Odds and the Lottery

[SkepticalScience]

So - I always hear of how unlikely it is to win the lottery.

This weekend someone said (with some authority) that getting hit by lightning 4 times is more likely than winning the lotto.

Later on, he mentioned that getting bit by a poisonous spider and then dying from that bite is also more likely than winning the lotto.

However, spontaneous combustion of sleepwear (meaning, you go to bed, and your PJ's burst into flames) is about the same odds as winning the lotto.

Here's what I can't get then. Every few weeks, someone wins the lotto. But every few weeks someone doesn't get hit by lightning 4 times, or die from a poisonous spider bight, or have their PJ's burst into flames.

I haven't ever heard of those stories before, but I always hear about someone who wins the lotto. . . what gives??

SS

 

[Mojo]

It depends on how the odds have been calculated. Did they mean the odds of these things happening to a person in a particular week, or over an entire lifetime, for example? If the odds are correct and comparable, there should be more people dying of spider bites than winning the lotto. Maybe "spider bites man" is not considered as newsworthy as "man wins lotto."

 

[ranson]

I think this has been discussed elsewhere. As a layman who has forgotten most of his statistics text, the basic argument is this:

The odds of any individual hitting the lottery are astronomical. However, given the nature of the game and the number of people playing, the odds of someone hitting it are pretty good. The probabilities as applied to an individual and a group including that individual are different.

Anyone have the actual math on this lying about?

 

[SkepticalScience]

". However, given the nature of the game and the number of people playing, the odds of someone hitting it are pretty good. "

Ah. Well, now that's interesting. Hmm, so given the fact that someone has to win, the odds of winning the lotto should be "1/number of people playing". It's interesting that that's a different figure entirely than the odds of getting the exact lotto combination correct.

But that the end result is the same - you get the winning ticket.

Ah - it's almost as if there were different odds from PLAYING the actual game, than if you were to simply write down on a piece of paper what you think the lotto numbers are going to be.

 

[Donks]

Ah. Well, now that's interesting. Hmm, so given the fact that someone has to win, the odds of winning the lotto should be "1/number of people playing". It's interesting that that's a different figure entirely than the odds of getting the exact lotto combination correct.

I belive you are mistaken. 1/#players is the odds of winning a raffle, where someone must win every drawing. In the lotto, typically there is no such restriction. They just increase the winnings for the next drawing.

 

[Number Six]

The odds of a particular person winning the lotto or a raffle is 1/N. But the raffle is set up so that exactly one person must win it whereas the lotto is set up so that any number of people can win it.

I don't know the odds of getting hit by lightning but I think it's possible that the odds of getting hit by lightning four times are better than the odds of winning the lotto (depending on which lotto we're talking about.

I've read tales of people getting hit by lightning many times. If we have 300,000,000 people in the country and 3 of them get hit by lightning four times in their life then that is 1 in 100,000,000. That is roughly the same odds as winning the multi-state lottos Powerball and Mega Millions. But we have a lot more lotto winners because people play over and over whereas those 300,000,000 people only get one life in which to be struck by lightning four times.

The calculation I'd like to see someone do, and maybe I'll do it myself sometime if I can find the data, is an estimate of how many people die trying to play the lotto. There are many ways to die but let's just consider car accidents. There are probably statistics somewhere that say "On average there is one fatality per X miles driven." We could use that along with an estimate of how much people drive to come up with an estimate of how many die.

But estimating how much people drive would be hard. Some people live in cities and walk. Other people drive 100 miles to get to play in the big multi-state jackpots but once they get there they buy a couple hundred tickets for themselves and their friends. It's hard to say for sure but the odds of winning the multi-state lottos are so large that I bet that for every winner there is at least one person that died trying to play.

 

[epepke]

Florida has the most lightning deaths of any state in the US. There are an average of 8 deaths per year and 46 injuries. That averages to about one strike per week.

There are two lotteries a week. They aren't won every week, but when they roll over, usually multiple people win.

So the number of lottery wins is a bit more than the number of human lightning strikes.

 

[Just thinking]

There are two lotteries a week. They aren't won every week, but when they roll over, usually multiple people win.

So the number of lottery wins is a bit more than the number of human lightning strikes.

The above somewhat misleading --- why? Because if the lottery isn't won and the winnings roll over, you usually get more people playing (or more tickets purchased) the next time around; this is why you usually then get multiple winners. This now throws off the general statistic due to a disproportionate number of players. If no one gets struck by lighting one week I doubt if somehow the following week people are doing something that will more likely get themselves struck.

I guess what it boils down to is this (to respond to SS) ...

People are not going to change their behavior if no one is struck by lighting, dies by spider bite or poisonous snake or whatever. They will not keep increasing their risk one week to the next. You will not see new people on the scene (that normally do what gets people struck -- like play golf) just because no one is killed. They will however drastically change their lottery ticket puchasing behavior if the winnings keep rolling over -- sometimes to the point of waiting hours in lines hundreds of poeple long. (People that normally don't play the lottery will even buy a few tickets.) If they purchased tickets the same way they do when the winning is only the standard amount for when it's tens of millions, I believe you would see far fewer lottery winners throughout the year. And it's this statistic that you must consider when comparing your chances to getting killed by some unusual means.

