I do not care what you say. (Part 2)

[peppe1]

Since you are not at home continue your test you can continue wherever you are, i assume you can find a penny somewhere and start flipping. Record your results for each set of 100 flips. If it doesn't come out 50/50 ask the universe for a reset.

Google said to read this -> http://www.fourmilab.ch/rpkp/experiments/statistics.html

I thought there was also a popular school project involving coin flips and variability of the results. Basically in a small sample size you can size widely different results.

 

[Jet]

It's a derogatory term. It's the OP's methods or reasoning that were given a derogatory label. That is name calling.

 

[r_rolo1]

1. Boudica does not get combat 1 from worldbuilder axemen.

This is wrong. By default, units placed in WB recieve the traits promos.

 

[TheMeInTeam]

What name-calling? laughably is an adjective (or is it an adverb?) describing the extent to which I believe 100 trials to be insufficient.

It's an adverb. And the object of it isn't a person, but rather the experiment.

IMO, the burden of proof is on the people claiming the odds are wrong, not the other way around.

What kind of confidence interval are we going for here? I've not done any stats for a long time but I'd venture a guess we'd need more than 100 trials for 99% for example.

Also, a bit off topic, but aren't some coins weighted slightly more on a side, thus not yielding perfectly even results ?

 

[ParadigmShifter]

That's why we assume fair coins and spherical cows in maths.

 

[Volapyk]

There were a mathematician, a physicist and a biologist taking a train though Wales.
Looking out the window the biologist spots a black sheep and exclaims "Look there is the proof that black sheep exists". The physicist looks out and says "No there is the proof that there exists at least one black sheep". The mathematician then looks out and says "No there is the proof that there exists one sheep which is black on at least one side".

Sorry but just had to say it, you guys are going way off point here.

 

[ParadigmShifter]

Hmm the thread is about statistical trials so not really

I don't know the number of trials for 99% CI myself but I could easily calculate it 16 years ago

 

[UWHabs]

Hmm the thread is about statistical trials so not really

I don't know the number of trials for 99% CI myself but I could easily calculate it 16 years ago

Yay math!

As for the test, it's binomial - win or lose. Quick search online found this:http://onlinestatbook.com/stat_sim/normal_approx/index.html

Start it up, plug in N=100, p=0.5, you get the Prob of getting between 38 and 63 wins as being 99.07%, so you're right within the confidence interval.

Now, I would check the odds. If the axeman does start with combat 1 and the other doesn't, then you should have I think it's 60-something percent chance of winning. Then, your second trial would line up perfectly, but the first is off.

Maybe a better way is to just put stacks of like 100 axemen each on a square and stack attack, then check how many you have left. You should always be fighting strongest vs. strongest, and it might go faster.

 

[VoiceOfUnreason]

"No there is the proof that there exists one sheep which is black on at least one side".

... at least part of the time.

 

[JBossch]

I feel nauseous. This thread is already reminding me of the 400 page treatise on the barrage promotion.

 

[sfnhltb]

Since you are not at home continue your test you can continue wherever you are, i assume you can find a penny somewhere and start flipping. Record your results for each set of 100 flips. If it doesn't come out 50/50 ask the universe for a reset.

Google said to read this -> http://www.fourmilab.ch/rpkp/experiments/statistics.html

I thought there was also a popular school project involving coin flips and variability of the results. Basically in a small sample size you can size widely different results.

One I remember was a homework assignment to flip a coin 100 times and record the results of each flip (like HHTHTHTH...). The next week the teacher then assigned extra homework of doing it again properly to all the ones that had cheated and just written down what they thought would be a random sequence. It seems most people "over randomize" or rather expect the next result to be different more often that it should be statistically. So a real string of 100 flips is almost certain to have several 5,6, 7 or more in a row, but if people try to fake it they tend to avoid long sequences like that, and might not even have 4 in a row.

 

[popejubal]

One I remember was a homework assignment to flip a coin 100 times and record the results of each flip (like HHTHTHTH...). The next week the teacher then assigned extra homework of doing it again properly to all the ones that had cheated and just written down what they thought would be a random sequence. It seems most people "over randomize" or rather expect the next result to be different more often that it should be statistically. So a real string of 100 flips is almost certain to have several 5,6, 7 or more in a row, but if people try to fake it they tend to avoid long sequences like that, and might not even have 4 in a row.

I did this for my algebra class. Any of my students who didn't have at least 6 of one type in a row got an F for the 50 point homework (HW assignments are normally 5 points each) and a detention where they did the coin flips again while I was watching. I didn't tell them that they had to have at least 6 in a row of one type in order to "pass" the homework, I just told them that I knew which ones pretended to record the coin flips and which ones actually did the real work.

I shocked and amazed them with the fact that I was able to look at each homework for 30 seconds and then hand it back to them with a 50/50 points or a 0/50 points score while they watched. One or two protested that they "really did do all the flips!" - and then they admitted that they hadn't when I called their bluff.

