is a tax. The government owns the gambling devices, and the house always wins. We have enough of that crap already. We have to pay GST (Goods and Services Tax) on tobacco and alcohol products, even though over 90% of the price of the originals is already tax. How the hell can you legitimately tax a tax?

 

[DaveC426913]

In a class I teach, I always get asked why we don't deorbit all satellites after we're done with them. It takes the same amount of energy to deorbit a satellite as it did to put it into orbit in the first place. Only the sign has changed. The only difference is you fire the thrusters in the opposite direction.

What?? This is not true.

To deorbit a satellite, all you have to do is make a very small adjustment to its orbit; the atmo will do the rest.

What you're describing is how much energy it would take to bring the entire satellite plus all its discarded bits back to the launchpad with a final velocity of zero (gentle, powered touchdown, not even using parachutes) - which is an outrageous idea.

omg, I hope you don't teach science.

 

[DaveC426913]

All these calculations early in the thread for how much money you really waste on a lottery ticket don't take into account that some of the money spent on lottery tickets goes back into making the prize pool larger. I pick Maryland here only because I found this first on their website

http://www.mdlottery.com/benefits.html

60.3% of the money brought in by revenue was spent on prizes to players, so you're really losing 40 cents on each ticket that you buy on average

Sorry. This is completely illogical.

I may buy a ticket for a dollar, but I don't get that 60 cents back! Sure, technically someone is, but it's not me.

 

[Office_Shredder]

Sorry. This is completely illogical.

I may buy a ticket for a dollar, but I don't get that 60 cents back! Sure, technically someone is, but it's not me.

I never said you would get 60 cents back. But for example on the first page you see people saying that the expected gain on a lottery ticket is -70 or 80 cents and that's not true

Also Danger, that's not my post

 

[Danger]

Also Danger, that's not my post

Oops...
My apologies to both you and Jack. That's what I get for trying to watch STTNG, drink copious amounts of beer, and respond to threads all at the same time.
I stand chastized, but I'm damned well going to finish this beer anyhow.

 

[BoomBoom]

I started many years ago buying just one ticket for each drawing using the same numbers everytime. Over that period of time, I've won almost as much as I have paid in (most of which came in a 5 out of 6 winner for $1,000).

I feel like since I am using the same numbers, that I am now compelled to keep playing, because my worst nightmare at this point would be to NOT buy a ticket and then see my numbers come up!

 

[Danger]

I feel like since I am using the same numbers, that I am now compelled to keep playing, because my worst nightmare at this point would be to NOT buy a ticket and then see my numbers come up!

And we now witness the birth of a new addict.

That's how this **** works; it's insidious. Back to the VLT's here, or the slots in Vegas: You would not believe the number of people of my acquaintance who don't understand how the machines work. I've seen some idiot plop $500 into a terminal, walk away due to lack of money, and then get irritated when the next person to sit down at the same machine hit big. "That's mine!", they inevitably wail. "If I'd put in another Looney, I would have won that!" (Yeah... and if a bullfrog had wings, it wouldn't bump its *** so much. ) It doesn't matter a damn what has transpired before; every single card draw, handle pull, keno pick, or whatever ends up the same way, as a number that is spit out by the on-board computer, and has the same odds of winning as if it was the first time. The machines have 2 pseudorandom number generators running in tandem. At the exact microsecond that you close the switch by pulling a handle, touching a screen, or whatever, the microprocessors poll themselves and decide upon a verdict as to what should result to the gambler. I could come along after you've lost $1,000 and win $1,000 with the push of a single button. The machine is not 'due' to hit any more than it was the last time. Addicted gamblers can't suborn themselves to that reality; they have to try because they feel that it is their right to win. They figure that a machine that has been dry for a couple of days is overdue for a huge payout. It doesn't work that way.

 

[leroyjenkens]

I started many years ago buying just one ticket for each drawing using the same numbers everytime. Over that period of time, I've won almost as much as I have paid in (most of which came in a 5 out of 6 winner for $1,000).

