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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, tho

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 http://adamlamers.com/lottery_simulator

ecshafer 3y ago
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.
- vikingerik 3y ago
  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.
- angry_moose 3y ago
  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/ https://bigthink.com/starts-with-a-bang/math-of-powerball/
  - panarky 3y ago
    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 https://en.wikipedia.org/wiki/Kelly_criterion
- assbuttbuttass 3y ago
  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
  - leoedin 3y ago
    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.
mlyle 3y ago
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.
- dylan604 3y ago
  Isn't there another study of people that won big have also lost it/squandered it all within a fairly short amount of time?
  - chmod775 3y ago
    Gamblers hardly intersects people who spend their money responsibly.
  - Night_Thastus 3y ago
    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.
    - CodeSgt 3y ago
      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.
      - dylan604 3y ago
        >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
londons_explore 3y ago
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%).
frud 3y ago
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.

ecshafer 3y ago

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.

vikingerik 3y ago
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.
angry_moose 3y ago
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/ https://bigthink.com/starts-with-a-bang/math-of-powerball/
- panarky 3y ago
  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 https://en.wikipedia.org/wiki/Kelly_criterion
assbuttbuttass 3y ago
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
- leoedin 3y ago
  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.

mlyle 3y ago

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.

dylan604 3y ago
Isn't there another study of people that won big have also lost it/squandered it all within a fairly short amount of time?
- chmod775 3y ago
  Gamblers hardly intersects people who spend their money responsibly.
- Night_Thastus 3y ago
  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.
  - CodeSgt 3y ago
    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.
    - dylan604 3y ago
      >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

londons_explore 3y ago

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%).

frud 3y ago

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.