Against all odds!

[cyric100]

Originally posted by Axxaer
Remember that mathematical probability is not the absolute probability of the possible chance of something happening given all known forces, but is rather a prediction based on current/prior knowledge, and will thus rarely equate to the absolute probability.

I think the major problem for me with this is the terminology. Mathematical probablility IS the absolute probablility, since probablility itself is a mathematical concept. What you are calling "mathematical probability" is better termed a statistical prediction or statistical probability if you must.

Statistics is an ugly child of mathematics. None of the cool kids want to play with it...

[wattro]

Originally posted by wattro
The coin analogy was used because it (generally) has only two results similar to combat in civ

Originally posted by uberloz
Coin flipping is not a 50/50 prospect.

Having a modern coin land on its edge is unlikely but still probable.

Note that I said generally, please make sure you are reading thoroughly and not jumping to conclusions. For the purpose of this game, you will only get one of two results.

Originally posted by Mergle
I think you've misunderstood what the game tells you using the 1.52 patch (thanks to DeepO). It tells you the overall chance of winning the whole combat, not one round. So if it says 80%, you will (on average) lose 1 in 5 times. In any decent war, that will happen several times.

You're right

Originally posted by Mergle
You seem to be accusing the programmers of deliberately messing with the RNG - effectively, of making the odds screen lie to you. I really don't think that's happening. Firaxis has a long history of troubles with RNG (see the random map problem) but accusing them of deliberate skewing is I think unfounded.

I would be interested to hear a response from Firaxis from this...

Originally posted by uberloz
Is it possible that I experienced a 'statistically improbable game'?

I have no 'evidence' so feel free to dismiss this entire thread.

Entirely possible - not every sample reaches the mathematically probability of 50% heads, 50% tails (a coin might always end up heads if you flip it 10 times). This is more likely the smaller the sample size is. The larger the sample, the more the actual results should converge towards the mathematical probability.

Originally posted by Aeson
I have never taken a pack of cards and thrown them out of an airplane and then verified that they didn't re-order themselves. Does that mean it's statistically impossible that they will not re-order themselves?

No

Originally posted by cyric100
I think the major problem for me with this is the terminology. Mathematical probablility IS the absolute probablility,

AFAIK, absolute possibility is restricted to looking at the current coin flip. There is a 50% chance it will be heads and a 50% chance it will be tails (and 1^-10% it will be on its side). Mathematically probability is not restricted to this, I believe. I can say the mathematical probability of flipping a coin 1000 times and having it land heads up 500 times is 50%. It's pretty subtle and maybe I'm wrong about the distinguishment between absolute and mathematical.

[uberloz]

Originally posted by wattro
Note that I said generally, please make sure you are reading thoroughly and not jumping to conclusions. For the purpose of this game, you will only get one of two results.

Yes, I saw that you said generally, and you are right the odds would probably be 99.9999999999....% of the time that coin flipping would result in heads or tails.

As for the game only producing one of two results ( win or loss ) you seem to be forgetting flanking which produces neither result, so the 3rd result is still there.

[Bhruic]

Actually, no, "win or loss" does not equal "live or die". A unit with flanking still loses, it just doesn't die.

Of course, you could get really silly, and suggest that it's "win, lose or crash", where your computer could crash instead of giving an outcome. or "win, lose, crash or explosion", where your computer explodes before giving an outcome. And we could continue. As those options really are unlikely ones, we can assume you'll not likely have those ones happen.

Bh

[uberloz]

Originally posted by Bhruic
Actually, no, "win or loss" does not equal "live or die". A unit with flanking still loses, it just doesn't die.
Bh

I don't find that to be completey accurate.

If an artillery piece attacks an enemy in order to damage as many units as possible and flanks out before it's killed I would refer to that as a 'win'.

I frequently give my artillery pieces, 'flanking' promotions in order to accomplish that result as often as possible.

[Bhruic]

How you interpret it doesn't matter. All flanking does is prevent a unit from being killed when it loses. The fact that it did lose (and hence would have died, were it not for flanking) is the only relevant bit.

Bh

[Kataphraktoi]

I have never taken a pack of cards and thrown them out of an airplane and then verified that they didn't re-order themselves. Does that mean it's statistically impossible that they will not re-order themselves?