We talked about the results on the day after the detention.

In short, for a relatively small number of trials, you should expect at least some sections in your data that look fairly wacky to our human expectations. And yes, I did give them the 50 points for the assignment after they served their flipping detention.

 

[popejubal]

Did not check the combat odds for these test because I just assumed fifty fifty with the defensive bonus

If you're going to claim that the combat odds calculator is incorrect, it might be helpful to look at the combat odds before running your trials. There were some instances where the combat odds calculator was incorrect in Vanilla Civ (maybe also in early Warlords as well, but I don't remember exactly), but I believe that they were all ironed out with one glaring exception.

If you are attacking across a river (and you aren't Amphibious), you give the defender an extra bonus to their strength. This is correctly taken into account by the combat odds calculator. If you are more than 1 tile away and you will end up attacking across a river, but you are not next to the river yet, the combat odds calculator will not realize that you are going to be attacking across a river and will not take that bonus into account. This can make a dramatic difference in the real combat odds that you will end up facing.

One thing that I really do miss having in this game is a defensive odds calculator. Ctrl-click on an opposing unit and drag to your unit (or something similar) to find the combat odds that come from them attacking your unit. It would give you a much better idea of whether to leave your unit on the hill or just have them run away to fight another day.

 

[TheMeInTeam]

One I remember was a homework assignment to flip a coin 100 times and record the results of each flip (like HHTHTHTH...). The next week the teacher then assigned extra homework of doing it again properly to all the ones that had cheated and just written down what they thought would be a random sequence. It seems most people "over randomize" or rather expect the next result to be different more often that it should be statistically. So a real string of 100 flips is almost certain to have several 5,6, 7 or more in a row, but if people try to fake it they tend to avoid long sequences like that, and might not even have 4 in a row.

Isn't that kind of iffy? Certainly, any outcome the student generates is POSSIBLE, the teacher can prove they cheated no more than I can prove the combat odds wrong by losing 3 95% battles in a row.

Now, if we were to consistently get results outside the expected confidence ranges, then we'd have a problem. The code itself can be looked at too though, and it has been IIRC.

PS: The easiest way to do a test like this is to put 100 axes next to 200 axes. Stack attack with the 100, and assuming nobody has any promotions to start, every battle will be guaranteed to be between two full-strength axes.

You can do this between any units. I'm already pretty convinced the odds are accurate though...

 

[wioneo]

And yes, I did give them the 50 points for the assignment after they served their flipping detention.

Pfft...forgiveness is for hippies, why not just let them suffer? You won't be gettin a white cat to stroke any time soon...

On topic, I don't understand your logic for not countin all 4 reloads as one test. You also seem o be contradicting your own train of thought by considering each of the pairs of reloads as one test...

How is grouping the first and second load different than grouping the second and third? and Mr. Winzeler told me that addition is both commutative and associative, so adding all 4 loads would be the same as having had all 200 battles in one go.

That is except for the change in random seed, which I know nothing about, but as far as I know, it does not increase or decrease *randomness,* and therefore it is entirely possible(though highly unlikely) to return results that are exactly the same.

 

[Ai Shizuka]

What's with the spherical cows?

 

[bobbyboy29]

A picture says a thousand words. The comic applies to the joke made earlier. (Insert explanation of binomial distribution here)

 

[popejubal]

What's with the spherical cows?

I happened to find the joke on wikipedia first, but I heard this joke long before there even was an internet.


Ever lower milk prices were driving a dairy farmer to desperate measures. Two years ago, he had his barn wired for sound and tried "Beethoven for Bovines" but milk production dropped 2%. Last year he signed up for "hex the herd" where Genuine Santa Barbara WitchesTM remotely hexed your herd for health and higher production. (The ad had said its hexes were the cause of California's improved milk production, but it didn't seem to work in Wisconsin.) So this year he drove to town to consult the ultimate power source: a theoretical physicist. The physicist listened to his problem, asked a few questions, and then said he'd take the assignment, and that it would take only a few hours to solve the problem. A few weeks later, the physicist phoned the farmer, "I've got the answer. The solution turned out to be a bit more complicated than I thought and I'm presenting it at this afternoon's Theory Seminar". At the seminar the farmer finds a handful of people drinking tea and munching on cookies---none of whom looks like a farmer. As the talk begins the physicist approaches the blackboard and draws a big circle. "First, we assume a spherical cow..."




...basically, physicists and mathematicians like to work with simple problems more than they like to work with difficult problems. This is because people in both of these professions are lazy just like people in every other profession.

A sphere is a much more simple shape to consider than a cow shape. Amazingly, turning everything you consider into spheres of appropriate volume works very well because so many things work on proportional volume instead of specific shapes.

 

[popejubal]

An astronomer, a physicist and a mathematician (it is said) were holidaying in Scotland. Glancing from a train window, they observed a black sheep in the middle of a field.

