Wiki Entry on Events in Incorrect

[Decomposition]

So, doctor, what you're saying is that if I happen to flip a coin 50 times, and it turns up 50 heads, then a coin flip does not have a 50% probability? It is unlikely yes, but 50% is most definitely correct.

Also, you have only done one test (you). You do not seem to have considered the possibility of there being a nation that gets a new event every week.

Yes, that is exactly what I am saying. If I give you a coin claiming that it has an equal chance of coming up heads or tails on every coin toss and it comes up heads fifty times in a row then you have every reason to suspect that I am lying to you. Even if I were the only nation that had experienced this among 30,000 nations things would still look very fishy since a 1 in 300 million chance is very unlikely to occur across 30,000 nations. Since there are many, many other nations that also have not had events occurring for extensive periods of time this issue is obviously moot.

I, and others, have tried to figure out what additional factors may play a role in determining the likelihood of an event but have thus far come up short. The only things that are clear is that the 10% figure is way off and that events are not distributed randomly and independently.

[Magicman657]

If you were to have 9 red balls and one blue ball in a bag, and were to draw 9 balls before refilling the bag. You 1 in insert large number probability figures would be accurate for the blue ball always being the last out the bag in 300 draws.

The possibility of an event on day X is an unrelated contingency to whether an event occured on day Y.

It is a 10% chance.

That's not how it works when you're looking at the probability of an event not occurring multiple times.

[HYPERiON]

Yes, that is exactly what I am saying. If I give you a coin claiming that it has an equal chance of coming up heads or tails on every coin toss and it comes up heads fifty times in a row then you have every reason to suspect that I am lying to you.

What if it's my coin? My coin, which definitely has a probability of exactly 50%?

[Magicman657]

There's a theory that desired government affects event rates and that makes sense since most people always use Monarchy. I just got a Great Monument so after a week or two hopefully I'll see some results. I haven't had an event in multiple months but I rarely collected with desired.

Update- first collection with Great Monument (made my gov desirable), and I got an event.

Interesting to note that a few weeks ago a friend had also reported getting an event for the first time in months after collecting under desired gov as well.

Conspiracy?

[Kingdom of Royalty]

What if it's my coin? My coin, which definitely has a probability of exactly 50%?

The fact is though that you aren't going to get 50 heads consecutively because the chances are 1 in millions, this is just the same as winning the lottery 50 times in a row then saying "the chances are 1 in 50 million", it is just not going to happen.

[HYPERiON]

The fact is though that you aren't going to get 50 heads consecutively because the chances are 1 in millions, this is just the same as winning the lottery 50 times in a row then saying "the chances are 1 in 50 million", it is just not going to happen.

Sorry, but I just don't know how to respond to this. It's pretty hard to discuss probability with someone who doesn't understand it.

[US of Europe]

If you were to have 9 red balls and one blue ball in a bag, and were to draw 9 balls before refilling the bag. You 1 in insert large number probability figures would be accurate for the blue ball always being the last out the bag in 300 draws.

The possibility of an event on day X is an unrelated contingency to whether an event occured on day Y.

It is a 10% chance.

Exactly what I was saying, amen.

If there would be a chance of 0.001% I would win a large price, and I would play for 100,000 days, it is still very likely I haven't won the great price. The problem is that the OP thinks that if you didn't have it one day, the next day it won't be 10% anymore, but the odds increase you get an event. And if you haven't recieved an event in 100 days, the chance would be somewhere around 1000%, etc. It simple stays 10% daily (and does not know you haven't got an event in the last 10, 100, or even 1000 days)

Edited February 3, 2008 by US of Europe

[Kingdom of Royalty]

Sorry, but I just don't know how to respond to this. It's pretty hard to discuss probability with someone who doesn't understand it.

I don't understand it? The fact that when the probability of something happening based on a figure is millions to one, it is very very likely the figure is incorrect! If the case was that despite probability being millions (billions, or trillions) to one, we cannot draw a conclusion, because it might be a "freak case", then the whole laws of probability would collapse.

[US of Europe]

I don't understand it? The fact that when the probability of something happening based on a figure is millions to one, it is very very likely the figure is incorrect! If the case was that despite probability being millions (billions, or trillions) to one, we cannot draw a conclusion, because it might be a "freak case", then the whole laws of probability would collapse.