I feel like since I am using the same numbers, that I am now compelled to keep playing, because my worst nightmare at this point would be to NOT buy a ticket and then see my numbers come up!

That seems to be the most common lottery story. An incredible number of people, who play the same numbers each week, had their numbers come up the one week they didn't play.

 

[Danger]

Law of averages, Leroy.
The universe is an evil place, within which we are lucky enough to exist.

(I'll maybe elaborate upon that further if/when I reintroduce myself to sobriety. For now, blissfully pissed is working quite comfortably. )

 

[BoomBoom]

And we now witness the birth of a new addict.

Well, I wouldn't consider $3/week to be a huge gambling problem. Lord knows, I waste much more $$ on far more frivolous things. To me, for that small price of admission, a slim chance is better than none...and besides, the money goes to a good cause IMO.

 

[BobG]

What?? This is not true.

To deorbit a satellite, all you have to do is make a very small adjustment to its orbit; the atmo will do the rest.

What you're describing is how much energy it would take to bring the entire satellite plus all its discarded bits back to the launchpad with a final velocity of zero (gentle, powered touchdown, not even using parachutes) - which is an outrageous idea.

omg, I hope you don't teach science.

The atmosphere is really, really thin where geosynchronous satellites orbit. Geosynchronous satellites are about 36,000 km above the Earth. Atmospheric density tables go up to about 1500 km. After that, the atmosphere is so thin, it's not worth calculating atmospheric drag.

But, true, once the satellite gets down somewhere around the altitude of the space station, atmospheric drag is going to be the device sucking energy out of the orbit instead of thrusters (but it's still the same amount of energy regardless what the source is).

(Usually, the question is asked in reference to why we push geosynchronous satellites higher once we're done with them instead of deorbiting them.)

 

[Danger]

Well, I wouldn't consider $3/week to be a huge gambling problem. Lord knows, I waste much more $$ on far more frivolous things. To me, for that small price of admission, a slim chance is better than none...and besides, the money goes to a good cause IMO.

It's not the amount that he's spending that worries me; it's why he's spending it. He makes it sound as if it's an obligation rather than a recreation.
I won't fault anyone for gambling any more than I would accept someone trying to fault me for my drinking and smoking. All of the aforementioned are out of our conscious control.

 

[BobG]

When you buy insurance, you reduce risk that exists. When you gamble, you create risk where there was none.

What risk? The dollars gone. It's not at risk any more. Same as the money you spend on insurance is gone as soon as you mail it into the insurance company. You won't have a chance of losing more dollars just because you already spent one dollar.

In one instance, you spent money to reduce risk. In the other, you spent money to create a chance of benefit.

I would still revise my statement about insurance being a bad deal mathematically. Insurance companies actually pay out more money in claims than they take in from premiums. The profit comes from the sporadic nature of paying out a large amount of claims. Money taken in each month is invested and it's the increase in value of the investments that provides the profit.

 

[hamster143]

As lisab said, its a tax on people who are bad at math and statistics.

The monetary value of playing a game of chance is easy to calculate, for each instance of playing the game you multiply the amount you could win by the probability of winning and the amount you could lose by the probability of losing.
<math skipped> There is no financial reason to play such a game, so you shouldn't think to play it for the chance of winning rather than the fun of playing.

No offense, but this is what happens when you couple excessive knowledge of mathematics with insufficient understanding of the real world: you're able to make incorrect conclusions from correct data. It is people like these who made the Great Financial Meltdown of 2008 possible.

Yes, the expectation value of payout of one lottery ticket (less the price of ticket) is typically negative.

HOWEVER, the expectation value is deeply irrelevant, unless you intend to invest the amount of money that is at least remotely close to inverse chance of winning a jackpot.

