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The Powerball Jackpot is $425M. Should you play?
- stevekemp 13y agoInteresting article. In the past I've used the powerball simulator to get a feel for things. Buying two tickets a week for hundreds of years, and tracking profit/loss: http://justwebware.com/powerball/powerball.html http://justwebware.com/powerball/powerball.html
- MrFoof 13y agoThe odds are beyond terrible, but they are exactly zero if you don't play. My minimum required jackpot for me to play is a $320,000,000 jackpot. I increase the minimum every year. Keeps my maximum spending to about $4 or $6 a year, which is worth it for the entertaining daydreaming it provides.
- gunn 13y agoIn fact the return is 100% if you don't play.
- jere 13y ago$0/$0 The return is undefined actually.
- seanmcdirmid 13y agoI thought that was infinity? Ah, but that would cause problems.
- aplusbi 13y agoIt depends on which 0 is bigger.
- tinco 13y agoThis concerns real things, not mathematical approximations. So, we divide 0 dollar over 0 people, that means 0 people get 0 dollar. The answer is clearly 0.
- jordanthoms 13y agoBut _each_ person, of which there aren't any, gets an undefined amount.
- Deestan 13y ago> The answer is clearly 0. No, because there are no people to get 0 dollars; the concept of "each" makes no sense when there are no eachees. The answer is clearly undefined.
- Dylan16807 13y ago1/0 is inf, 1/-0 is -inf, 0/0 is undefined
- pedrocr 13y agoUsually "returns" are measured as profit over invested amount so it would be 0%.
- Avshalom 13y agoMeh. I'd rather take my chances waiting for a winner and then sueing the crap out of them. Seems like much better odds.
- chiph 13y agoIn that case, you should be playing right after a jackpot is paid out. Your chances of winning are the same, but the chances of splitting a jackpot go way down because there are fewer people playing. Sure, you'll have to suffer with only a $40 million payout, but it's still nice.
- nullc 13y agoSad to see it not make the Kelly criteria argument for ruin, even where there is a positive scalar expectation: http://r6.ca/blog/20090522T015739Z.html http://r6.ca/blog/20090522T015739Z.html
- jmharvey 13y agoO.P. here. The Kelly criterion is a product of the logic outlined in the section about utility being the log of wealth. In short, assuming a jackpot of under $1 trillion, you'd need to have a bankroll on the order of eight digits to justify spending $2 on a ticket under the Kelly criterion. Also, the Kelly criterion doesn't exactly apply here because this is more like a one-off event than a repeated game. But a lot of the same principles apply.
- nullc 13y agoKelly criterion has nothing to do with the marginal utility you gain from more money, it's about the risk of ruin in an iterated game. And indeed, you can say that purchasing one ticket is a one-off event... but if you buy that one, why not every one that happens when the expectation is in your favor? Thus the risk of ruin becomes interesting to consider.
- jmharvey 13y agoThe Kelly criterion is designed to optimize the long term growth of your bankroll in an iterated game. And the strategy that optimizes your bankroll in an iterated game is the one that maximizes the expected value of the log of your bankroll after each iteration. Strictly speaking, the Kelly criterion isn't concerned with maximizing expected utility, but the math works out the same.
- RockyMcNuts 13y agonot sure I agree with you. Kelly says, if there is a positive expected value, there is an optimal amount to bet, which maximizes the growth rate of your stack per bet, if you were to bet repeatedly. If you overbet, your expected growth rate is negative... because over the long run, by the time you hit the jackpot you've lost too much of your stack to get back to even. Basically, I think Kelly says you can't just go by expected value, ie your edge, you have to look at your stack. Overbetting turns a +EV bet into a -EV bet and eventual loss of your whole stack. So 1) I don't think Kelly is a product of log utility, it just requires that you are trying to maximize your growth rate (As an aside, in many settings people are much more risk averse than log utility implies; and in many settings people don't have consistent cardinal utility, a time-inconsistent utility like prospect theory is more predictive) and 2) since you are presented with interesting bets every day, if not this particular one, Kelly generally applies, since if you don't heed it you fall victim to gambler's curse.
- rverghes 13y agoIn my opinion, using expected value to evaluate lotteries is not correct. Realistically, there are only two outcomes. Either you win millions, or you lose a few thousand over several years. The future where your outcome matches the expected value never actually occurs. This is unlike games like blackjack, poker, or roulette, where the expected value does match the eventual outcome. So if you can live with the second outcome, playing the lottery is fine. But using expected value does not seem appropriate to me.
