0
$\begingroup$

I'm a very simple man with basic understanding of mathematics and theory. This question has bugged me for the last few years, ever since I learned about lottery tickets.

When I talk with people about lottery they say:

You can't win because it's like 1 in 25,000,000 chance.

or like

You can't win because chances are astronomical.

Stuff like that.

However you hear every day in the news that someone has won $100,000,000 or similar somewhere in the world.

How is that possible? Why would the lottery wouldn't work for me when I buy it, but yet it works for someone else? Why wouldn't I be the person who wins the lottery?

This seems like the biggest unsolved paradox of modern mathematics/quantum theory.

$\endgroup$
  • 3
    $\begingroup$ "This seems like the biggest unsolved paradox of modern mathematics/quantum theory"?? $\endgroup$ – user133281 Jan 24 '15 at 10:56
  • 2
    $\begingroup$ Yeah, "the biggest unsolved paradox of modern mathematics" alone, would not be impressive enough. $\endgroup$ – Did Jan 24 '15 at 11:21
  • 1
    $\begingroup$ @user133281 I mean how else do you explain that...? I've heard of quantum theory - if you observe something you break chances of it happening. So I was thinking maybe it was related - I observe my own ticket you know, so I break my chances of winning the jackpot... Quantum theory is all the time in the news, don't blame me for cross referencing it. I'm a simple man. $\endgroup$ – bodacydo Jan 24 '15 at 13:39
  • $\begingroup$ Who's downvoting all the answers... and this post...? $\endgroup$ – bodacydo Jan 24 '15 at 13:41
  • $\begingroup$ @did what do you mean sir? $\endgroup$ – bodacydo Jan 24 '15 at 13:42
4
$\begingroup$

They don't mean you literally can't win the lottery, they just mean that the expected value of buying a ticket is negative, or that winning is so unlikely that buying a ticket is a bad investment.

However, you should read How Not to be Wrong by Jordan Ellenberg, which (among other things) tells the story of some students from MIT who noticed that some lottery tickets actually had a positive expected value...

| cite | improve this answer | |
$\endgroup$
2
$\begingroup$

If you have a lottery with $10^6$ tickets, the probability you win with a ticket is $10^{-6}$. If $10^3$ people buy one ticket for each, then the probability that someone wins is $10^{-3}$, that is $1000$ times your probability of winning. But clearly if you buy $10^3$ tickets...

When you hear, frequently, that someone has won the lottery, the event "someone wins the lottery" (wich has probability $10^{-3}$) is realized. On the other hand if you fix a person $X$ and every day of your life you verify if $X$ has won the lottery, how many times this event happens? Frequently?

| cite | improve this answer | |
$\endgroup$
  • 1
    $\begingroup$ Distinct tickets. ;-) $\endgroup$ – knedlsepp Jan 24 '15 at 11:04
  • $\begingroup$ I never played at the lottery. Aren't they distinct? $\endgroup$ – Dubious Jan 24 '15 at 11:05
  • 1
    $\begingroup$ This may depend on the country, but where I live you can choose your numbers yourself. $\endgroup$ – knedlsepp Jan 24 '15 at 11:06
  • $\begingroup$ Ahahah, "lucky numbers". $\endgroup$ – Dubious Jan 24 '15 at 11:08
1
$\begingroup$

The thing is that if you take one specific person, say me, then the chance of me winning the lottery is very small.

But the chance of someone winning the lottery is much larger, because so many people play the lottery. This is because the chance of someone winning the lottery is equal to the chance of me winning OR you winning OR my neighbor winning OR ... and so on, for all people who play the lottery.

| cite | improve this answer | |
$\endgroup$
0
$\begingroup$

When they bought the ticket, they were also not having 100% chances of winning, because probability is same for everyone, which neglects randomness(*) involved in the process and takes everyone equally likely. Probability just gives a likelihood of an event happening and becomes truer as the number of experiments approaches infinity, for one or two events, you may take out probability of happening something and judge likelihood but it would be increasingly true for repetitive cases. The winner could be anyone so no one had 100% chance.

| cite | improve this answer | |
$\endgroup$
0
$\begingroup$

It could also work for you. But the probability is very low. One criteria for playing lottery is the expected value. If the expected value is negative, then it is maybe not useful to play lottery.

For example: You can win 1,000,000 dollars with a probability of 1:200,000 and you have to pay 5 dollars. Then the expeceted value is $ \frac{1,000,000}{200,000}- 5=5-5=0$.

But in general the expected value is negative. Thus the company has a positive expected value for its profit.

The only reason to play lottery is, that your amount of winning can be very high, although your payment is relative low. And the expected value should not be too far away from 0.

| cite | improve this answer | |
$\endgroup$
0
$\begingroup$

However you hear every day in the news that someone has won $100,000,000 or similar somewhere in the world.

Those people are extremely lucky. That's exactly why you hear about them in the news in the first place.

| cite | improve this answer | |
$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.