Well, you’ve used a value for the likelihood of winning the lottery that’s dramatically higher than it is in real life, and it’s a lot harder to make the numbers come out in favor of buying the lottery tickets when you keep the winnings on the same order and decrease the chances of winning by more than two orders of magnitude.
The cost of a lottery ticket is a lot more than the jackpot times the likelihood of winning.
I earn around £28,000 per year. Currently, I can’t save any money—in fact I have to find extra sources of income to meet expenses for me and my wife.
Accounting for holiday time, and so on, I earn £15 an hour, give or take, so a £1 lottery ticket is worth four minutes of my work time.
Currently, I do not have any savings, or any prospect of saving any money. Thus, I expect to work for at least the next thirty-five years, or 64,400 hours.
If I won the average £2,053,984 prize for the UK National Lottery jackpot, I would not only be able to retire, thus saving those 64,400 hours, if I stuck that in a bank at 5% interest I would get £102699.20 a year—nearly four times my current salary. So I could actually be saving 239,631 ‘hours’ over that 35-year period.
The odds of winning the national lottery jackpot are 1 in 13,983,816, which would mean my expected winning (only counting the jackpot, not the lower prizes) would be 0.017 hours, or 1.02 minutes.
That suggests that for me, at a relatively high wage, the lottery is still irrational to play. However, it also suggests that for anyone whose earnings are below £3.82 per hour (for example someone working a minimum wage job but also doing unpaid overtime or an intern) it could be rational to play the lottery.
If I won the average £2,053,984 prize for the UK National Lottery jackpot, I would not only be able to retire, thus saving those 64,400 hours, if I stuck that in a bank at 5% interest I would get £102699.20 a year—nearly four times my current salary. So I could actually be saving 239,631 ‘hours’ over that 35-year period.
I’m not sure how it works in the UK, but in the US, the advertised jackpot figures are lies—they actually give you an annuity which pays out a total of that amount over its lifetime, and then tax the payouts.
That suggests that for me, at a relatively high wage, the lottery is still irrational to play. However, it also suggests that for anyone whose earnings are below £3.82 per hour (for example someone working a minimum wage job but also doing unpaid overtime or an intern) it could be rational to play the lottery.
British pounds are currently 1.6USD:1GBP conversion. I’m somewhat disturbed by the notion that $24/hr is described as a “relatively high” wage, as that works out to a roughly $50k/year salary. Wikipedia indicates you’re pretty accurate, however.
That’s… enlightening, actually. Also, very fascinating.
The difference is that in the UK we don’t have to pay health insurance and so on, and most people don’t have to travel significant distances by US standards, so the cost of living is significantly lower (food and rent costs are higher, but the travel and health insurance savings more than make that up). It’d still be solidly average household earnings for the US, anyway.
(The reason I can’t save anything despite being on a high wage is that I have debts that need paying off, and have to support my wife who’s too unwell to work. Most people on my income outside London would be living very comfortably indeed).
The reason I can’t save anything despite being on a high wage is that I have debts that need paying off,
Here’s the thing: I have a below average income, and I earn more—currencies converted—than you do. To your equivalent 24USD/hr I earn (sole earner of my household) 27USD/hr (I also do not pay out-of-pocket for health insurance, and my cost-of-mileage is far less than yours [gasoline/petrol taxes are fractional here compared to yours]). Now, I also live in a part of the US where the average 1400 Sq.ft home costs ~$50,000USD. And I’m in a metropolitan area at that.
So I’m experiencing a touch of culture shock here.
You don’t have a below average income then—according to http://en.wikipedia.org/wiki/Personal_income_in_the_United_States , “The overall median personal income for all individuals over the age of 18 was $24,062 ($32,140 for those age 25 or above) in the year 2005. The overall median income for all 155 million persons over the age of 15 who worked with earnings in 2005 was $28,567”—I can’t find a mean, or data more recent than that, but it can’t have changed that much. Unless you’re only working 26-hour weeks, you’re earning more than average for the US—significantly so.
In fact, according to that table, a $50,000 salary, which you were thinking of as low, would be in the top 25% of income for the US...
And yes, your cost-of-mileage would be lower, assuming I was driving. But in the UK we have a far more efficient, and cheaper, public transport system, and most people live significantly closer to our places of work than in the US. I work from home quite a bit of the time, but in a week where I have to travel in to work every day, my total transport costs for the week would be £8.50 (five return train journeys at £1.70 each). People in metropolitan areas, especially, are as likely to cycle or walk to work as to drive, if not more so.
Because it was in the context of me saying that £28,000 p.a. is a good wage in my original comment. £28,000 is a pretty good income for an individual, but not a wonderful one for two people, and that was the comment Logos01 originally picked up on.