- rodly 13y ago> In my opinion, using expected value to evaluate lotteries is not correct. Realistically, Expected value is realistic. The relation to casino games is silly seeing as the timelines for a few hands of blackjack are several orders of magnitude shorter than buying a ticket for a $300+ million dollar lottery.
- modeless 13y agoThe math for split jackpots assumes that people pick randomly distributed numbers in their tickets. But that's clearly not true, and that means by choosing numbers carefully you should be able to significantly reduce the chance you'll have to split a win without changing your chance of winning. I'd love to see an analysis of how beneficial this could be and which numbers you should pick.
- jmharvey 13y agoDefinitely. Next time there's a big jackpot (maybe this weekend, if no one wins tonight) I'll do a follow-up post that looks at that.
- ryandvm 13y agoChoose 1, 2, 3, 4, 5, 6. Nobody ever chooses that set.
- doktrin 13y agoBecause choosing that sequence destroys the illusion by highlighting the infinitesimally small chances any given ticket has of winning. Rational people who play the lottery know their chances are laughably low, and that a $1 or $2 ticket is just a license to daydream about riches and wealth.
- mserdarsanli 13y agoThere are many people who think the same.
- jonnathanson 13y agoThe laws of large numbers make any edge supposedly gained by "picking what nobody else picks" almost entirely moot. The probability is still incredibly small that any given sequence will come up. Getting the right sequence is the much taller hurdle to clear before tackling the problem of how many others have also picked correctly.
- cmsmith 13y ago
- ChuckMcM 13y agoI love this analysis. Growing up in Las Vegas we did probability analysis on Casino games as a homework exercise. And it explained exactly why Casinos are a license to print money. It's even weirder when you consider the case where you gamble $10/week versus save/invest $10/week in a compound interest account. Guess who is happier 20 years later? But of course our gambler is more entertained so there is something to be said for that too.
- seanmcdirmid 13y agoLots of investments are very risky, almost like gambling but the odds aren't supposed to be stacked (return related to risk). Many people are addicted to playing the market would be (and often are) the same ones who would be addicted to games of chance. I don't see why we have casinos at all. Just replace them with exquisite trading houses with over blown transaction fees.
- erehweb 13y agoBetteridge's Law of Headlines continues to apply. http://en.wikipedia.org/wiki/Betteridge%27s_law_of_headlines http://en.wikipedia.org/wiki/Betteridge%27s_law_of_headlines
- lcedp 13y agoThe return is so huge compared to investment that you should play based on... what ticket cost means to you. Would you play if ticket's cost would be $0.01? Of course you should - $0.01 won't make any difference to you.
- sgloutnikov 13y agoInteresting article, but hard to put mathematical facts over psychology in cases like these.
- wcchandler 13y agoI've never really thought of playing as an investment. I've always thought of it as a donation to the education system that also has a potential for a large payout. I don't play very often -- 2 or 3 times a year. I never feel bad about losing the money. The way I see it, I would've donated it to some cause. That, to me, makes it worth playing for.
- DamnYuppie 13y agoUntil you realize just how little of that money makes it to the schools :-/
- MartinCron 13y agoEspecially as it becomes an excuse to fund the schools by that much less from the general budget. It's an exquisite accounting lie.
- pivotandconquer 13y agoThis post shows one of the limitations to medium.com, namely, a lack for math/LaTeX formatting. This post was well written, but occasionally difficult to parse.
- coherentpony 13y agoIf you don't play, you definitely won't win it.
- jrs235 13y agoIt's darn near impossible to justify buying a ticket as a rational, wise investment (as the article points out) due to the odds, split jackpots at that size, and then taxes. But, if you include the intangible of a night or three of "dreams" of what you would do... then maybe one ticket (and only one ticket) might be okay... $2 for 60 hours of dreaming or a soda?... But then again you might be better without that money as most go broke and their relationships and lives are ruined over money. I'd recommend purchasing a $1 pick 5 game, often times with odds around 1:170,000 if you want to but a dream and not win enough to completely ruin your life. Or don't buy a ticket at all.
- markdown 13y ago> https://medium.com/p/28c5a31cd41d https://medium.com/p/28c5a31cd41d What kind of URL is that?