Odds of winning California Super Lotto are 1 in 41,416,353. One ticket is $1. Therefore, if you were to spend, say, $400,000,000 on tickets over your lifetime, you'd be able to use the expectation value to predict your expected winnings (-0.71 * 400,000,000) and, with some more advanced probability theory, to put some sigmas around that.

On the other hand, if you're only going to buy 1000 tickets over your lifetime, the expectation value does not tell you squat.

Instead, you should estimate your expected lifetime earnings, estimate relative desirability of different end-of-life financial outcomes, and then use probability theory to ask yourself "what strategy gives me the best expectation of outcome?"

For most people, the optimal strategy is to spend as much money on the lottery as they can without otherwise constraining themselves financially (maybe, 1% of after-tax earnings?), because that maximizes their chances of retiring rich (say, with $10,000,000 or more by the age of 65).

 

[turbo]

My wife and I spend 2-4 bucks a week on high-odds lottery tickets. No biggie. We don't have any loans (haven't for decades) and don't owe anybody anything. We get lottery tickets just for the entertainment. If we hit a good prize, OK. If we hit the Superball, we'll set up trusts for the grand-nieces and grand-nephews so they can all go to college, and we'll probably set up a trust to benefit low-income children and their families for a LONG time. We would still live here and garden. We'd probably like to buy a camp on a remote trout pond to the north of here, but what else do we need? We've already got what we need, and a camp out in the boonies would only be a "want" not a need.

 

[Danger]

My wife and I spend 2-4 bucks a week on high-odds lottery tickets. No biggie. We don't have any loans (haven't for decades) and don't owe anybody anything. We get lottery tickets just for the entertainment. If we hit a good prize, OK. If we hit the Superball, we'll set up trusts for the grand-nieces and grand-nephews so they can all go to college, and we'll probably set up a trust to benefit low-income children and their families for a LONG time. We would still live here and garden. We'd probably like to buy a camp on a remote trout pond to the north of here, but what else do we need? We've already got what we need, and a camp out in the boonies would only be a "want" not a need.

I am herewith offering myself up for adoption. I am, after all, an orphan... and a mere child by your standards.

 

[turbo]

I am herewith offering myself up for adoption. I am, after all, an orphan... and a mere child by your standards.

I see a border-issue at hand in the adoption process.

Despite our common interests, you cannot come here, and frankly, I cannot go to Canada anymore. This ain't the EU.

 

[russ_watters]

Instead, you should estimate your expected lifetime earnings, estimate relative desirability of different end-of-life financial outcomes, and then use probability theory to ask yourself "what strategy gives me the best expectation of outcome?"

For most people, the optimal strategy is to spend as much money on the lottery as they can without otherwise constraining themselves financially (maybe, 1% of after-tax earnings?), because that maximizes their chances of retiring rich (say, with $10,000,000 or more by the age of 65).

1% of your after-tax income spent on lottery tickets? Is that a joke?

If you add money to a typical 401k at $1000 a year and earn 8% return, at the end of 40 years, you'll have $260,000 with which to retire (a typical 401k is more like 5-10% - and includes free money from your company). If you do the same with lottery tickets, you'll likely have about $28,000, with still a rediculously small chance of having a whole lot more (around 1:1000). Why on Earth would you think the small odds of doing a lot better is worth the risk of being broke vs the reward of a comfortable lifestyle in retirement?

 

[hamster143]

1% of your after-tax income spent on lottery tickets? Is that a joke?

If you add money to a typical 401k at $1000 a year and earn 8% return, at the end of 40 years, you'll have $260,000 with which to retire (a typical 401k is more like 5-10% - and includes free money from your company). If you do the same with lottery tickets, you'll likely have about $28,000. Why on Earth would you think the small odds of doing a lot better is worth the risk of being broke vs the reward of a comfortable lifestyle in retirement?

If you make $100,000/year after tax and you max out your contributions, and you can really get 8%, you'll have $4 million in your 401k by the time you retire. You can put an additional $1000 there to be at $4.26m safely, or you can put that $1000 for a small chance to have $20 ... $50 million (with interest).

