Siege Rolls; Confirmation Bias my ARSE!!!

[tbhayward]

To clarify, I am not specifically talking about "wall breaches" versus "disease outbreaks", that is the results of the rolls. All I am considering in this exercise is the dice rolls themselves and whether or not they have a fair and equally weighted outcome distribution. I understand the randomness of any singular roll, statistically, any dice roll should have a 1:14 chance of occurring. The data set thus far suggests that the game mechanics "may" be purposefully skewed. That is the goal of this exercise, to compile enough data points to confirm or discredit this hypothesis. As demonstrated by tbhayward, getting the results I got for the original post had a 0.006% chance of occurring naturally. As rare as that may seem, it is not conclusive at this point in time because that means it can repeat itself 6 times for every 1000 sets of 100 dice rolls.
I would like to think PDX is being honest with their claim that the random dice generator is truly random. However, my own experience suggests otherwise and that may be my "confirmation bias" at work. Thus, I need to definitively convince myself with actual data sets and not a gut feel. Maybe others posting here have already run this experiment and they are frustrated that this topic keeps surfacing. That is also why I want to post the results once I get the data sets compiled.

I did the calculation wrong in my haste. My post is accurate now.

 

[pikaemperor]

It's not confirmation bias, the siege rolls roll lower for the player than the AI(especially the lucky ones).

 

[tbhayward]

I loaded up as the Ottomans twice and spent a few decades walking around fighting people that I had cores on. I recorded 247 die rolls and I plot them here. I calculate a chi^2/degree of freedom of 1.0071 which means that it is almost perfectly random.

 

[Sfan]

You must understand why the player feels this bias. The good human player doesn't go for a move if it requires him to finish the siege at 7% with immense luck. The good human player goes for a move if the move requires the AI not to finish the siege at 7% with immense luck.
Simply put, you say "oh this siege stack is fine as long as I finish this 42% siege before he finishes his -7% siege". Double disease outbreak for you, breach and siege falls for the AI, you are mad.
The opposite situation is exactly as likelybut you simply don't risk it so you don't see it ingame. If you were the one that needed to finish the -7% before the AI finishes his 42% you would retreat. The human plays safer amd cannot have insane luck because of that. Insane luck comes when you do crazy things and the AI does crazy things.
For 1 time where the AI has lucky rolls, there are 9 times where it went as expected amd you just say "lol AI is bad, he gives me free stackwipe, he should have abandonned the siege".

 

[by_curling]

You don't need to calculate all of that stuff. We call it "unlucky".

It's great lots of people try to explain what random is but after those messages, he is still come up with new arguments. I even saw some stuff from my Statistics class back in University.

 

[grommile]

It's not confirmation bias, the siege rolls roll lower for the player than the AI(especially the lucky ones).

I suggest presenting either substantial statistics, official confirmation, or retraction.

 

[alexti]

Every time this topic comes up PDX is quick to give the default reply that it's confirmation bias. I never accepted this as it appeared to me that "Disease Outbreaks" are much more common that "Wall Breaches" when I am sieging a hostile fort. Therefore, I took it upon myself to write down the actual siege rolls during a Brandenburg campaign. This is early on before cannons but all we are concerned with is the dice rolls, not what they do. In case you are not aware, a dice roll of "1" is a disease outbreak while a dice roll of 14 is a wall breach. Since the game is based on a 14 sided die, it would seem they both have equal odds of happening at a rate of 1:14. I wrote down all the siege rolls to acquire a sample size of 100 rolls. This should be large enough to illustrate the point. With 100 rolls, and 1:14 odds, we should see approximately 7 rolls of a "1" and 7 rolls of a "14". However, the actual data is much much worse. I got 18 rolls at "1" and 2 rolls at "14". So these supposedly equal odds are not so equal after all to the tune of a disease outbreak being 9 times more likely than a wall breach. I realize a sample of 100 rolls may not accurately reflect the 9 times more likely occurrence but the point of this post is to illustrate that a dice roll of "1" is not at all equal odds of happening as a dice roll of "14". The only rational explanation of this is that the random dice roll generator is skewed to give lower dice roll results for the player versus truly random dice. PDX, the evidence is indisputable, your confirmation bias excuse is complete and utter CRAP!
If the community would like, I can continue to gather data in this regard. However, I am convinced of the results and will be waiting for the 1.19 patch before seeking more data sets.