True. The problem is, your propability is incorrect, and it is not being millions (billions, or trillions) to one. It is uhm... 10%, or ten-to-one. So I think we can survive one day longer, and the laws of propability wn't collapse yet.

(don't know how to explain this in proper English, but uhm... we used to have a model here with small balls, with all kind of colors. Your calculations assume we have 9 red balls and 1 green ball. Now if we take on the first day a red ball (propability is 90% we will), there are only 8 red balls and 1 green ball remaining. The propabilities will now be different.

The correct model is that we have 9 red balls, and 1 green ball, and on every day there are 9 red balls, and 1 green ball, so the propability stays 10% we will draw a green ball)

Edited February 3, 2008 by US of Europe

[Sebastian]

About that ball thing. It isn't completely correct.

9 9 81

- * - = ---

10 10 100

And this is only two days. THe figures goes up as we advance...

[US of Europe]

About that ball thing. It isn't completely correct.

9 9 81

- * - = ---

10 10 100

And this is only two days. THe figures goes up as we advance...

Yes, though I don't see the error in it actualy.

[Kingdom of Royalty]

About that ball thing. It isn't completely correct.

9 9 81

- * - = ---

10 10 100

And this is only two days. THe figures goes up as we advance...

Indeed

I should make it clear though, I do see where you are coming from with your 1/10 argument, I am not dismissing that, what I am saying though is that it is very unlikely (if it was 10%) that events would be as rare at they are...

[US of Europe]

I completely agree that it is unlikely, highly unlikely even. Though it is possible the chances are 10%, while a lot of nations haven't got an event in months, or even years. I think we're looking here at a small amount of nations, and most nations simple get their events once in a while, like we would expect normally. So, though the expected rate is that the OP would have got an event, it does not give any proove the 10% is wrong. If we asked 100 nations indepenently, at random, I think such conclusions might have been made, if a rather large portion hasn't got an event for such a long period. Though a propability of 10%, does not mean (with 600 days), that I also got 60 events.

[Syzygy]

well i think the main problem expressed in this thread is "the law of great numbers":

if you have 10% chance for *something*, this something will *over time* appear almost exactly in 10% of all cases.

Simple example:

The ideal D6 dice has exactly 1/6th probability for each number. Now, if you throw it 10times, you could easily end up with this streak:

4 4 3 4 1 1 4 3 2 5 : which in NO WAY reflects a 1/6th probability for each of the numbers. but still, it would not be a result anyone would wonder over.

BUT: if you throw the dice 60 million times. you will have ~10million results for each of the numbers 1 2 3 4 5 6. Some maybe only 9.6M and some even 11.2M - but nearly 10M for each of them.

Now we have the problem, that from almost *everyone* you speak to you get the same answer: no way he had in 10% of his collections triggered an event. not even close.

The main point is not, if it is impossible to have 500days without event. or 400 or 300. the point is, there are a LOT of players saying they are facing WAY below 10% events at their tax collections, and you have almost NO ONE who says the opposite. If there are players with only 1 or 2 events in 500days, there should also be players with 100 events in 500days (its only logical, because bad and good streaks should equal each other out, narrowing to 10% over time) - but obviously this is not the case.

From all the guys I have spoken to in my own alliance (and they are ~100 very active players), the fewest got a noticable amount of events during the lifetime of their nations - which should not be the case.

[HYPERiON]

the point is, there are a LOT of players saying they are facing WAY below 10% events at their tax collections, and you have almost NO ONE who says the opposite.

Would you complain if you were getting events every 10 days or so?

[Decomposition]

well i think the main problem expressed in this thread is "the law of great numbers":

if you have 10% chance for *something*, this something will *over time* appear almost exactly in 10% of all cases.

Simple example:

The ideal D6 dice has exactly 1/6th probability for each number. Now, if you throw it 10times, you could easily end up with this streak:

4 4 3 4 1 1 4 3 2 5 : which in NO WAY reflects a 1/6th probability for each of the numbers. but still, it would not be a result anyone would wonder over.

BUT: if you throw the dice 60 million times. you will have ~10million results for each of the numbers 1 2 3 4 5 6. Some maybe only 9.6M and some even 11.2M - but nearly 10M for each of them.

Now we have the problem, that from almost *everyone* you speak to you get the same answer: no way he had in 10% of his collections triggered an event. not even close.

