Let's prove it! Roman deity competition

So basically Mylene just proved you can do just as well building HA's(which every Civ can build) instead of Praets. Now, there's no reason to not use Praets if your Roman and they are a good unit but Mylene showed that HA and other unit rushes are just as effective. Based on some of the other saves, I have to conclude that as long as you have the resource to build a certain unit, you can rush with it and Praets aren't any more/less successful than other units.

Withdrawl isn't really a win, it increases Survival Chance rather than Winning Chance. Iirc you have to be losing for it to even have a chance of happening, for ease I'd just discount all Withdrawls. Still over a 500% gain i think, so averaged around 10% better than odds suggested.

Habitus said:

Withdrawl isn't really a win

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That's irrelevant to the statistical test. The percentages shown are^* the odds of surviving the fight, and so surviving counts as a successful trial.

Anyways, the two of you really ought to work out the variance too. For the calculation you're doing, you have to add up

then you could work out how many standard deviations your computed statistic is away from the predicted mean (0).

*: I've not looked at the logs myself, so I'm taking his word for it

@Seraiel
A more interesting comparison is the wins/losses below/over 50%.

Roman HA vs Greek Sowrdsman (25%) : HA wins
Roman HA vs Greek Spearman (45%) : HA wins
Roman HA vs Greek Swordsman (30%) : HA wins
Roman HA vs Greek Spearman (40%) : HA wins

Roman Cat vs Greek Archer (55%) : Cat loses

Withdrawals work just as they are supposed to and don't enter too well in the comparison.

Beware comparing different odds together in a case such like this.

Rough summary:
-slightly more lucky in tough odds

kossin said:

Beware comparing different odds together in a case such like this.

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Any statistic could be used to give a perfectly reasonable statistical test, so long as it is properly analyzed. For a random variable adhering to the advertised percentages, the one he computed has mean 0 and variance
While it might be questionable to assume this statistic is normally distributed, we can always be extra-conservative and apply Tchebyshev's inequality to get a lower bound on the unlikelihood of a result far from the mean.

(of course, simply looking at 800% and saying "that's big" is very definitely not a proper analysis)

Seraiel said:

Wrong. Try to fight the ones having Jumbos or LBs, Duckweed did that successfully, Mylene will have to sit in her strong Position until Cuirrassiers arrive.

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Or, you know, Maces. And you can build elephants yourself as well if you have ivory. With his position at 50 AD, shouldn't be that hard to pull off a victory sooner or later.

MyOtherName said:

Any statistic could be used to give a perfectly reasonable statistical test, so long as it is properly analyzed. For a random variable adhering to the advertised percentages, the one he computed has mean 0 and variance

sum p(100-p).​

While it might be questionable to assume this statistic is normally distributed, we can always be extra-conservative and apply Tchebyshev's inequality to get a lower bound on the unlikelihood of a result far from the mean.

(of course, simply looking at 800% and saying "that's big" is very definitely not a proper analysis)

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I'm really bad at statistics, but I guess p = percentage?

Is it then 800 * (100 -800) = -559186

But what does this mean?

p is the probability of winning a specific fight. so if the odds were 40%, p = .4 and 1-p = .6; the product is .24. Then you add them up over all the fights.

Fallen Angel Lord said:

Or, you know, Maces. And you can build elephants yourself as well if you have ivory. With his position at 50 AD, shouldn't be that hard to pull off a victory sooner or later.

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Elepult would be possible, didn't see she was close with Shaka and got Ivory from him. Maces would be a long way, nobody has Machinery or even Metal Casting, but where's the point in building Elephants or Maces if you have Praets?

dalamb said:

p is the probability of winning a specific fight. so if the odds were 40%, p = .4 and 1-p = .6; the product is .24. Then you add them up over all the fights.

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Ok, I will do this now. You'll help me after that with this Tchebyshev's inequality MyOtherName speaks of.

My last statistics class was in 1973, so I've forgotten most of it. I suppose I can go back and remind myself but MyOtherName might be able to help out faster.

Amazing, all cos i had some luck on my 2nd last city attack...(with enough HAs as backup, so it saved me whipping a few more but not much more)

Tachywaxon said:

Mylene also pointed me as (somehow?) a dumbluck player about my chariot rush (which had for goal to get at least one city) and the fact I may lose at any moment because of Mao.

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Iam losing my faith here, good thing sgotm starts...
all i said was chariot rushes fail very very often, or everyone would take easy ways out of Deity every time they got horses. Why bother with HAs?
If you cannot accept statements like this one from someone who played 100s of Deity games, and think i called you dumblucked, i don't know what to reply anymore.
Keep living in your own world peoples, i stopped caring today.

Mylene said:

Iam losing my faith here, good thing sgotm starts...
all i said was chariot rushes fail very very often, or everyone would take easy ways out of Deity every time they got horses. Why bother with HAs?
If you cannot accept statements like this one from someone who played 100s of Deity games, and think i called you dumblucked, i don't know what to reply anymore.
Keep living in your own world peoples, i stopped caring today.

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Okay, okay. Sorry. I retreat myself. Why are you that angry for? I never insulted you in any way in that post.

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Anyways, I still wish Duckweed may explain how he secured Mao all for himself avoiding all peacevassaling. Just to make it actuality once again.

Come on guys,

1) This is a just a game. You might want to repeat that phrase to yourself a couple of times.
2) This used to be a nice forum, where civilized players discussed strategy. You guys are behaving like a bunch of 12 year olds.

Can we please get back to discussing content? If you want to argue anecdotes, argue anecdotes. If you want to argue math or stats, do so properly. If you think someone is cheating, ignore them.

I haven't been coming to the civfanatics forums for very long, so forgive me for speaking out on this.

