For the curious, you can conduct your own rate of return analysis.
You multiply the dollar amount of the prize by the probability of winning that prize. Do that for each of the prize options. (all but the jackpot will be fixed) Add the total together. That’s your average return-for-a-dollar.
If I bet on a game that costs a dollar to play, that has a 50% chance of giving me two dollars, and a 50% of giving me nothing :
50% x 0 = 0.
50% x 2 = 1.
Adding together, I get 1. So on average, for each dollar I spend, I get a dollar back. That’s a break-even point.
If you’re getting better than 80 million to 1 on your money, it is a good bet.
1 - I specifically said that “it isn’t a smart investment.” That’s in the same sense that a pepperoni pizza isn’t a good investment. However, that doesn’t mean that it isn’t a “good bet” in the mathematical sense. It’s better than craps and blackjack, for one thing.
2 - I’m speaking of probability and game theory. Expectation in this sense has a specific meaning; it doesn’t mean that I buy a lottery with anything resembling certainty of winning on that specific ticket. It DOES mean that if I were to play the lottery long enough, I would come out ahead, if I only bought tickets when the payout is greater than the odds against winning.
Let me illustrate on a smaller scale. Say I put 9 black marbles in a bag, plus a white pebble. You get one try to pull out the white pebble. You have a 1 in 10 chance of doing so, and you have to pay a buck per try. So, how do we make this fair?
I pay out two dollars for getting the white pebble. In this scenario, you are getting the shaft.
I pay out ten dollars for a win. Now it’s balanced, and in the long run, you will neither lose nor win money, assuming you don’t simply go broke in the process on a cold streak.
I pay out 15 dollars. Now, this is a winnable game for you. You still only have a 10% of winning on any individual pull, but you net enough money on the wins to more than make up for the losses, and you should come out ahead in the long run.
The same principles apply to the lottery. I checked Powerball, and the odds against winning the jackpot are slightly worse than 1:146 million. Therefore, if the jackpot hits (breaks out calculator) 220 million, you are playing the exact same game* as example #3 above, just for much bigger stakes.
Note that example #1 is representative of playing the lottery right after the jackpot is won, and illustrates why it’s a really terrible idea, even worse than usual.
*Yes, I’m oversimplfying some aspects of game theory. Bear with me.
For those interested, professional gamblers call this expected value. Also, what the above analysis leaves out is that the number of players also affects your expected value because two or more players can hit the lottery and split the pot. So in the end, as the pot value goes up, more people play, increasing the odds you’ll split the pot and reducing your expected value. It’s rare for playing the lottery to have a positive expected value even with big pots.
Obviously not, or they wouldn’t play. (Okay, some would, but you get the idea.)
Probably. However, according to oregonlottery.org, the demographics of the state coincide with the demographics of lottery players pretty closely:
I’d imagine that many people see the jackpot top 200 million and buy tickets when they woudn’t otherwise, figuring that now “it’s worth it.” And they’re right, even if they haven’t actually done the math on it.
@duality: Yes, that’s certainly one factor that I left out. Another, though, is the idea that one dollar has close to zero value for many people. For that reason, playing a single ticket is high potential reward with essentially zero risk, since that player puts no real value on a single dollar. There’s much more to it, but we’ve probably derailed this thread enough.
Some of us enjoy fantasizing about what we’d do with all that money if we won the lottery. Buying a lottery ticket isn’t required for that, but it does make it possible (if not probable) that it will happen. We might not be thinking about all the things we’d do with the money at the moment we buy the tickets, but that doesn’t mean we don’t ever think about what we’d do with the money.
But I agree that it’s definitely not an investment.
I know people who only play the lottery when the pot is above a certain size, based on the expected value argument. The problem with discussing expected value in the context of the lottery is the fact that winning is such a rare event as to make statistical arguments irrelevant. Knowing the expected value of JSexton’s marbles in a bag game is useful precisely because one can conceivably play enough times to allow for a statistically meaningful outcome. If the white marble pays $2, you will lose money in the long run, whereas if it pays $15 you will win money. No one can play the lottery enough to generate the statistics needed to make the expected value relevant. It’s no smarter to pay a dollar for a 1 in 100 million chance to win 500 million dollars than it is to pay a dollar for a 1 in a million chance to win 80 million.
I absolutely agree. That is what I came in here to post. These essence of value is that you use statistical probabilities to ensure that that you come out ahead or at least break even given a lifetime of trials. That doesn’t apply with the lottery.
For those of you that advocate this, I am going to make the ultimate lottery. The odds are one in quinvigintillion but it pays out a cool googol dollars. Gather your investment buddies up and get in on this sure thing.
Maybe it’s like the Darwin Awards. Some people manage to kill themselves in ways that just flummox me.
That kind of money, intelligently managed, could establish a family dynasty that would last generations before someone screwed it up. I find it pathetic, and the fact they’re now dead doesn’t make it less pathetic to me.
