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Comment by acomjean | Hacker News Reader

When I was young I had a friend who bought one Massachusetts (US) lottery ticket a week. I remember he "won" (basically got his money back). When he went to cash out the cashier asked him, "do you want the money.. or another ticket". He took the another ticket and promptly lost. lesson learned. You can't win if you don't play, but 2 tickets doesn't increase your odds significantly.

Where I worked there was a convenience store store. I got to know the owners a bit. One day they were posting a sign "People at our store won $850,000 on the lottery last year". I said, "wow thats a lot". She turned, shook her head and said "I know what they've spent... its not a lot." and proceeded into a mini tirade against gambling, which she promptly stopped when a customer entered the store. Its profitiable. But in the US with sports gambling everywhere, I wonder if lotteries have lost their luster.

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There's a few Powerball Simulators (largest US lottery) out there - simulate buying 1 ticket a week indefinitely.

It usually works out to about a -90% ROI, though I did just somewhat undermine my point by hitting $2,000,000 (5 white balls + powerplay) after 246 years and becoming profitable. First time I've ever hit on one of these, I let one go for several millenia one time.

http://adamlamers.com/lottery_simulator

There is a point where the expected return is positive. Its around $1B or some large number like that. Sure the expected return is like 1% positive, but its positive.

If the jackpot splits in the case of multiple winners, it's not positive - enough tickets will be bought until the expected number of winners is more than one and the expected value is no longer positive.

Only if you don't factor in taxes and multiple winners.

This article added in sales numbers to estimate the actual expected value and it peaks around a $500 million jackpot with an expected value of $.85 from a $2.00 ticket. (very close to the bottom)

https://bigthink.com/starts-with-a-bang/math-of-powerball/

You can use the Kelly Criterion [0] to compute the optimum bet amount given the odds, the payoff, the cost of a ticket, and the size of your bankroll.

Usually the optimum bet is zero because the expected value is negative.

But when the jackpot gets big enough, occasionally the Kelly Criterion will advise buying a ticket or two if your bankroll is really big, like $10 million.

[0] https://en.wikipedia.org/wiki/Kelly_criterion

How does that work? By linearity of expectation, if the expected value of buying 1 ticket is negative then the expected value of buying multiple tickets should be even more negative

Typically lotteries roll over the jackpot if nobody wins. So if there's a streak of no winners, the total jackpot amount can be more than the cost of buying every possible ticket.

Of course, if you did this you might get unlucky and find that there's another winner in that draw, in which case you'd have to split the winnings and probably wouldn't make your money back.

Of course, spending a few bucks per week isn't necessarily irrational. The hope and entertainment has some value.

And, of course, the marginal value of a couple bucks more in your pocket may be nil, but the life-changing experience of a win may have considerably more value; that is, marginal utility may not just flow smoothly downwards.

Isn't there another study of people that won big have also lost it/squandered it all within a fairly short amount of time?

Gamblers hardly intersects people who spend their money responsibly.

Even those who would be deemed "responsible" (already somewhat wealthy, otherwise stable) often end up far worse off.

It often ends in losing friendships, ties with family, death/kidnapping/blackmail threats both close and far away, endless frivolous lawsuits, financial ruin, etc.

The ratio of "happily ever after" stories to horror stories for winning the lottery seems a bit low for my tastes.

That’s just survivorship bias (or perhaps, the opposite).

You don’t hear the happily ever after stories because they don’t tend to reach out to the media after a few years and say “Hey! FYI I’m still rich and my life is perfect.”. They’re off enjoying their money somewhere. The scandals seem more common because those are the only situations that really get publicized.

>they don’t tend to reach out to the media after a few years and say “Hey! FYI I’m still rich and my life is perfect.”