For most people, there's no difference between $4m and $4.26m, but there's substantial difference between $4m and $50m.

Now, the reality is that most people don't make $100,000/year after tax at the age of 25, nor do they put away 15% of their income for retirement, nor does the market provide 8% annual returns for everyone any more (on this day 10 years ago, Dow-Jones closed at 10733), and realistically an average person can expect to have $500k..$1m in savings by retirement, and this number could be boosted by 20-40k by foregoing the chance to retire on 50 million.

One interesting corollary is that the chance of winning the lottery is almost irrelevant! It only matters to the extent that there's no other safer way of turning 20-40k into 50 million. For example, roulette has better odds and higher expectation value per play, but the existence of a maximum bet (on high-stakes tables, often $10,000 or $20,000) can be demonstrated to result in an astronomically low probability of a large win. It would be interesting to do the numbers to estimate the chance of making a lot of money using a high-risk/high-reward trading strategy in the stock market.

 

[Danger]

I see a border-issue at hand in the adoption process.

Despite our common interests, you cannot come here, and frankly, I cannot go to Canada anymore. This ain't the EU.

We are just going to have to circumvent those obstacles, ol' buddy. I most assuredly want to meet you in person sometime before I bite the biscuit.

 

[alt]

No, I don't think so. Once one adopt the attitude of using probabilities for your advantage and then starts benefiting from it, why would one occasionally abandon the philosophy that has brought on the riches?

Most very rich people I know aren't using probability. They use gut feeling, speculation, risk taking, aggression .. but they're not beancounters - though I'm sure there are also rich and poor beancounters.

But to answer your question;

I have a philosophy (using your term) of high personal safety, but I drive a car - fast sometimes. I even went up in a hot air balloon last year (WOW !) I ride a motorbike for fun, too.

I have a philosophy of healthy, clean living, but I drink a couple of beers a day. Heck, I even smoke a few cigs a day. I even venture out into a highly polluted city occasionally.

I think riches are meant to be enjoyed, else, what's the point ? And to enjoy them, you MUST abandon the philosophy that bought them to you - but only by small degrees.

I don't have any dislike of money - in fact, I like money a lot !

 

[robheus]

Yes, probability gives you laughable chances at winning. However, what about all the stories where one person plays for the first time and hits a goldmine? Is it worth it to play occasionally? Often? Very seldom? Never? Thoughts anyone?

The chances of winning the lottery are always against you. If not, such a lottery would have nett-loss instead of gain. The lottery always has the better chance (well not chance obviously, but about sure) to win.

So instead of playing a lottery, you should instead consider organizing a lottery.

 

[russ_watters]

If you make $100,000/year after tax and you max out your contributions, and you can really get 8%, you'll have $4 million in your 401k by the time you retire. You can put an additional $1000 there to be at $4.26m safely, or you can put that $1000 for a small chance to have $20 ... $50 million (with interest).

Yes...

For most people, there's no difference between $4m and $4.26m, but there's substantial difference between $4m and $50m.

There will be a difference between $4 and $4.26 million if they get to be 95 and run out of money!

The problem here is:

One interesting corollary is that the chance of winning the lottery is almost irrelevant!

That's absurd. The fact that the odds of winning are rediculously low is the entire reason the strategy is flawed. You're only considering the reward and ignoring the risk.

It only matters to the extent that there's no other safer way of turning 20-40k into 50 million. For example, roulette has better odds and higher expectation value per play, but the existence of a maximum bet (on high-stakes tables, often $10,000 or $20,000) can be demonstrated to result in an astronomically low probability of a large win.

Wrong. All it takes to turn $20,000 into $20 million is two wins in a row! And the odds of that are 1:1369. By your previous estimation, that's a pretty good deal, so clearly whenever a person saves up an extra $20k, they should go to their nearest casino and bet all of it on Roulette.

Absurd.