Of course, reading my words in your quote box, I see my last sentence makes no sense (both cases should be 1 in 100 million chance to win), so it’s perhaps unfortunate that you didn’t beat me here.
Also, I’d like to buy one of your lottery tickets, please. I’ve got a good feeling about this!!
There are points in my life where if I had had millions of dollars, it probably would have been the death of me.
That amount of money would have let me get away from facing the consequences of my alcoholism/addiction. Instead I had to face it and decide to get well, because I had nowhere I felt I could run. Money would have allowed me to run more.
Now however, I feel I’m well enough to handle a multi-million jackpot. Bring it on!
That is a potentially valid point. However, where’s the line? Odds of 1 in 80 million not good enough? What about 1 in a million? No? OK, same odds, but the payout grants you ownership of every piece of property on earth. How about then?
I wouldn’t say that the argument is “irrelevant”, but I’ll concede that it’s less relevant, and I think it’s an important distinction. For one thing, in the case of office pools, you start to approach a statistically significant sample size. My wife works at a hospital. When Powerball topped 300 million, they did a pool with an entry of five bucks. More than 500 hundred people participated. Something like 2600 tickets were purchased. That brings the odds against winning down to 1:58,400. Granted, you’d only be winning around 500k, but it’s still a nice chunk of money.
However, my main purpose behind all that exposition was to attack the “tax on people who are bad at math” by showing that mathematically, it’s a good deal. Whether it is a wise use of your money in the real world is a different argument altogether, and I think we’d be in agreement on that point.
Their lives were crap before they won the lottery. Yet they managed to be generous, which is better than you’re being right now.
The guy was an alcoholic. Alcoholics drink themselves to death everyday. It makes very little difference if they have a large bank account or a small one, if they were born with a large or earned a large one or given a large one late in life. An alcoholic drinking themselves to death is not something that I would mock, nor would I be proud of someone that I knew, who mocked someone who drank themselves to death.
As far as being sensible when you strike it rich? Maybe you should watch The Treasure of the Sierra Madre sometime.
NEWS FLASH! Average couple with average house, average jobs, and average cars wins a bajillion dollars! The continue life unchanged and manage their money well.
Doesn’t let you feel near so superior as ‘freaks win big, lose big, die.’
The lottery is a license to dream. Nothing more. It’s provided great benfits that otherwise wouldn’t have passed a mill levy increase vote.
It’s like the kids that play violent videogames then go do something violent. The GAME didn’t make them do it, it it wasn’t there, there would be some other enabler.
There was a time where the Lottery would send me off on flights of new cars, new big house, new this and that. Now, if it’d just pay off my meager debt 8 months early, I’d be happy with that…I managed to get the rest of the stuff on my own (well, with the help of my lovely wife)
Somewhat reminds me of a favorite quote- “Inherited wealth may be something easily squandered, but inherited poverty is a legacy almost impossible to lose.”
I would define the crossover point as being where the odds are remote enough that one is highly unlikely to win once even after playing regularly over the span of one’s lifetime, and where the prize is large enough that changing it by a factor of two in either direction wouldn’t significantly change the resulting lifestyle of the winner. After all, to an average joe winning $80 million is really no different than winning $180 million.
Say they decreased the odds by a factor of ten and increased the prize by a factor of ten. The expected value is the same, but the practical effect is much worse for the average player, as he/she is now ten times less likely to win untold riches. If you do win, you aren’t significantly better off with $1 billion than you would have been with $100 million.
As you point out, office pools are a good way to increase the relevance of expected value. There you’re moving in the other direction, toward the limit where expected value is meaningful, by increasing the odds to win while decreasing the size of the prize. Having a 1 in 50,000 chance to win $50,000 vs. $500,000 is of course a big difference, so it makes sense to take the size of the prize into consideration when deciding whether or not to play.
In any event, I’m going to go buy lottery tickets now. You gotta play to win!
The man who won the lottery obviously had a drinking problem when he won. What probably kept him from bottoming out sooner was that survival instinct that makes many of us get out of bed in the morning-- we know we have to work, have to function, despite whatever monkey’s on our back. This guy was probably a functioning alcoholic who likely would have lived a decade or two longer with his habit and died of it eventually. Probably would have had some good times and bad times in there, and it would have been a life.
Winning the lottery changed everything. Suddenly, Mack doesn’t have to go to work anymore. He doesn’t have to struggle to survive and support his habit-- no boss to answer to, no more bills to pay, no limits on how hard he could binge. Of course he’s going to flame out in spectacularly quick fashion; all the limits that kept him function have been removed.
I guess Mack needed those limits, and without them, he could not live. I bet he never would have seen it that way, but the same crap that oppressed him (crap job at the factory, small paycheck, etc) kept him alive. I find that a sobering thought and I feel bad for the guy. No schadenfreude here. Who knows what invisible threads keep all of us from the edge? It takes an extreme event like this to show them to us, and even then it might be too late.
(Okay, some would, but you get the idea.)