The main point is not, if it is impossible to have 500days without event. or 400 or 300. the point is, there are a LOT of players saying they are facing WAY below 10% events at their tax collections, and you have almost NO ONE who says the opposite. If there are players with only 1 or 2 events in 500days, there should also be players with 100 events in 500days (its only logical, because bad and good streaks should equal each other out, narrowing to 10% over time) - but obviously this is not the case.

From all the guys I have spoken to in my own alliance (and they are ~100 very active players), the fewest got a noticable amount of events during the lifetime of their nations - which should not be the case.

You are on the right track but if you throw a unbiased dice 60 million times you will get very very very very close to exactly 10 million 1s, 2s, 3s etc. If you got 11.2 million of any one number you should be even more suspicious than if you threw 50 heads in a row with a supposedly unbiased coin.

[HYPERiON]

You are on the right track but if you throw a unbiased dice 60 million times you will get very very very very close to exactly 10 million 1s, 2s, 3s etc. If you got 11.2 million of any one number you should be even more suspicious than if you threw 50 heads in a row with a supposedly unbiased coin.

It's pretty obvious you don't have a PhD in statistics, mate. (DAC)Syzygy explained it perfectly.

[JoshuaR]

In regards to the OP. No, the odds are not 10%. Others using statistical (well, actually they aren't using any methods) methods to justify that never getting events is possible fails in the light that this is not an isolated occurence.

The figure I had heard was 1/30. But when I heard it, I thought that it was based on fact, or an admin guide. Maybe it's unknown.

[Decomposition]

It's pretty obvious you don't have a PhD in statistics, mate. (DAC)Syzygy explained it perfectly.

Oh dear! OK - here's what you need to do - buy yourself any intro to stats textbook and then use a simple test for the difference in proportions to determine the probability of throwing 11.2 million sixes out of 60 million throws of an unbiased dice (or use binomial theory - there are a couple of different approaches that will give you the same answer) . The odds are so unbelievably small that any calculator will be unable to express how unlikely the event is because it will run out of zeroes behind the decimal point. The innumeracy of your post is so cute that I am bringing it to my introductory stats class this afternoon. Thanks for the great example - I am sure my students will enjoy it.

btw - would I have the ruler name, nation name, and capital name combo (Decomposition, Cholesky, Monte Carlo) if I was not the ultimate stats geek?

Edited February 4, 2008 by Decomposition

[Kingdom of Royalty]

In regards to the OP. No, the odds are not 10%. Others using statistical (well, actually they aren't using any methods) methods to justify that never getting events is possible fails in the light that this is not an isolated occurence.

The figure I had heard was 1/30. But when I heard it, I thought that it was based on fact, or an admin guide. Maybe it's unknown.

I was also thinking 1/30

[Kingdom of Royalty]

I think there is only one 100% certain way of finding out exacly how many of each sides the dice will land on if you throw it 60 million times, anyone want to voulenteer ?

[osdeath]

I think there is only one 100% certain way of finding out exacly how many of each sides the dice will land on if you throw it 60 million times, anyone want to voulenteer ?

i dont think i have a spare life right now, but when i do ill be sure to get in touch

[HYPERiON]

Thanks for the great example - I am sure my students will enjoy it.

Be my guest! With a sample size of 1, I'm sure they'll find it hilarious.

http://forums.cybernations.net/index.php?showtopic=13690

[Decomposition]

Be my guest! With a sample size of 1, I'm sure they'll find it hilarious.

<a href="http://forums.cybernations.net/index.php?showtopic=13690" target="_blank">http://forums.cybernations.net/index.php?showtopic=13690</a>

Again - a very funny response. You have to think of every day of tax collection as an independent event and my entire experience as a series of independent events (191 by today's count). This has nothing to do with what you call "sample size" by which I assume you mean the number of individuals experiencing something.

[Yenisey]

I think the 10% is a very, very old figure. Events were far more frequent when they were first introduced.

About 18 months ago there appears to have been a change in the code that reduced the odds of an event occurring.

I suspect I had more events in the first few months after they were added than in the last year.

I'd estimate 10 events in the past year.

They do appear to come in bunches, you get no events for a few months, then several within a period of days.

No idea how it's currently coded, but it's no longer a random 10% chance at tax collection, unless Admin is using an extremely funky random number generator.