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I don't think there's anything wrong with buying a lottery ticket if its cost is a trifle for you. Buying one when the expected value is positive is not a soun

I don't think there's anything wrong with buying a lottery ticket if its cost is a trifle for you. Buying one when the expected value is positive is not a sound gamble however. Suppose there is a jackpot of $300M and you have a 1 in 150 million chance to win. It's obvious that you have an edge, so you calculate how large part of your bankroll you should bet with the Kelly criterion[1] and get: f=3.33e-9 Oh well, if you are a centimillionare you can buy a ticket and be rational. [1]http://en.wikipedia.org/wiki/Kelly_criterion http://en.wikipedia.org/wiki/Kelly_criterion

jrs235 12y ago
You need to factor in ticket price, odds of winning, cash payout, taxes. Powerball is $2 a ticket. The cash payout is around $338 million. The odds of winning with a ticket is about 1 in 175. Assume taxes will take half. You shouldn't buy a powerball ticket using reason unless the cash payout is at least $700 million. Problem then is so many people are playing there's likely more than one winning ticket which would mean the numbers don't work. Edit: the payout tonight is $338m
- kryptiskt 12y ago
  I assumed a $1 ticket in the example. The point is that even if the expected value is high, buying a ticket means that you are likely overbetting by several orders of magnitude.
  - jrs235 12y ago
    Yes. And even if you get to pot odds or better after taxes and decide to spend $20 (10 tickets), $200 (100 tix), or even $2000 (1000 tix) because you're at pot odds... 1 in 17.5 mil, 1 in 1.75 mil, even 1 in 175,000 are still very long odds. So, you can't win and dream if you don't play but if you play buy just one ticket. Buy it more for the fantasy you get to play in your dreams at night in your head, because that's most likely the greatest payout you'll get. $1 or $2 for a bottled drink or for some sweet dreams... Your choice, both are okay choices in my mind. Edit: typos.
PhantomGremlin 12y ago
Chinjut's multiple posts here have argued much more eloquently than I can about "utility" or what is "rational" to different people. Here's my simple way of explaining why I will buy a ticket tomorrow if the prize isn't won tonight: If, for a $1 bet, you offer people a 1/2 chance of winning $2, most people won't bother. However, if you offer those same people a 1/1000000 chance of winning $1000000, many more people would become interested. Winning $2 isn't meaningful to most people. But a chance of winning a sufficiently large amount of money that they could significantly change their lifestyle is a much more "rational" decision for them to make. And that, in a nutshell, is why lotteries exist at all. I do love the idea of the Kelly criterion, and I do try to keep it in mind when investing. Unfortunately my "edge" in most investment situations so small that I shouldn't be betting, err I mean "investing" anything!
kerkeslager 12y ago
The Kelly criterion is a way of choosing a number to bet from the set of rational numbers between 0 and your bankroll (inclusive). However, this isn't the set you're choosing from when playing the Powerball. You're rightly accounting for this. However, you're accounting for this incorrectly by adjusting the size of the bankroll ("Oh well, if you are a centimillionare you can buy a ticket and be rational."). Your bankroll is fixed. The correct adjustment is to change the set of values from which the fraction of the bankroll can be chosen. The optimal bet for a +EV bet is always positive when the set of possible bets includes positive numbers, because a zero bet has effectively a zero EV. My intuition is that you want the number in the set of possible bets that is closest to the Kelly Criterion number when weighted along some curve (I'm too lazy to calculate which curve on my mobile device). If this is correct (I haven't proved my "closest on a curve" idea) then the optimal bet is to buy a $2 Powerball ticket (the smallest positive bet). That said both these ideas assume an infinite number of future bets following the same strategy, with no other games to play. If you play the Powerball every time the EV is positive, this is like an investment that will yield a return, on average, long after you are dead. And there are alternate games (the stock market, education, job searching) which yield more consistently and possibly with a higher EV. Finally, the goal isn't to maximize your bankroll. I just spent the cost of a Powerball ticket on a coffee, which has a -EV, and I couldn't be happier with my decision.

jrs235 12y ago

You need to factor in ticket price, odds of winning, cash payout, taxes. Powerball is $2 a ticket. The cash payout is around $338 million. The odds of winning with a ticket is about 1 in 175. Assume taxes will take half. You shouldn't buy a powerball ticket using reason unless the cash payout is at least $700 million. Problem then is so many people are playing there's likely more than one winning ticket which would mean the numbers don't work. Edit: the payout tonight is $338m

kryptiskt 12y ago
I assumed a $1 ticket in the example. The point is that even if the expected value is high, buying a ticket means that you are likely overbetting by several orders of magnitude.
- jrs235 12y ago
  Yes. And even if you get to pot odds or better after taxes and decide to spend $20 (10 tickets), $200 (100 tix), or even $2000 (1000 tix) because you're at pot odds... 1 in 17.5 mil, 1 in 1.75 mil, even 1 in 175,000 are still very long odds. So, you can't win and dream if you don't play but if you play buy just one ticket. Buy it more for the fantasy you get to play in your dreams at night in your head, because that's most likely the greatest payout you'll get. $1 or $2 for a bottled drink or for some sweet dreams... Your choice, both are okay choices in my mind. Edit: typos.

PhantomGremlin 12y ago

Chinjut's multiple posts here have argued much more eloquently than I can about "utility" or what is "rational" to different people. Here's my simple way of explaining why I will buy a ticket tomorrow if the prize isn't won tonight: If, for a $1 bet, you offer people a 1/2 chance of winning $2, most people won't bother. However, if you offer those same people a 1/1000000 chance of winning $1000000, many more people would become interested. Winning $2 isn't meaningful to most people. But a chance of winning a sufficiently large amount of money that they could significantly change their lifestyle is a much more "rational" decision for them to make. And that, in a nutshell, is why lotteries exist at all. I do love the idea of the Kelly criterion, and I do try to keep it in mind when investing. Unfortunately my "edge" in most investment situations so small that I shouldn't be betting, err I mean "investing" anything!

kerkeslager 12y ago

The Kelly criterion is a way of choosing a number to bet from the set of rational numbers between 0 and your bankroll (inclusive). However, this isn't the set you're choosing from when playing the Powerball. You're rightly accounting for this. However, you're accounting for this incorrectly by adjusting the size of the bankroll ("Oh well, if you are a centimillionare you can buy a ticket and be rational."). Your bankroll is fixed. The correct adjustment is to change the set of values from which the fraction of the bankroll can be chosen. The optimal bet for a +EV bet is always positive when the set of possible bets includes positive numbers, because a zero bet has effectively a zero EV. My intuition is that you want the number in the set of possible bets that is closest to the Kelly Criterion number when weighted along some curve (I'm too lazy to calculate which curve on my mobile device). If this is correct (I haven't proved my "closest on a curve" idea) then the optimal bet is to buy a $2 Powerball ticket (the smallest positive bet). That said both these ideas assume an infinite number of future bets following the same strategy, with no other games to play. If you play the Powerball every time the EV is positive, this is like an investment that will yield a return, on average, long after you are dead. And there are alternate games (the stock market, education, job searching) which yield more consistently and possibly with a higher EV. Finally, the goal isn't to maximize your bankroll. I just spent the cost of a Powerball ticket on a coffee, which has a -EV, and I couldn't be happier with my decision.