All of you are coming close to ruining this place for other people. Both sides of this Praetorian debate are equally to blame--the level of vitriol regarding disagreements about a game is totally disproportionate. We have had half a dozen threads like this now in the last couple weeks, including wild acts of necromancy on threads 6 or 7 years old.

Please, please give it a rest now.

Improbable events, by definition, have some chance of occurring. I've had some remarkable streaks of good luck playing Civ, but also equally remarkable streaks of bad luck. The fact that this small number of trials appears to indicate better than average luck is not, in itself, an indication that something nefarious is going on.

It's straightforward to make a reasonable guess for what the mean should be, that good luck should balance out bad luck, but what is the variance of whatever probability distribution you want to model this with? Based on my own experiences playing Civ 4 on deity, I'd be surprised if the 'suspiciously good' luck here is any more than say, one standard deviation from the expected value, if we were to suppose that Civ 4 combat outcomes are Gaussian distributed. (While a Gaussian distribution might not be the most accurate description for this, it's at least a reasonable guess for a first order approximation.) In other words, there is no sound basis to imply that anybody has cheated.

Seraiel said:

Elepult would be possible, didn't see she was close with Shaka and got Ivory from him. Maces would be a long way, nobody has Machinery or even Metal Casting, but where's the point in building Elephants or Maces if you have Praets?

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It really depends on what the other side as, if Khan has a bunch of Keshiks, then yeah, elephants are a lot better. If your facing a lot of axes, swords, maces are worth the extra hammers.

RNG odds will go both ways sometimes. He really wasn't all that lucky at +15% a fight. That happens fairly often. There are plenty of times when I lose an entire stack while the enemy loses like 1 unit even though the odds are 50/50. It goes both ways. I've won battles where I'm 10% favored and lost when I'm 90% favored.

And the vast majority of battles he won, he had odds to win. If each combat is independent of the previous ones, then the RNG should favor him a lot in most of those fights and he should win most all of them. He could have lost a few more I guess, but he still would have conquered the cities either way in a few more turns.

It happens, and its random. With the 3-5 gold starts, its not random. You specifically drew or made that map for the purpose of an easy game or a high score.

Most of us don't play for high score, we simply play to achieve victory conditions and most of us value being able to consistently win on random default settings on a certain difficulty than trying to get an ultra-high score given a really awesome start.

Seraiel said:

Sum is 81135 which sounds extremely similar to my 800%, or is this something totally different?

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This means the variance of your statistic is 81135. The standard deviation is its square root -- 285.

The value of the statistic you computed -- 800 -- is 2.81 standard deviations away from the mean (0).

The odds of seeing that is no better than a one in 7.8 chance. (ignoring selection bias)

If we boldly assume the statistic is normally distributed, it means it's closer to 1 in 200 or 1 in 300. (I don't have a table handy to do the lookup) But such an assumption is probably too bold.

If someone was motivated, they could work out the precise significance of the result. Alas I'm not motivated at the moment.

@Seraiel:

First of all, we had the "Mylene cheats" discussion already, when someone digged out the log of her games out in a thread where i posted a save, and that she played to actually show it was winable (which i doubted; to make it short, it was an awful start to say the least).

Furthermore, every time someone states something like "this is a incredible streak of luck" the underlying message is "that person did something to force this kind of luck". Even if you argue that this wasn't what you were trying to say, be aware that this is how it is read. I've played alot of online games and have been active in alot of forums, and trust me: this kind of message "between the lines" always has been used in this very special kind of way. If this wasn't your intention, you will still have to deal with how it's understood. Just like you can not say you love someone, when what you're trying to say is that you just like that person. Think you got my point...

With so many battles won, it's pretty save to say that she actually did something to even get that far. It's not like she just had sheer luck out of nowhere. And in this regard a streak of luck differs alot from things like favourable starts or an easy map layout - the latter gets thrown at you no matter what you do. But to get such a lucky winning streak, you HAVE TO FIGHT. You have to make the decision to rush with HAs, you have build up the army, you have to pick your target and everything else. This is very different from a favourable start.

One thing you didn't consider - if Mylene had lost some of the battles she won with low odds, would she still have been able to take the city? Would she had have backup units to take the city? Or where those won battles gamebreaking in the "when i don't take the city this turn, the AI will reinforce it and the game is almost lost because ..." way?
Yes, those luckstreaks make things alot easier, but they do not win you games most of the time.

Last but not least - she is not my friend, neither am i her friend. I like and appreciate her just like i appreciate other people in the forum that i learned from or whom i had an interesting discussion with, like Dirk. There was a time when Gwaja reanimated the civfanatics IRC chat, and Mylene, Dirk, TMIT, some other folks and me used to hang out there for a few days - but that's about it. Yes, i care somewhat more for her than i care for people from the forums that i know less, but we're far from being friends. Which is sad, but true.

Frankly speaking, i'm not too happy that i have to spell all that out, but i somehow feel i'm forced to do so. And now, please, would you let it go... there's no conspiracy of players protecting each other or a certain way to play Civ4.

I haven't seen this kind of abuse of statistics since the last major political debate.

Mylene had winning odds in nearly all of those battles. She won most of them. She only won against bad odds, what, three times? That's not abnormal, I don't think.

If you flip a coin, the odds of getting heads are 50%. If you flip it again, the odds are still 50%. The coin does not remember what your last flip was.

If you flip eight times and get eight heads in a row, it's not because it's a trick coin; it's because the odds of getting heads are 50% each time, and that's what happened.

To look at all that and imply that something was off--and then to throw out a number that means nothing from a statistics standpoint (800% gained!)--is nuts. What about damage? How hurt were her units? How long did they have to take to heal? That's not an insignificant figure, either.

It's true that you can use numbers to prove anything, but at least try to do so in a way that makes some kind of sense.