So I’m experiencing a touch of culture shock here.
And consider that you’re still talking about the AngloAmerican world. If British salaries shocked you like that, do I want to know what you think about Greek ones? When I first started working (just after getting my master’s degree and completing my standard year of military conscription) my yearly salary was about 14.000 euro, after taxes.
In Slovakia a high school teacher receives 600 € / month, before taxes. To get above 1200 € / month, one has to be a manager, financial specialist, IT specialist, etc. On the other hand, we get 25 paid vacation days.
Sure, we need to be careful not to compare apples with oranges. For example, do people receive free healthcare for their taxes? This may be difficult to evaluate, for example in Slovakia there is a nominally free health care, but sometimes one has to pay some additional costs, or pay for higher quality or sooner treatment, and it can get pretty expensive. Also the tax system is complicated (income tax, property tax, value added tax, special taxes, mandatory insurances, tax for having an employee, media tax, etc.) -- I suppose this is intentional to prevent average people from finding out how much exactly do they pay.
The hours worked by a US worker (+- 1800 a year) is lower than the hours worked by Greeks (about 2100 a year), and higher than those of the UK (approximately 1650 hours a year). Only the Koreans work more hours a year than Greeks, so the amount of hours put in is not very relevant to the yearly salary.
The cost of a lottery ticket is a lot more than the jackpot times the likelihood of winning.
In lotteries with rollover jackpots, lottery tickets can become positive expected value… as long as you don’t take into account the possibility of having to split the jackpot with another winner.
But that possibility is present regardless of whether the jackpot accumulates or not, or am I missing something?
Certainly lotteries with an oversized jackpot will sell more tickets, thus increasing the risk, but it doesn’t seem obvious to me that the player pool will increase fast enough to keep the EV down.
Well I suppose that it depends on the rules of that specific lottery, but I suspect that most U.S. state lotteries with large jackpots do split the total prize between all winning tickets. It’s just that the odds of having to split your prize are a lot harder to know than the odds of winning the jackpot at all.
I picked numbers that are easy to work with to illustrate a theoretical point. Whether any actual lottery can do the same thing for the particular situation of any real person is a separate issue. Again, the part of the lottery ticket’s price that covers overhead and profit is only relevant in the context of real lotteries. The question I’m asking is whether it is possible for a bad or neutral deal in dollars to become a good deal in hours of life.
Well, you’ve used a value for the likelihood of winning the lottery that’s dramatically higher than it is in real life, and it’s a lot harder to make the numbers come out in favor of buying the lottery tickets when you keep the winnings on the same order and decrease the chances of winning by more than two orders of magnitude.
The cost of a lottery ticket is a lot more than the jackpot times the likelihood of winning.
OK, so let’s look at actual numbers.
I earn around £28,000 per year. Currently, I can’t save any money—in fact I have to find extra sources of income to meet expenses for me and my wife.
Accounting for holiday time, and so on, I earn £15 an hour, give or take, so a £1 lottery ticket is worth four minutes of my work time.
Currently, I do not have any savings, or any prospect of saving any money. Thus, I expect to work for at least the next thirty-five years, or 64,400 hours.
If I won the average £2,053,984 prize for the UK National Lottery jackpot, I would not only be able to retire, thus saving those 64,400 hours, if I stuck that in a bank at 5% interest I would get £102699.20 a year—nearly four times my current salary. So I could actually be saving 239,631 ‘hours’ over that 35-year period.
The odds of winning the national lottery jackpot are 1 in 13,983,816, which would mean my expected winning (only counting the jackpot, not the lower prizes) would be 0.017 hours, or 1.02 minutes.
That suggests that for me, at a relatively high wage, the lottery is still irrational to play. However, it also suggests that for anyone whose earnings are below £3.82 per hour (for example someone working a minimum wage job but also doing unpaid overtime or an intern) it could be rational to play the lottery.
I’m not sure how it works in the UK, but in the US, the advertised jackpot figures are lies—they actually give you an annuity which pays out a total of that amount over its lifetime, and then tax the payouts.
It’s different in the UK—it’s paid out as a tax-free lump sum.
British pounds are currently 1.6USD:1GBP conversion. I’m somewhat disturbed by the notion that $24/hr is described as a “relatively high” wage, as that works out to a roughly $50k/year salary. Wikipedia indicates you’re pretty accurate, however.
That’s… enlightening, actually. Also, very fascinating.
The difference is that in the UK we don’t have to pay health insurance and so on, and most people don’t have to travel significant distances by US standards, so the cost of living is significantly lower (food and rent costs are higher, but the travel and health insurance savings more than make that up). It’d still be solidly average household earnings for the US, anyway.
