Never Buy Two Lottery Tickets

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29 thoughts on “Never Buy Two Lottery Tickets

    • Thanks – though I suspect that lottery-ticket buyers are no more immune to sense than most people (which is to say, like the rest of us, they are probably *very* immune to it).

  1. My mother lived in World B. Lottery, horse race, free admission,extra night’s stay, youname it. BUT: always small. Ten dollars max. Or a free stay at a hotel she hated. She got as much fun as if she’d won big.

  2. The Mega Millions is now $285 million. Probability of hitting the jackpot is 1 in 225 million. The expected value of a $1 ticket is about $1.27, assuming only one winner. Therefore, you should buy as many tickets as you can afford! Where else can you get a 27% return?!?

    • John Cowan makes a good point below (lots of these jackpots wind up getting split, which spoils the rate of return); but even if there’s no shared jackpot, the fact that we don’t all go do this seems like good evidence that expected value isn’t a very complete tool for decision-making!

  3. Ha ha, I love it. I tell people who urge me to play the lottery “but if I don’t play, I’m a winner every time. I win the money I would have spent on the lottery.” I’m really not so interested in the voluntary taxation that the lottery system is.

  4. Brett Parker: The kicker is “assuming only one winner”, an unsafe assumption.
    Multiple winners are common.

    Ben: I think you are wrong about buying two tickets. I compare lottery tickets to roller-coaster tickets. In each case the payoff is excitement, but people are excited by riding the roller coaster twice, though probably not twice as excited. Likewise, in a boring life a bit of excitement each time lottery numbers are announced makes sense. But perhaps you mean “Don’t buy two tickets for the same lottery.”

    • Yes! I should have been a little clearer – that’s more what I was going for.

      Although perhaps, as with roller coasters, too many iterations will lead to nausea…

  5. I disagree with the analyses. You should purchase (or not purchase) lottery tickets based on their expected value. If the payout is high enough, you should buy, and if it is not (which is almost all the time) you should not.

    • Yeah, I see the argument – the problem is that you can never buy enough! Like, if I’ve can pay $1 for a 1 in a billion chance at $10 billion, then the expected value is great ($10 per ticket!), but even if I spend all my money on it, the 99.99% likelihood is that I’ll just go bankrupt.

  6. So I’m a “Math Guy”, and unsurprisingly, I’ve always told people to not buy lottery tickets, for all the usual reasons. However, I’ve recently told my wife the opposite. Here’s why:

    (1) I’m 45 and have been retired since I was 41. Part of being a “Math Guy” is that I was a good engineer and understand personal finances well. I married my wife when we were both 40 and we agreed to keep our finances separate. She still works, but plans to retire around age 52.

    (2) She’s somewhat glum that we have to wait until she retires to begin our travels around the world, etc., since her job just doesn’t give enough vacation time to do so now. Don’t bother recommending that I just pay her way; SHE wouldn’t allow it if I wanted to.

    (3) We live in NC, and there’s a lottery called Carolina Cash 5 that (a) is 1-in-750,000 to win — $1 to play, match all five numbers from 1 to 41, (b) the jackpot is usually in the $100k-$300k range, but pays up to $1M-$2M if no one wins for a while, and (c) it pays the whole amount at once, rather than in installments. So, knowing that splitting the jackpot is a risk and that taxes would take about half of it, it starts making sense to play from an expected value standpoint at around $2M.

    (4) You can greatly reduce the odds of splitting your potential jackpot by picking at least two or three numbers in the 32-41 range, which rules out all the players who want to pick days of the month as their numbers. You still run some risk of sharing with an “easy pick” winner, but I’ve looked at past jackpots and split prizes and sure enough — there’s extra value in the higher numbers.

    (5) We both realize that the utility of winning $2M is about the same to her as winning $200M, because we don’t have expensive tastes. So this is definitely the right lottery to play, if she’s going to play one (as opposed to PowerBall or any of the gargantuan-prize lotteries). That’s because . . .

    (6) The real prize is earlier retirement. If she buys 50-100 lottery tickets per year, she has a chance — maybe better than 1-in-2000 or so over the next few years — of actually winning and being able to gain 3-7 years of additional retirement. The alternative, not buying tickets, saves her $500 or so, but that gives her ZERO chance of earlier retirement. There’s no investment strategy I can think of that could even have a chance, however small, to provide her with a 2000x return on investment. Not penny stocks, not digital currency gambling — nothing (if you have any ideas, I’m all ears!). I suppose she could take the money to a casino and put $500 down on the roulette wheel and try to hit a number, twice, and then go double or nothing — but we’d have to travel to a casino to do so.

    So that’s what I told her: when the jackpot gets big enough, buy a bunch of tickets (all different and not the easy-pick — so the number of tickets she buys is limited by her patience). If this strategy works out, I’ll be sure to come back and let you know! 🙂

    • Thanks for sharing, and keep me posted! I love this analysis; it’s a very inventive kind of asset to include in your retirement portfolio, but totally sensible for the conditions you’ve described.

  7. Reminds me that the chances of their being a bomb on an aircraft are tiny. The chances of two bombs are *astronomically* tiny. So to be extra safe, take the first bomb on yourself, thus reducing the chances of their being a second bomb.

    In retrospect I think there may be both moral and statistical flaws in this…

  8. I’ve had people tell me that “If you don’t play you can’t win” and have tried to explain that buying a ticket does not significantly improve your chances of winning.

    If the odds of winning are a million to one, then your chance is 0.000001.

    The odds of finding any lottery ticket before a drawing is tougher to calculate, but let’s say it’s ten thousand to 1, or 0.0001. Multiplying that by the the odds that the ticket you found happens to be the winning ticket yields 0.000000001.

    That means that the buying a winning ticket improves your odds by 0.0000009999. A difference of +/- 0.0000009999 isn’t significant by any standard.

    Therefore, if you want to buy the dream of winning the lottery, remember that you can get the dream of finding the winning lottery ticket for free, with almost no difference in the actual probability involved.

    • I like this point!

      The analysis gets undercut slightly if you look at ratios, rather than differences (“how many times likelier am I to win the lottery?”), in which case buying a ticket multiplies your odds of victory by 10,000 (according to your estimates).

      Even so, the probability of finding a free ticket on the ground is probably higher than the probability of winning given that you have a ticket. So when people buy tickets, they’re only solving the easy step, not the hard one.

  9. A bit of historical context: Has anyone else observed that the rise in state-sponsored legal lotteries has coincided with the movement to reduce taxes at all costs? Yes, I know that co-incidence is a type of correlation, not necessarily causation. Still….

  10. Pingback: Never Buy Two Lottery Tickets — Math with Bad Drawings | i am become computational

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