# Should a scientist never buy a lottery ticket?

1. Jul 23, 2012

Some people educated in math say, "I never buy a lottery ticket or play the roulette because I know that on average, you are bound to lose."
I don't think that argument is valid - because in most games of chance you are not very likely to end up with the expectancy value! Indeed, if you have a science education, you know that in statistics there is not only expectancy value, but also standard deviation and higher moments.
When you buy a lottery ticket, the relevant facts are these: You pay a small amount, taking the large risk of losing that money but gaining the very small chance of winning big. Are you willing to do that? There is nothing to stop a scientist from answering "yes" to that question.

My point: Averages only pertain to the population as a whole, or if you do a very large number of tries. (And speaking of large numbers - the real problem with chance games is, of course, that they are addictive! But that's beyond mathematical reasoning.)

2. Jul 23, 2012

### Number Nine

The problem with the lottery is that the expected gain is negative. On average, you would have to spend far more on tickets in order to win than you would gain from winning. The lottery is an elaborate scheme designed to siphon money from the lower classes by convincing them that they have hope to become financially well off, and funnel it directly into the pockets of shareholders. It's a tax on the poor that funds the rich; that's all it is.

A gambling problem is only a problem when the expected gain is negative.

3. Jul 23, 2012

### Ryan_m_b

Staff Emeritus
Playing the lottery, or gambling in general, really depends on how much disposable income one has and one's idea of a fun risk. I don't see anything wrong with someone using some of their money that they don't care about loosing and gambling in a way that excites them.

4. Jul 23, 2012

### BobG

Wrong question.

Other people educated in math say, "My chances of saving enough money for retirement on my own are even lower than the chance of winning the lottery."

Of course, the problem with that statement is that people educated in math usually have a career that pays more than minimum wage and would probably have a much better chance of saving for their own retirement than winning the lottery.

But the expected net value isn't a way to compare the probabilities of meeting some objective.

5. Jul 23, 2012

### DaveC426913

Except the most destitute, almost anyone can afford one dollar a week. Even knowing it will almost assuredly never pay off, the cost of that one dollar per week is outweighed by the payoff of possibly winning millions. Assuming that dollar isn't taking food out of the mouths of your children.

The trick to gambling is, as always: live within your limit. Risk only that which you can afford to lose.

6. Jul 23, 2012

### Andre

In some countries and for some organisations you'd have the comfort that the lost money is very very partly used (after all the fees) for a Good Cause.

7. Jul 23, 2012

### daveb

It depends upon the risk to benefit ratio. First, the ratio isn't the same for everyone. Someone who thinks nothing of spending 6 dollars every day for a latte wouldnt have as high a risk as someone who barely lives paycheck to paycheck. Second, even if the ratio is the same for two different people, their personal tolerance of the risk is different. One person might decide it's stupid to risk any money unless it's a sure thing, and snother might decide that since it doesn't matter if I lose that 1 dollar every week, then it's OK to play.

Which is wy (IMO) it's pointless to use scientific maxims such as "a scientist chould never play the lottery" when it comes to the "human equation" since the so-called human equation has a different variable for each human involved.

8. Jul 23, 2012

### Travis_King

I hope you meant "you spend more on tickets than you generally actually wind up winning" as I find it hard to believe that anyone has ever spent 350 million dollars on losing tickets. And if they did, I'd like to know why the rich SOB was playing the lottery in the first place.

Last edited: Jul 23, 2012
9. Jul 23, 2012

### Dickfore

OK, let's look at the standard deviation of the profit if betting on one number on a roullette wheel (in the U.S.):
$$\sigma^2 (P) = \frac{1}{38} \, \left(36 + \frac{2}{38} \right)^2 + \frac{37}{38} \, \left( 0 + \frac{2}{38} \right)^2 \approx 1.822 \times 10^{-5} \Rightarrow \sigma(P) \approx 4.296 \times 10^{-3}$$
where we used that the average profit is $-2/38$. The relative uncertainty is:
$$\frac{\sigma(P)}{\vert E(P) \vert} \approx 8.111 \times 10^{-2} \approx \frac{1}{12}$$
This means you need a deviation of at least 12 standard deviations from the (negative) expected profit to have a net gain.

If you remember the hunt for the Higgs boson, their criterion for certain was 5 sigma. This is why scientists say gambling is a sure loss.

10. Jul 23, 2012

### Monique

Staff Emeritus
I've often won with gambling, also at the roulette table. The trick is to realize it's going to be lost money and to start running the moment that you win.

I don't buy lottery tickets on a regular basis, since the chances of winning are so low, but sometimes it's worth the thrill of tempting luck.

11. Jul 23, 2012

### Ryan_m_b

Staff Emeritus
I completely agree. The problem with such maxims is it assumes winning money is the one and only goal of gambling.

12. Jul 23, 2012

### Ryan_m_b

Staff Emeritus
This is very true. I've worked for a hospice that ran its own lottery, the prize was capped at £1000 and a ticket was £1 so any ticket sold after the 1000th was money in the charity's pocket. Many people liked to play it simply because they know that if they loose part of their money is going to a charity they support.

13. Jul 23, 2012

### Ibix

David Brin argued that people play the lottery in the hope that they will win, and therefore that it is a tax on hope - a deeply depressing perspective.

Of course a scientist can play the lottery. The only difference between a scientist and a regular Joe is that the scientist ought to be able to figure out exactly how much they are throwing away... As others have noted, it's actually more complex than that because people don't just play for the monetary gain. For example, in the office Secret Santa last year, a (mathematically literate) colleague bought another (also mathematically literate) colleague £5 of lottery tickets. Didn't win anything, but it was a clever solution to the hell that is Secret Santa. Wish I'd thought of it.

14. Jul 23, 2012

### Galteeth

If you're going to gamble, it's a silly way to go, as the odds are so much worse then anything at a casino and IMO the game is less fun.

A fun way to gamble- play the minum bet at a roulette wheel and bet double your total losses every time you lose. Over the long run, the expected gain is still negative, but it changes the distribution to more frequent small wins and less frequent large losses.

EDIT: Clarification, I'm referring to betting on colors.

15. Jul 23, 2012

I play the lottery so does this make me "poor" and one of the "lower classes"?

16. Jul 23, 2012

### NeoDevin

If you're doing it as a plan to make money, then the answer is clearly no. It's illogical, because the expected return is negative.

If you're doing it for entertainment, then it's no different from any other form of entertainment, be it movies, video games, travel, etc. Set your budget and have fun.

17. Jul 23, 2012

### AlephZero

I wouldn't argue with anybody doing that, provided they get some personal pleasure from the process of paying their dollar and then losing it.

Personally I find that about as exciting as just throwing the dollar in the trash, so I don't bother.

18. Jul 23, 2012

### Travis_King

Yea...but it's like throwing a dollar into the trash knowing that one day it is possible, however extremely unlikely, that the trash can will spit out a quarter-of-a-billion dollars.

50 bucks a year is, in my opinion, well worth at least having your name in the hat. If you play, you most likely wont win. If you don't play, it's assured that you won't.

With that said, I don't generally play the lotto.

19. Jul 23, 2012

### Dickfore

So, do you lose sometimes?

20. Jul 24, 2012

### Monique

Staff Emeritus
Not more than I've won.