Thats one side of things. The first time you say,flipped a coin, you would have examplesize1 and 100% not heads(if tails). everytime you increase examplesize and its not heads, its still 100% that it wont happan. if you plotted that out after 1 billion reiterations, it would be looking like it couldnt,even though i have flipped coins that are tails. but, if you never had flipped a coin or seen a coin, how would you know that?

another example,say i have an ak-47(i do,infact) and(these numbers for example only) empty a clip into a target. 7\30 hit the first time,then second 13\30 and third 10\30 for a averaged 33.3% accuracy.if you tested it out enough, and at some interval forecasted the outcome and tested it to that interval and it came as expected, i would say you have some idea of its odds of hitting.

now, say you knew the exact air pressure,wind, position of hand, surface of coin, and landing surface and ammount of energy put into the coin and how you threw it.(perfect knowledge) would you not be able to say weather or not it would be heads or tails? you could calculate the exact spot, see how many times it will bounce,and know where and what it will be.there is no random elements. of course, we dont have that knowledge so it seems like random outcomes. its only random if you dont know whats going on...

now those cards would have to overcome all those sources of energy(being blown out of the plane, the air resistance, gravity, yadayada) and somehow just come together. isnt that a bit fantastic? what exactly is forcing them back together? all the physics i know indicate the universe likes taking things apart, not putting them together. there isnt anything that wants them back together. i cant think of a single force that is working towards the effect of flipping them together

i have never seen anything 'just happan'. the desk in front of me cant just 'poof' into existance because its component materiel started out in peices and would have forever gotten into smaller peices until the universe ends. temporary conditions like inside of sun or core of earth may change things with intense energy to higher states of existance but they expend huge sums of energy,and eventualy the whole universe will be 1 type of matter at the exact same tempature. it wont just 'flip' itself back together.

If i may ask, what are you basing your arguments on that it could happan? firm belief in magic or paper-statistics? i think statistics as means of 'odds' are pretty meaningless, myself. things either happan or they dont

clarification on my references to examplesize; i dont mean to say flipping a coin 50 times and heads results in always being heads. it just reflects the past chances. you can use that to try and decide what the odds are next time of getting it, which is the primary use of such statistics afaik

uh...yeah that was huge disclaimer: havnt spellchecked\proofread

[Kataphraktoi]

I would be perfectly willing to change my views on that, if someone can come up with some actual facts or reasons, not probability crap keep that stuff on the paper,where it belongs

[Bhruic]

Originally posted by Kataphraktoi

now those cards would have to overcome all those sources of energy(being blown out of the plane, the air resistance, gravity, yadayada) and somehow just come together. isnt that a bit fantastic? what exactly is forcing them back together? all the physics i know indicate the universe likes taking things apart, not putting them together. there isnt anything that wants them back together. i cant think of a single force that is working towards the effect of flipping them together

Posts like this just demonstrate a lack of understanding of the basic concepts. The universe does not "like" doing anything at all, as it's not a conscious entity. Is there anything that "wants" the cards back together? Nope. Is there anything that "wants" the cards apart? Nope.

The cards do not have to "overcome" any sources of energy, because the effects that various elements have (wind, gravity, etc) are all having their effect - period. Wind is not a force that attempts to blow cards apart. That is to say, the wind is not actively trying to affect the cards - it simply does so.

The only issue here is whether it is possible for the cards to come back together. Unless you've managed to prove a negative (which is as close to impossible as you are likely to come in this universe), you can't prove they can't. And since you can't prove they can't, that means it's possible they can.

If i may ask, what are you basing your arguments on that it could happan? firm belief in magic or paper-statistics? i think statistics as means of 'odds' are pretty meaningless, myself. things either happan or they dont

You're right. I mean, what's the point of trying to figure out the odds of winning a hand of blackjack? You either win or you don't. Trying to figure out the odds is pointless (hey, want to put $100 on a few hands of blackjack? You either "win" or "don't", and I'll use those "meaningless" odds).

Bh

[wattro]

wow

Originally posted by Kataphraktoi Thats one side of things. The first time you say,flipped a coin, you would have examplesize1 and 100% not heads(if tails).

Sample size, not example size. I refuse to believe that you know what you are talking about if continually make a mistake like that (sorry).

