4 ms·

Remember reading in some book on probability and statistics that one will be better off betting insignificant amounts of money rather than not playing at all.

Semaphor 4y ago
Sounds wrong, that would essentially be saying one should play the cheapest level of all lotteries.
- mellavora 4y ago
  naw, it is probably based on the assumption that the payout can be life-changing big. risking pocket change to win big is quasi-reasonable, even though it is a loosing bet. Because you don't notice the downside/drawdowns. risking more than pocket change is not reasonable, because it is a loosing bet. NB: I don't play the lottery.
  - lupire 4y ago
    Similarly, you should make small high-upside bets bets like "strike up a chat with a as stranger"
317070 4y ago
You might be thinking about the Kelly criterion [0]. It does go the other way around: even if the expected value of a lottery were positive, you should only bet insignificant amounts. If I have a lottery, and you have a 1 in a billion chance to gain 10 billion utility, tickets cost 1 utility. How much of your current utility wealth should you put in? Classical expected value reasoning would pour in everything, even though you are almost guaranteed bankrupt at the end of that transaction. The Kelly criterion recommends an exact (small) percentage for this style of lotteries, and is therefore probably more sensible than decision making based on expected values. [0] https://en.m.wikipedia.org/wiki/Kelly_criterion https://en.m.wikipedia.org/wiki/Kelly_criterion
- Semaphor 4y ago
  That sounds sensible
- FeepingCreature 4y ago
  Notable: Kelly only works if you're playing a multi-round game. Also careful; I believe money-to-utility is already logarithmic for most people. We don't have a good intuition for what "billions of utility vs 1 utility" represents.
  - ReflectedImage 4y ago
    How can you have a game that isn't multi-round? Surely after you finish playing one game, the next game you play (even if it's a completely different game) is the second round.
    - lupire 4y ago
      You have considered if the number of rounds is large enough. A weekly lottery doesn't have many rounds. A "huge jackpot" is even more rare.
      - kgwgk 4y ago
        > A weekly lottery doesn't have many rounds. It doesn't if you're a house fly. Average life expectancy at birth in OECD countries is around 4'000 weeks.
- kgwgk 4y ago
  Kelly maximizes (logarithmic) utility. Kelly is equivalent to decision making based on expected values (of the logarithm of wealth). Maybe you wanted to say "[...] gain 10 billion dollars, tickets cost 1 dollar. How much of your current dollar wealth [...]".
- lupire 4y ago
  Kelly criterion assumes you will increase your bet when you win, to increase overall final value, and the EV is positive. It doesn't work when you expect to only win at most once.

Semaphor 4y ago

Sounds wrong, that would essentially be saying one should play the cheapest level of all lotteries.

mellavora 4y ago
naw, it is probably based on the assumption that the payout can be life-changing big. risking pocket change to win big is quasi-reasonable, even though it is a loosing bet. Because you don't notice the downside/drawdowns. risking more than pocket change is not reasonable, because it is a loosing bet. NB: I don't play the lottery.
- lupire 4y ago
  Similarly, you should make small high-upside bets bets like "strike up a chat with a as stranger"

317070 4y ago

You might be thinking about the Kelly criterion [0]. It does go the other way around: even if the expected value of a lottery were positive, you should only bet insignificant amounts. If I have a lottery, and you have a 1 in a billion chance to gain 10 billion utility, tickets cost 1 utility. How much of your current utility wealth should you put in? Classical expected value reasoning would pour in everything, even though you are almost guaranteed bankrupt at the end of that transaction. The Kelly criterion recommends an exact (small) percentage for this style of lotteries, and is therefore probably more sensible than decision making based on expected values. [0] https://en.m.wikipedia.org/wiki/Kelly_criterion https://en.m.wikipedia.org/wiki/Kelly_criterion

Semaphor 4y ago
That sounds sensible
FeepingCreature 4y ago
Notable: Kelly only works if you're playing a multi-round game. Also careful; I believe money-to-utility is already logarithmic for most people. We don't have a good intuition for what "billions of utility vs 1 utility" represents.
- ReflectedImage 4y ago
  How can you have a game that isn't multi-round? Surely after you finish playing one game, the next game you play (even if it's a completely different game) is the second round.
  - lupire 4y ago
    You have considered if the number of rounds is large enough. A weekly lottery doesn't have many rounds. A "huge jackpot" is even more rare.
    - kgwgk 4y ago
      > A weekly lottery doesn't have many rounds. It doesn't if you're a house fly. Average life expectancy at birth in OECD countries is around 4'000 weeks.
kgwgk 4y ago
Kelly maximizes (logarithmic) utility. Kelly is equivalent to decision making based on expected values (of the logarithm of wealth). Maybe you wanted to say "[...] gain 10 billion dollars, tickets cost 1 dollar. How much of your current dollar wealth [...]".
lupire 4y ago
Kelly criterion assumes you will increase your bet when you win, to increase overall final value, and the EV is positive. It doesn't work when you expect to only win at most once.