The result you've recorded (18 rolls of '1' out of 100 from U(1,14) distribution) is very unlikely. It is not exactly the proof, but it's hard to discard as a random fluke. I doubt Paradox has implemented bias on purpose, however there might be some interaction between the way pseudo random number generator is constructed and they way uniform distribution is drawn from it. If some low-quality algorithms are used it's possible to get some interaction on a bit level which would lead to strange results. For example, if underlying generator has poor quality lowest bit distribution and you convert to uniform distribution by using modulo operation you may see many more odd numbers than even. Or vica versa.

 

[tbhayward]

The result you've recorded (18 rolls of '1' out of 100 from U(1,14) distribution) is very unlikely. It is not exactly the proof, but it's hard to discard as a random fluke. I doubt Paradox has implemented bias on purpose, however there might be some interaction between the way pseudo random number generator is constructed and they way uniform distribution is drawn from it. If some low-quality algorithms are used it's possible to get some interaction on a bit level which would lead to strange results. For example, if underlying generator has poor quality lowest bit distribution and you convert to uniform distribution by using modulo operation you may see many more odd numbers than even. Or vica versa.

It's really not that unlikely. It's 2.5 sigma away from the expected value of 100/14 = 7.14. That means there is about a 1% chance of it happening.

 

[alexti]

It's really not that unlikely. It's 2.5 sigma away from the expected value of 100/14 = 7.14. That means there is about a 1% chance of it happening.

It doesn't sound right to me. Probability of getting exactly 18 '1's in 100 trials is C(100,18)*pow(p,18)*pow(1-p,100-18), where p=1/14. That's 0.00016 unless I am miscalculating something

 

[ywxiao]

I was laughing hard while watching deserved dice rolls stream. Practically every single siege race was a loss. AI's 7% beats player 70% LMAO.

 

[tbhayward]

It doesn't sound right to me. Probability of getting exactly 18 '1's in 100 trials is C(100,18)*pow(p,18)*pow(1-p,100-18), where p=1/14. That's 0.00016 unless I am miscalculating something

Sorry, I should more precisely say "1% chance that it is statistical variance." Almost every individual result is unlikely, actually.

 

[alexti]

Sorry, I should more precisely say "1% chance that it is statistical variance." Almost every individual result is unlikely, actually.

That makes sense. And it brings us back to the point that there's 99% probability that OP's guess that there's something to it correct.

Strange thing is that if this was a stable patterns everyone would see it too. I am curious how Paradox seeds their RNGs. Perhaps the used something derived from the system characteristics and, for whatever reason, on OP's system it goes wrong leading to seeding with zero (or some other bad value) and that consequently leading to a poor distribution.

 

[Alienatu]

good thing you don't play poker. there are some deviations from the expected runnouts that last tens of thousand of hands played. even hundred thousands at the extreme (this equals a few months of play). but that's pretty normal.
you d need waaay more than a 100 siege tick sample to check the chances. don't dwell over it.

 

[iquabakaner]

That makes sense. And it brings us back to the point that there's 99% probability that OP's guess that there's something to it correct.

Strange thing is that if this was a stable patterns everyone would see it too. I am curious how Paradox seeds their RNGs. Perhaps the used something derived from the system characteristics and, for whatever reason, on OP's system it goes wrong leading to seeding with zero (or some other bad value) and that consequently leading to a poor distribution.

No, it just means that such an "unlucky" situation happens around once in a hundred times. How many sieges does an average player gets into? How many players are there in EU4? One in a hundred is not unlikely at all.

 

[tbhayward]

That makes sense. And it brings us back to the point that there's 99% probability that OP's guess that there's something to it correct.

