I really like Colin McMillen's comments on this matter:<p><a href="https://plus.google.com/107814003053721091970/posts/6sPpxMo6JTM" rel="nofollow">https://plus.google.com/107814003053721091970/posts/6sPpxMo6...</a><p>Some choice quotes from his Google+ post: "The lottery is not a tax on people who are bad at math. It's trading a little bit of expected-value for a lot of variance."<p>"There are many other cases in real life where mean/variance tradeoffs arise, and there are perfectly plausible objective functions under which it makes sense to follow a policy that doesn't maximize expected value.<p>The obvious example is insurance, where you pay a small bit of money each year to reduce the chance that you end up suddenly needing to pay a lot of money. Same with forming or joining a startup; on average you'll make less money than if you take a "normal" job, but there's some small chance that you'll have just joined the next Apple or Google and you'll end up rich.... "
Some vaguely interesting statistical analysis, but here's the money quote at the end (TL;DR)-<p>"So why do I still buy lottery tickets? <b>Definitely not for the expected monetary return on investment.</b> I think of it as a discretionary entertainment spend. I get literally hours of enjoyment from fantasizing what I’d do if I won."
Per the Kelly Criterion, unless you have a big bankroll, the minimum bet is an overbet, which turns it into a losing strategy.<p>Suppose you have $100,000, and repeatedly bet .001% of your net worth on a single ticket in the lottery at 100,000,000:1 with a 2x EV (disregarding that you can’t bet more or less than the price of a ticket). You do it 2,000,000 times, and then you hit the jackpot – pretty lucky since the odds are 100,000,000 to 1, right? But by the time you hit the jackpot, your bankroll has been so depleted that winning 200m x your bet, you only get back to 41% of your original net worth – because you overbet!<p>A longer discussion (by me) of why only millionaires should play Powerball -
<a href="http://blog.streeteye.com/blog/2011/11/why-only-millionaires-should-play-powerball/" rel="nofollow">http://blog.streeteye.com/blog/2011/11/why-only-millionaires...</a>
In the book "Thinking fast and slow" by Daniel Kahneman, it is claimed that there is a growing body of evidence that we really have two brain systems. A fast one, which uses heuristics to quickly approximate the answer, and a slow one, capable of deliberate and rational thought. He argues that the fast brain system is really responsible for a lot of our cognitive biases.<p>For example, our fast brain does not really understand probability. It only knows three categories: either something is impossible, it is possible, or it is a certainty. A lot of human behaviour with regards to probability can be explained by this simple assumption.<p>Why do people buy lottery tickets? For their intuition, it moves an impossibility into a possibility. The fast brain system that fuels their intuition does not care what the actual probability is and does not understand anyway.
Lottery, as a form of innocent betting, can really provide a lot of fun for a small price. I would be bored to death to watch a soccer game, but when I bet 1€ on it, it suddenly becomes 2 hours of fun. And I don't expect to "win the ticket", cause I already got more than I paid for.<p>Looking at everything from the profit/cost point of view can lead to a very boring life, for most of the people.
Lotteries are a tax on people who are desperate, not ignorant. Even if you understand the math, your utility function changes so that you're willing to trade a small expected loss for the long shot chance of solving all your problems. I don't buy the idea that swathes of lottery players really think they're making a value bet. Just because they respond with anecdotal evidence when you confront them with the true odds, doesn't mean they're really arguing the facts, they're just protecting their hopes.
Simple evidence that gambling (rather than just lotto) is a tax on poor people - check out where the gaming/'slot' machines are. Last time they ran the map in the paper, the venues were heavily clustered in the poorer northern and western suburbs of Melbourne, with another cluster down in Frankston.<p>Then of course there's the simple point that less money comes out of lotto than goes in, simply to pay for overheads and profit of the gaming company (as with all gambling) plus a bit of tax on the ticket. The ticket sale simply can't be a zero-sum game; less has to make it back to the winners than was paid in the first place.<p>That being said, I also pay the idiot tax every month or two, and for the same reasons as the author - entertainment.
This is all bad probabilities if you don't take into account the fact that you repeatedly buy tickets. I'd like to see a more detailed study counting the probability of never winning when playing systematically for 20 years, for example.<p>But nevertheless. Yes, the lottery is a tax for the poor. And if you expect your life to change for the better by winning a big bag of money (that you will have taken to the other suckers who lost, minus the organiser's fee), then you just need to reconsider what makes a happy life. You should also consider how many people get isolated after they have won, not knowing how to deal with such a change, such a "responsibility", such a social pressure from family and friends after they have won.<p>I'd never play the lottery not because of the ridiculously low chances of winning (I also am a statistician), but because what I would win would change nothing to my human condition. I prefer reading Epictetus instead. It's cheaper and the effect lasts longer.