 

[TeaBag420]

I'm sorry, I must have stumbled into the "no retards allowed" board, because any retard could tell you there is someone who is paid to make sure you hear about it when someone wins the lottery. That way, more retards will play the lottery.

Hey, somebody won! Go play!

 

[epepke]

The above somewhat misleading --- why? Because if the lottery isn't won and the winnings roll over, you usually get more people playing (or more tickets purchased) the next time around; this is why you usually then get multiple winners. This now throws off the general statistic due to a disproportionate number of players. If no one gets struck by lighting one week I doubt if somehow the following week people are doing something that will more likely get themselves struck.

But it doesn't matter, because interstate use of the Florida lottery is negligible, especially since Georgia got its own lottery. So all this means is that a higher percentage of Floridians are going to play the lottery when there is a rollover.

This necessarily means that a smaller percentage are going to play it when there isn't a rollover.

Anyway, the original statement used the general "you," so it only makes sense to divide the number of incidents by the total population. Since that's the same in both cases, the number of incidents itself can give a reasonable measure of the probability.

 

[Jyera]

1. Lottery odds is designed to be won.
Thus it easily undersood that it is easy for some of the many players to win.

On the other hand.
2. Lighting, Spider, PJ flames do not have odds favouring the "house" because there is No "house". It's not designed to win the players, and the player do not consciously try to "win" by getting struck or bitten.

However, ...

3. Lottery, like all game of chance that involves a "house", are designed such that, it takes lots of hard work to tip the odds very slightly towards the player.(I don't mean better than 50/50, just better than the odd the "house" gives). So that theoretically, if you play for a very very very long time, and play the most perfect game in a very very disciplined fashion, on the whole, you may get profitable, in a very slight and gradual fashion. Moreover, there will be many temption to be greedy and thus to give back all the winnings.

4. Lighting, Spiders are different, it is very very easy to tip the odds heavily against nature. If you want, you can walk over a flat field famed for lighting on a storming day. And you have changed the odds of getting struck greatly.

While normal people do not try to get killed by lighting, it is very possible to arrange for lighting to strike you once a day.
(It is very easy to play the "perfect game" ,to get struck by lighting, against nature.)

 

[Soapy Sam]

Florida has the most lightning deaths of any state in the US. -epepke

Really? That surprises me. I would have expected Colorado or Wyoming- one of the high altitude states on the Rocky frontrange where sudden thunderstorms are common. (I've seen some crackers in New Mexico too). Florida is flat and low, but subject to big temperature fluctuations and has higher average population density than the mid west. I wonder if that's why?

 

[Ladewig]

Re: Re: Odds and the Lottery

3. Lottery, like all game of chance that involves a "house", are designed such that, it takes lots of hard work to tip the odds very slightly towards the player.(I don't mean better than 50/50, just better than the odd the "house" gives). So that theoretically, if you play for a very very very long time, and play the most perfect game in a very very disciplined fashion, on the whole, you may get profitable, in a very slight and gradual fashion. Moreover, there will be many temption to be greedy and thus to give back all the winnings.

When you say "all games of chance" are you including casino games like keno? Because I can assure you that in that game there is absolutely no way that "hard work," perfect play, or length of play will tip the odds towards the player in any manner whatsoever. Keno is a losing proposition that might be overcome by pure, dumb luck; but there is no strategy that can improve a player's chances of winning. Craps, roulette, and bacarrat also fall into the category of negative expectation games in which no player actions can tip the odds even a fraction of a percetage point.

As for tipping the odds in U.S. lotto games, the only thing that reduce the negative expected gain is a jackpot rolling over from one week to the next. There is nothing that a player can do to tip the odds in any manner.

But perhaps I misunderstand what you are saying. Would you elaborate?

 

[Luke T.]

Florida has the most lightning deaths of any state in the US. -epepke

Really? That surprises me. I would have expected Colorado or Wyoming- one of the high altitude states on the Rocky frontrange where sudden thunderstorms are common. (I've seen some crackers in New Mexico too). Florida is flat and low, but subject to big temperature fluctuations and has higher average population density than the mid west. I wonder if that's why?

I believe 80 percent of all thunderstorms in the U.S. are in Florida. That's why.

 

[Luke T.]

http://www.lightningtalks.com/lightningfacts.htm#Top 10 States for Casualties

Ten US locations with the most casualties
(deaths and injuries combined)
due to lightning from 1959-1994 in Storm Data.
Rank State No. of deaths and injuries
1 Florida 1523
2 Michigan 732
3 Pennsylvania 644
4 North Carolina 629
5 New York 577
6 Ohio 545
7 Texas 498
8 Tennessee 473
9 Georgia 410
10 Colorado 394

Tampa, FL is the thunderstorm capital of the country with an average of 87 thunderstorm days each year. (New York Times)

 

[Just thinking]

But it doesn't matter, because interstate use of the Florida lottery is negligible, especially since Georgia got its own lottery. So all this means is that a higher percentage of Floridians are going to play the lottery when there is a rollover.