No, that's what social media is for

Afaik (and I watch this fairly closely) there hasn't been a study. There are a lot of anecdotes, typically of the form "a person won a few million but spent like they had an income of a few million per year," sometimes of the form "a person won a huge amount of money but it turns out money doesn't solve all problems," and sometimes of the form "a person won a huge amount of money and invested it poorly." But most people who win a big lottery are still rich a decade or two later.

> isn't necessarily irrational

I used to say this to justify buying 20 tickets twice a week.

It's not irrational I can afford it, right? And the purchase gives me the psychological reward of dreaming about a big win.

But then after every draw I'd check my numbers and suffer a twinge of buyer's remorse. For me, that (small) regret more than offset any positive psychological benefit. It was a minor addiction that did more harm than good.

So now I've cured my addiction by turning Buyers Remorse into whatever the opposite of that is.

I have a cron job that generates 20 picks twice a week before each Mega Millions (US) draw.

I never buy these numbers -- the script just saves them in a Google Doc so there's evidence of the numbers and the timestamp when they were chosen.

Then after the draw, it checks them against the winning numbers, and emails me the results.

Now twice a week I get the (small) psychological benefit of realizing I didn't waste $40.

Maybe the opposite of Buyers Remorse is "Decliners Delight".

Wow, I hope that this cron job won't win anything significant. Imagine the remorse of nut buying those lucky numbers!

Anything in excess is bad. Having a couple drinks throughout your week is fine, going on a bender and downing 20 drinks one night per week isn’t.

Having a snickers bar is fine if you make it a rare reward, eating several every day isn’t.

Etc etc etc.

Everything's different for everyone.

I buy a few tickets every time the expected value might be weakly positive, even though this still doesn't make it a "good purchase."

And I've played blackjack under conditions (rules and my carefulness of play) where it's expected to be slightly money-losing, but had an exhilarating couple of hours and conversation. Cheap entertainment compared to many other things.

I believe the UK lottery has a required-by-law payout percentage of 42.47%.

28% also has to be donated to charity.

Which means, assuming you would donate to charity anyway, you are only wasting, on average, 30% of your money.

That is substantially better than the US powerball (at ~90%).

The typical expected value of a lottery ticket is 50% of what you paid for it. That includes hitting the one-in-many-millions jackpot, which you could go many lifetimes without hitting. If it's given you don't hit the jackpot, then your expected value is much lower.

In your friend's case he increased his odds by 0. New ticket means a new game probably, so any prior winnings does not factor in the next game. He did increase his odds of losing everything significantly!

The rational thing to do is not play again. I'm sure someone can model this with game theory or probability math for us.

Stated another way. National and State lotteries are the largest ongoing wealth transfer from the lower-income bracket in the US. The lotteries are overwhelming played by the lower-income and that money is used to fund a large number of things in state governments.

> You can't win if you don't play, but 2 tickets doesn't increase your odds significantly.

Going from 0 to 1 tickets increases your odds infinitely. The spread on your possible outcomes goes from $0-0 to something like -$2 to $100m heavily weighted toward the bottom.

Going from 1 ticket to 2 tickets to 40 tickets… increases your odds by a very minuscule amount. The spread on your possible outcomes is now like -$80 to $100m, still heavily weighted towards the bottom.

The marginal value of every ticket after the first is basically negative.

I don’t buy lottery tickets but buying _one_ makes sense to me. No more than that.

That's the Law of Large Numbers working. A friend of mine won a small but not insignificant amount in a lottery and then "reinvested" it in the lottery and, as expected, lost it all.

>She turned, shook her head and said "I know what they've spent... its not a lot." and proceeded into a mini tirade against gambling, which she promptly stopped when a customer entered the store. Its profitiable.

Curious, but was this surprising to you? These games are literally all designed to take in money and pay out a portion of it. They have to be profitable.

I was surprised the payouts from a small convenience store were so high. And the spending were so high. I'm a very infrequent gambler..

When I was at IBM one of the mathemeticians had a bumper sticker on his office door. “the lottery: a tax on people who are bad at math.” or some such thing. I took it to heart.

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