Nah, it really doesn't. As the poster above me says it merely means that unlucky situation happens about 1/100th of the time. That's not unlikely at all. For a little context, if I wanted to publish a physics "discovery" in a peer reviewed journal, I would need 5 standard deviation statistics, or 99.9999426697% chance that what I was observing wasn't statistical anomaly.

 

[nOxr]

Nah, it really doesn't. As the poster above me says it merely means that unlucky situation happens about 1/100th of the time. That's not unlikely at all. For a little context, if I wanted to publish a physics "discovery" in a peer reviewed journal, I would need 5 standard deviation statistics, or 99.9999426697% chance that what I was observing wasn't statistical anomaly.

Interesting. If you would translate that to the context of the first post, from 100 dice rolls how many would have to be 1's before you would conclude that something is wrong? I think it would be good to have as a future reference when threads like this pop up.

 

[tbhayward]

Interesting. If you would translate that to the context of the first post, from 100 dice rolls how many would have to be 1's before you would conclude that something is wrong? I think it would be good to have as a future reference when threads like this pop up.

5 = (x - 100/14)/sqrt(x)
x = 37.9.

Which isn't to say if you got 18 that it isn't worth a few minutes of extra sieging to check further!

 

[pikaemperor]

I suggest presenting either substantial statistics, official confirmation, or retraction.

Oh when you play as a nation that has fort defense stacked and pushed your enemies WE through the roof and yet they get from -56% to 7% in a instant such with no cannons no siege general such that you have to lift siege (keep 1k there to keep the progress) that you had full cannon bonus more than three times in a row to kick them out and have to do such a thing for multiple forts in the same war, you no longer see it as confirmation bias. As Ethiopia when fighting Ottomans, it got to the point of me having to get call for peace as soon as I got more than threshold. Why had I not had 100%, well despite not having lost a single battle and in fact have wiped their army the forts just didn't fall so I started to get WE because of that.
Another case of AI turbo siegeing was when I trolled AI France ally by dowing England for Gascogne and calling them in, the siege of Labourd (which I was the leader) took much more time then the 2 sieges that France did and led. Those sieges were done by the same army in sequence, with no siege general or cannons. All sieges were unblockaded ports, I had cannons in my and started it before they started theirs. Look at how outrageous fast they were siegeing Normandy, 2 months of war and they had walls breached and it did not stop there but I forgot to screenshot those. And it was not one siege but 2 in sequence, if there were more forts they might have taken a third one with that one army before Labourd fell.

It happened so many times of the AI turbo siegeing that remembering when it does not happen is much easier.

 

[Lilje]

I took the liberty of running a few sieges. 200 dice rolls is far from enough but I grew tired and we can always crowdsource more data...

It quickly becomes apparent that paradox is biased towards 9s and heavily discriminating 13s. Jokes aside, believing the distribution is skewed to screw players is obviously confirmation bias. Most likely from meeting lucky AI nations who finish sieges much faster because of their bonus siege ability and fort defense (which in no way affects dice rolls).

 

[pikaemperor]

I took the liberty of running a few sieges. 200 dice rolls is far from enough but I grew tired and we can always crowdsource more data...

Did you get AI rolls sample too, if not could you try doing that. That is something that does matter too in determining if siege rolls are biased against the player.

It quickly becomes apparent that paradox is biased towards 9s and heavily discriminating 13s. Jokes aside, believing the distribution is skewed to screw players is obviously confirmation bias. Most likely from meeting lucky AI nations who finish sieges much faster because of their bonus siege ability and fort defense (which in no way affects dice rolls).

It's only 5% siege ability and 10% fort defense, that siege ability gets completely negated by max WE and the 10% fort defense is negligible compared to siegeing ~70% fort defense(copitic+ideas+PP+terrain). How the AI is able to siege so fast in multiple occasions without cheating when each of their ticks takes twice is nonsense (as in that the siege game being so random is broken). I guess it's fine for the AI to cheat siegeing faster as they are stupid enough to lift walls breached 14% for no reason, just wished for them to admit that it's happening.
On another note there are a bunch of people that disagree on stuff but provide no counter argument, guess just pressing a button is much easier.