"How interesting," observed the astronomer, "all scottish sheep are black!"

To which the physicist responded, "No, no! Some Scottish sheep are black!"

The mathematician gazed heavenward in supplication, and then intoned, "In Scotland there exists at least one field, containing at least one sheep, at least one side of which is black."


----------------------------

A biologist, a statistician, a mathematician and a computer scientist are on a photo-safari in africa. They drive out on the savannah in their jeep, stop and scout the horizon with their binoculars.

The biologist: "Look! There's a herd of zebras! And there, in the middle : A white zebra! It's fantastic! There are white zebra's! We'll be famous!"

The statistician: "It's not significant. We only know there's one white zebra."

The mathematician: "Actually, we only know there exists a zebra, which is white on one side."

The computer scientist: "Oh, no! A special case!"

----------------------------

A mathematician, a biologist and a physicist are sitting in a street cafe watching people going in and coming out of the house on the other side of the street.

First they see two people going into the house. Time passes. After a while they notice three persons coming out of the house.

The physicist: "The measurement wasn't accurate."
The biologists: "They have reproduced".
The mathematician: "If now exactly one person enters the house then it will be empty again."


One day a mathematician decides that he is sick of math. So, he walks down to the fire department and announces that he wants to become a fireman.
The fire chief says, "Well, you look like a good guy. I'd be glad to hire you, but first I have to give you a little test."

The firechief takes the mathematcian to the alley behind the fire department which contains a dumpster, a spicket, and a hose. The chief then says, "OK, you're walking in the alley and you see the dumpster here is on fire. What do you do?"
The mathematician replies, "Well, I hook up the hose to the spicket, turn the water on, and put out the fire."

The chief says, "That's great... perfect. Now I have to ask you just one more question. What do you do if you're walking down the alley and you see the dumpster is not on fire?"
The mathematician puzzles over the question for awhile and he finally says, "I light the dumpster on fire."
The chief yells, "What? That's horrible! Why would you light the dumpster on fire?"
The mathematician replies, "Well, that way I reduce the problem to one I've already solved."



-----------------


A hot-air balloonist had drifted off course. He saw a man on the ground and yelled, “Excuse me, can you tell me where I am?”

“Yes,” the guy said. “You’re in a balloon.”

“You must work in I.T.,” the balloonist said.

“How did you know?”

“What you told me is technically correct, but of no use to anyone.”

“And you must work in management,” the man on the ground retorted.

“Yes. How did you know?”

“You don’t know where you are or where you are going, but you expect me to fix your problem. You’re in the same position you were in before we met, but now you think it’s my fault.”

 

[PieceOfMind]

It's a derogatory term. It's the OP's methods or reasoning that were given a derogatory label. That is name calling.

Call it derogatory if you will, but it is plainly not name-calling.

If you think my tone was overly harsh, perhaps you should consider the context in which I am offering my opinion. (see quotes below). With these quotes in mind the level of harshness is probably quite generous.

I do not care what you say.

I have actually tested this a little and I have the same conclusion.

The combat odds are not what they say.

Did not check the combat odds for these test because I just assumed fifty fifty

I am just saying that this test proves to me what i have believed all along and I can not see what could change my mind.

Ok I will remove any personal opinion (on other posters) from my posts from here on...

If these numbers really show an error (and I think they do), everytime you look at the odds there is a range of plus or minus 12.5% so there is a total range of 25% in which the true odds are.

This is absolutely false.



As another poster said earlier, the burden of proof is on he who calls the odds plainly wrong. The OP has offered zero evidence to support his claims. How can you possibly comment on the accuracy of the RNG if you do not even check what the RNG should be producing? That's like telling a police officer who is booking you for speeding that he is definitely wrong because even though you didn't ever look at your speedometer you always "knew" what speed you were doing.

The earlier example with the samurai and axeman was also poorly executed. There has been no scientific nor statistical argument so far to show the RNG is even close to having a problem. So far the results of the incomplete experiments have only confirmed the RNG is behaving as expected.

If I were to help the OP in learning about the relevant probability theory (assuming he might for a moment care about what I say), I might suggest googling "100 coin tosses" and reading through experiments of that type. I am not surprised to see people overly suspicious of RNGs. However I honestly consider it amusing when the arguments applied by such people could be used to say a true coin toss is not completely random. In probability you can't rely on your intuition because it is often misleading. To demonstrate this one only has to look at the classic experiment where you have the class do the 100 coin tosses for homework (as another poster talked about). When I first read about that experiment it was from a university professor who claimed that if he had half of his students go home and perform the experiment (100 coin tosses) and the other half go home and deliberately forge the results, then he would be able to guess with about 90% accuracy (I forget the exact number) which of the tests were genuine and which were forged. This suggests that even undergraduate level mathematics students do not necessarily have the authority to question the 'randomness' of a process.