If you're analyzing lotteries, one thing you have to think about is the diminishing utility of money. ( <a href="http://en.wikipedia.org/wiki/Diminishing_marginal_utility" rel="nofollow">http://en.wikipedia.org/wiki/Diminishing_marginal_utility</a> ). Your first dollar is a lot more useful than your millionth dollar. Or another way, having a million dollars is not a million times as useful as having one dollar - it's a lot less useful than that. This makes a lottery a pretty bad investment even when the expected-returns are in your favor.<p>Not to mention all those stories of people who win the lottery and then lose all their friends out of jealousy. But that's harder to analyze.
It might be an urban myth, but it's still funny:<p>The only weekend when casinos did not make a profit, in the entire history of Las Vegas, was when the annual U.S. statisticians conference was organized in Las Vegas :)
Poor statistics on the chance of winning aside, there is one reason for me to spend $1-$2 a week on tickets: Having a ticket ensures you have a chance of winning, while not having one ensures none at all. Losing the $50-$100 per year isn't too big of a deal for me, especially for the entertainment value.
Oddly, his real reasons for why he plays the lottery has nothing to do with probability and statistics, and is in the last two paragraphs. I feel the essay would have been better serveed if he had started with that, then said "But, given that, let's still explore what the actual expected return on investment is for the fun of it."
I always wonder about these calculations. According to <a href="http://www.michiganlottery.com/where_the_money_goes" rel="nofollow">http://www.michiganlottery.com/where_the_money_goes</a> out of every $1 players spend on the Michign lottery, $.58 goes to player prizes. Assuming they're actually counting that correctly, doesn't that mean the expected monetary return (to you, of course it's nice that you're donating to the school system) of $1 spent on the lottery <i>has</i> to be $.58?
- If you're so poor that paying 1 USD is a hardship, then you shouldn't play the lottery. Otherwise, where's the harm?
- The argument, "the lottery is a tax on poor / stupid people" is valid but useless when talking about small amounts of money.
- The difference(s) between winning the lottery and someone just giving you millions of dollars? - 1) You know where the money came from; 2) The person just giving away the millions isn't receiving payment for giving away the money.
Saying that the lottery is a tax on poor people is like saying that buying a bottle of Coke is a tax on poor people. Both of these events are completely voluntary. No government agency was involved in making you spend the money. You are not obligated to do it. And, if you choose not to spend the money you are not violating any laws. It is not a tax. That's the most ridiculous idea I've ever heard.<p>One could argue that spending money on a lottery ticket is actually better for you than spending the same amount of money on a soft drink. One gives you hope and entertainment and might have other positive "feel good" side-effects. The other fills you with sugar (high fructose corn syrup) and is not good for anything at all.
I have always had a hard time equating ROI on any windfall probability. I view lottery systems as a windfall system in that the chance of winning is zero and the expense of playing is trivial, so any investment has no expectation of return it only allows for the possibility of windfall. The $1600 investment over 30 years would not have noticeably increased or decreased my QoL so it is not a lose in my mind, only a technicality.
Best entertainment value ever: When one of the big jackpots was making the news I bought one as much to head off the conversation of why not than anything, but it triggered these incredible technocolor daydreams! I was not bored on the subway for days. Diminishing returns though, since then the occasional ticket never had the same internal result.
Amused at the claim that 1 & 1/4 million is 'just over [...] a million"<p>I tend not to think of an added 1/4th as "just over" but perhaps that's a difference in perception.
I love this argument. It gets juicy quick. Sugary, like cake. When they tell you "you can't win if you don't play", and you say, "nonsense, I can find a dropped lottery ticket on the ground that turns out to be the big one" and they say "really?? what are the chances of that happening?". Black forest, cherry on top. Just wonderful.
It makes perfect sense to simply purchase 1 lottery ticket. Takes your chances from 45,379,619:0 to 45,379,619:1, for a negligible cost.<p>Beyond that your time is wasted, statistician or not.
I was initially confused and annoyed by the author's lack of justification. But I enjoyed his conclusion, that there's an 'entertainment' value attached to the purchase.
It reminds me of this
<a href="http://www.wired.com/magazine/2011/01/ff_lottery/all/1" rel="nofollow">http://www.wired.com/magazine/2011/01/ff_lottery/all/1</a>
You may be able to increase your expected value by choosing numbers that are less popular. It would be interesting to research the psychology behind number selection and choose combinations less likely to have a multi-payoff outcome.
'The decision of whether to buy a lottery ticket shouldn’t be based on the probability of winning, or the expected return of a ticket, but on the entertainment value that comes from imagining a different life.'<p>sounds like college, s/entertainment/networking
It's posts and comments like these where I so miss the down vote click.<p>There's not even a hint of irony.<p>It's all about the 'entertainment' value.<p>Am I seeing a remake of the book/movie 'Hunger Games'?<p>"Oh Nigel, do kindly pass me two of your Entertainment cards. You'll get a treat if you do..."