Exactly my point, which I think you are misunderstanding. The behavior of Floridians playing the lottery (or puchasing numbers of tickets) will change in such a way that if there is no winner one week -- and the winnings are rolled over -- there will more likely be a winner the next week, or even more the week after. This behavior (I doubt) is not unique to Floridians; I'm sure it happenes wherever there is a rollover -- Georgia, New Jersey, you name it. So human behavior is increasing the chances of a winner as the lottery goes unwon. This is not true of people's behavior if no one is struck by lighting for a given week -- more people do not venture onto the golf courses during cloudy conditions, more people do not go where poisonous snakes dwell because no one was bitten last week. This is why we see more lottery winners than unusual deaths. And more lottery winners does not increase any one's chances of winning -- which would be much less often if the number of tickets purchased did not increase from week to week regardless of any winning roll overs.

 

[geni]

There are two lotteries a week. They aren't won every week, but when they roll over, usually multiple people win.

multiple winners don't mean much unless you assume that the distribution of numbers chosen is flat.

 

[epepke]

Exactly my point, which I think you are misunderstanding. The behavior of Floridians playing the lottery (or puchasing numbers of tickets) will change in such a way that if there is no winner one week -- and the winnings are rolled over -- there will more likely be a winner the next week, or even more the week after. This behavior (I doubt) is not unique to Floridians; I'm sure it happenes wherever there is a rollover -- Georgia, New Jersey, you name it. So human behavior is increasing the chances of a winner as the lottery goes unwon. This is not true of people's behavior if no one is struck by lighting for a given week -- more people do not venture onto the golf courses during cloudy conditions, more people do not go where poisonous snakes dwell because no one was bitten last week. This is why we see more lottery winners than unusual deaths. And more lottery winners does not increase any one's chances of winning -- which would be much less often if the number of tickets purchased did not increase from week to week regardless of any winning roll overs.

No, I got your point; I just don't see how it's relevant to the discussion. If there are more lottery winners per capita than lightning strikes per capita, whatever the reason, then winning the lottery is more likely than being struck by lightning. It's just a matter of division.

 

[epepke]

I believe 80 percent of all thunderstorms in the U.S. are in Florida. That's why.

In the Tampa area, it used to be the case that during the summer, every day there would be a torrential thunderstorm that started at 4:00 and ended at 4:30. These are really quite dramatic. You can be driving your car, and everything's fine, and in 30 seconds there's so much rain that you can't see anything even with the wipers on full blast.

The climate has changed a bit, though, and now we get that pattern a bit more north.

 

[Jyera]

Re: Re: Re: Odds and the Lottery

When you say "all games of chance" are you including casino games like keno?

I specifically mentioned 'all game of chance that involves a "house" '. Where the "house" has an interest to win you. On the other hand the "house" would lose it's profitable "business" if you would not play against it.

A "house" would, of all reasonable sense, make it such that there is a possible chance to "win" something from the "house".
The reason is obvious. If it is a clearly perceived as a sure-lose, then no one would join in the game.

Because I can assure you that in that game there is absolutely no way that "hard work," perfect play, or length of play will tip the odds towards the player in any manner whatsoever. Keno is a losing proposition that might be overcome by pure, dumb luck; but there is no strategy that can improve a player's chances of winning.

Even in a case where the odds are fixed and "sure-lose" to the player, it remains the player's responsibility to himself to refrain from doing even MORE stupid things. Lots of hard work and discipline is needed to avoid losing even more, or to win.

Let say a person knows he is just playing game of chance to entertain himself, with no hope of winning.
It make sense to try to lengthen his play at the table for as long as he can.

To buy a drink reduces his amount of money he can use to lengthen his seat at the table. To succumb to sudden intutitive temptation to bet it big in order to win is a sure way to suddenly shorten your stay at the gaming table.

Craps, roulette, and bacarrat also fall into the category of negative expectation games in which no player actions can tip the odds even a fraction of a percetage point.

True. But perhaps a new casino made the mistake of offering free flow of drinks. Or perhaps they give out free night of accomdation if you play there. The odds of getting "profitable"
would have tipped to your favour.

As for tipping the odds in U.S. lotto games, the only thing that reduce the negative expected gain is a jackpot rolling over from one week to the next. There is nothing that a player can do to tip the odds in any manner.

But perhaps I misunderstand what you are saying. Would you elaborate?

The "house" as a sustainable business, will ensure there is no loophole to drain their profit. They would have conducted, professional and empirical studies to ensure there is no major loop holes.

It is up to the player to find out what action to take to play at a slightly better odds.

Eg. he might find that, if there is a jackpot rolling over, the chance of winning is slightly higher. And perhaps the odds in terms of cost vs winning is better. Then he should strive to have the disicpline to play only during these time when the odds are better.