- Ackley 13y ago"permanent"
- jackschultz 13y agoI've always felt like the value of playing the lottery is not in the numerical outcome, but rather the enjoyment of thinking about what could happen if you win. How much enjoyment you get from dreaming about the outcome can, for some people, be well worth the few dollars it costs for the ticket.
- eliben 13y agoMore and more blogs moving to Medium for some reason. This makes me sad, because it means horrible formatting with anything code or math related. At least until they fix that...
- feral 13y agoIn the 'but then it gets even more complicated' spirit: When the author mentions buying a ticket in the end, for the entertainment of fantasising about a potential windfall, I was reminded of this interesting Less Wrong article: "Lotteries: A Waste of Hope" which argues even that is a bad reason to play lotteries. http://lesswrong.com/lw/hl/lotteries_a_waste_of_hope/ http://lesswrong.com/lw/hl/lotteries_a_waste_of_hope/
- MartinCron 13y agoEntertainment derived from fantasy is fine. I've found that I can cut out the whole "buying a lottery ticket" part and the fantasy is just as rewarding.
- jmharvey 13y agoOP here. Interesting article. "Fantasizing" isn't what I was trying to describe in the "entertainment" section. I 86'ed a longer explanation of what I meant, but here goes: When I say, "I also enjoy letting my mind wander and think about what I’d do with a nine-figure windfall," I actually mean that I think about it, not that I fantasize about it. Some of my problems would go away. Others wouldn't. I'd have a whole new set of issues to think about. And I'd still come in to work [0] tomorrow. When I think about what it would be like to win the Powerball jackpot, I tend to reflect on some of the issues raised in PG's "Cities and Ambition" essay [1], when he talks about the things different cities value: "New York is pretty impressed by a billion dollars even if you merely inherited it. In Silicon Valley no one would care except a few real estate agents. What matters in Silicon Valley is how much effect you have on the world." The utility I get from buying a lottery ticket isn't about dreams of private jets and caviar. It's the perspective I gain: if I didn't have to think about money ever again, what would I want to do with my life? I think I'd keep working on startups. What would I do differently? I'm not sure, but I'd start with buying a better set of wheels for my bike. In the bigger picture, I'd probably spend more time on projects that have the potential to have huge impact, and think less about whether a particular idea can be a profitable business. It's easy to get caught up in the patterns of daily life. Thinking about winning a jackpot makes me evaluate my life from 30,000 feet. I guess I could do that for free, but at least for me, that $2 gets me thinking a little differently. And to me, that's where the value is. [0] http://zeromailer.com http://zeromailer.com [1] http://www.paulgraham.com/cities.html http://www.paulgraham.com/cities.html
- arctangent 13y agoThis doesn't take into account the value of the "hope" that buying a lottery ticket gets you. Specifically, the owner of a lottery ticket has bought the right to dream about how their life could suddenly be turned around if only their numbers came up. I admit that this "hope" may not be worth much to some people, but to those who are scraping by it might be worth quite a lot. (I will leave discussion about whether lotteries exploit the poor to another day.)
- lifeformed 13y agoI don't think a high enough dollar value is enough to make it worth playing. Over a certain amount, the winnings are simply just "arbitrarily large". If the prize was a trillion dollars, but each ticket cost $100 to play, does that mean it's now worth it for everyone to buy a ticket? You're still not going to win. I think stuff like this should be weighted towards chance of winning. Given the choice between a 1 in a million chance of winning $2 million, or a 50% chance of winning $4, I'd pick the $4 one every time. They have the same expected value, but one of them gives me a chance of winning anything at all.
- chrisbennet 13y agoDoes anyone actually consider whether they will be happier if they win the lottery? (I don't play the lottery on purpose.)
- differentView 13y agoYou should play in a workplace pool situation. $5~$10 is a fair price for psychological insurance. If most of the people in your office win the jackpot, no matter how Vulcan you think you are, it will negatively affect you psychologically for many years.
- pallandt 13y agoSomething interesting for the mathematically inclined. "Statistical auditing and randomness test of lotto k/N-type games", available freely at http://arxiv.org/abs/0806.4595v1 http://arxiv.org/abs/0806.4595v1 Powerball is not like a typical k/N lotto game though, but you might still want to skim the paper.
- jmharvey 13y agoInteresting, I'll have to give that paper a deeper look. I have noticed seemingly skewed lottery results in the past, but I've never found a case where the skewness of the results made a material difference to the optimal strategy (excluding cases where computer RNGs were configured incorrectly).