(The reason I can’t save anything despite being on a high wage is that I have debts that need paying off, and have to support my wife who’s too unwell to work. Most people on my income outside London would be living very comfortably indeed).
Here’s the thing: I have a below average income, and I earn more—currencies converted—than you do. To your equivalent 24USD/hr I earn (sole earner of my household) 27USD/hr (I also do not pay out-of-pocket for health insurance, and my cost-of-mileage is far less than yours [gasoline/petrol taxes are fractional here compared to yours]). Now, I also live in a part of the US where the average 1400 Sq.ft home costs ~$50,000USD. And I’m in a metropolitan area at that.
So I’m experiencing a touch of culture shock here.
You don’t have a below average income then—according to http://en.wikipedia.org/wiki/Personal_income_in_the_United_States , “The overall median personal income for all individuals over the age of 18 was $24,062 ($32,140 for those age 25 or above) in the year 2005. The overall median income for all 155 million persons over the age of 15 who worked with earnings in 2005 was $28,567”—I can’t find a mean, or data more recent than that, but it can’t have changed that much. Unless you’re only working 26-hour weeks, you’re earning more than average for the US—significantly so.
In fact, according to that table, a $50,000 salary, which you were thinking of as low, would be in the top 25% of income for the US...
And yes, your cost-of-mileage would be lower, assuming I was driving. But in the UK we have a far more efficient, and cheaper, public transport system, and most people live significantly closer to our places of work than in the US. I work from home quite a bit of the time, but in a week where I have to travel in to work every day, my total transport costs for the week would be £8.50 (five return train journeys at £1.70 each). People in metropolitan areas, especially, are as likely to cycle or walk to work as to drive, if not more so.
How did you decide to use individual income, rather than household? You both seem to support other people.
Because it was in the context of me saying that £28,000 p.a. is a good wage in my original comment. £28,000 is a pretty good income for an individual, but not a wonderful one for two people, and that was the comment Logos01 originally picked up on.
And consider that you’re still talking about the AngloAmerican world. If British salaries shocked you like that, do I want to know what you think about Greek ones? When I first started working (just after getting my master’s degree and completing my standard year of military conscription) my yearly salary was about 14.000 euro, after taxes.
In Slovakia a high school teacher receives 600 € / month, before taxes. To get above 1200 € / month, one has to be a manager, financial specialist, IT specialist, etc. On the other hand, we get 25 paid vacation days.
Sure, we need to be careful not to compare apples with oranges. For example, do people receive free healthcare for their taxes? This may be difficult to evaluate, for example in Slovakia there is a nominally free health care, but sometimes one has to pay some additional costs, or pay for higher quality or sooner treatment, and it can get pretty expensive. Also the tax system is complicated (income tax, property tax, value added tax, special taxes, mandatory insurances, tax for having an employee, media tax, etc.) -- I suppose this is intentional to prevent average people from finding out how much exactly do they pay.
(Data source, unfortunately in Slovak only.)
Let’s make sure we’re comparing apples to apples here.
Mandatory paid vacation days, by country
US—None.
UK -- 20 (not counting public holidays, again for apples-apples purposes)
Greece -- 20 and up, depending on seniority
The average US worker works a lot more hours than the average UK or Greek worker does.
The hours worked by a US worker (+- 1800 a year) is lower than the hours worked by Greeks (about 2100 a year), and higher than those of the UK (approximately 1650 hours a year). Only the Koreans work more hours a year than Greeks, so the amount of hours put in is not very relevant to the yearly salary.
source: OECD statistics
In lotteries with rollover jackpots, lottery tickets can become positive expected value… as long as you don’t take into account the possibility of having to split the jackpot with another winner.
But that possibility is present regardless of whether the jackpot accumulates or not, or am I missing something?
Certainly lotteries with an oversized jackpot will sell more tickets, thus increasing the risk, but it doesn’t seem obvious to me that the player pool will increase fast enough to keep the EV down.
Well I suppose that it depends on the rules of that specific lottery, but I suspect that most U.S. state lotteries with large jackpots do split the total prize between all winning tickets. It’s just that the odds of having to split your prize are a lot harder to know than the odds of winning the jackpot at all.
I picked numbers that are easy to work with to illustrate a theoretical point. Whether any actual lottery can do the same thing for the particular situation of any real person is a separate issue. Again, the part of the lottery ticket’s price that covers overhead and profit is only relevant in the context of real lotteries. The question I’m asking is whether it is possible for a bad or neutral deal in dollars to become a good deal in hours of life.