Originally posted by Kataphraktoi
everytime you increase examplesize and its not heads, its still 100% that it wont happan. if you plotted that out after 1 billion reiterations, it would be looking like it couldnt,even though i have flipped coins that are tails. but, if you never had flipped a coin or seen a coin, how would you know that?

You have seen a coin, you know it has two sides. You are talking about something completely different. I guess you are correct if you don't know the number of outcomes and they all have a somewhat balanced chanced of occuring - but that is far from this discussion - we are talking about a unit winning or losing a battle.

Originally posted by Kataphraktoi
another example,say i have an ak-47(i do,infact)

You trying to scare someone? lol

Originally posted by Kataphraktoi
and(these numbers for example only) empty a clip into a target. 7\30 hit the first time,then second 13\30 and third 10\30 for a averaged 33.3% accuracy.if you tested it out enough, and at some interval forecasted the outcome and tested it to that interval and it came as expected, i would say you have some idea of its odds of hitting.

That 33.3% accuracy depends a lot more on having 30 bullets and hitting 30 times over 3 samples (90 bullets). We all know the odds of hitting depend on your accuracy and what you are shooting at - how far is it, what speed/direction is it moving, wind resistance, quality of gun, etc

Originally posted by Kataphraktoi
now, say you knew the exact air pressure,wind, position of hand, surface of coin, and landing surface and ammount of energy put into the coin and how you threw it.(perfect knowledge) would you not be able to say weather or not it would be heads or tails? you could calculate the exact spot, see how many times it will bounce,and know where and what it will be.there is no random elements. of course, we dont have that knowledge so it seems like random outcomes. its only random if you dont know whats going on...

If you knew the relationship between all the factors that dictate which way a coin will land, then yes, you can calculate 100%, without a shadow of a doubt, exactly what the coin flip outcome will be.

Originally posted by Kataphraktoi
now those cards would have to overcome all those sources of energy(being blown out of the plane, the air resistance, gravity, yadayada) and somehow just come together. isnt that a bit fantastic?

Yes, it is a bit fantastic and I would argue extremely fantastic, but not entirely fantastic. Read that carefully... Anything buy entirely fantastic means there is a slim chance of actuality.

Originally posted by Kataphraktoi
what exactly is forcing them back together? all the physics i know indicate the universe likes taking things apart, not putting them together. there isnt anything that wants them back together. i cant think of a single force that is working towards the effect of flipping them together

The same things that draw them apart, the same things you mentioned: wind force/air resistance/gravity/etc. Just that the chances of this happening are infinitesimal. There is no magical force putting them back together.

Originally posted by Kataphraktoi
i have never seen anything 'just happan'. the desk in front of me cant just 'poof' into existance because its component materiel started out in peices and would have forever gotten into smaller peices until the universe ends. temporary conditions like inside of sun or core of earth may change things with intense energy to higher states of existance but they expend huge sums of energy,and eventualy the whole universe will be 1 type of matter at the exact same tempature. it wont just 'flip' itself back together.

If i may ask, what are you basing your arguments on that it could happan? firm belief in magic or paper-statistics? i think statistics as means of 'odds' are pretty meaningless, myself. things either happan or they dont

Paper-statistics. The same factors that would force a deck of cards to not re-order themselves are the same factors that would force a deck of cards to re-order themselves. I agree that things usually happen or they don't. I'm not a big 'what-if' person, but at the same time, I am not ignorant of facts or possibility. As they say, luck favors the prepared.

Originally posted by Kataphraktoi
clarification on my references to examplesize; i dont mean to say flipping a coin 50 times and heads results in always being heads. it just reflects the past chances. you can use that to try and decide what the odds are next time of getting it, which is the primary use of such statistics afaik

uh...yeah that was huge disclaimer: havnt spellchecked\proofread

That's exactly what you said. You stated that if you flip a coin once, and it lands heads that you should always expect (probability) that it will be heads. Probability does not reflect past chances, probability reflects future chances. But that's just it - it is a chance.

[Xerxes712]

The universe does not "like" doing anything at all, as it's not a conscious entity. Is there anything that "wants" the cards back together? Nope. Is there anything that "wants" the cards apart? Nope.

If the end result that created humans is via the linear probability mutations; We have a conscious, thus the Universe (which is us in its basic essence) is self aware of itself and thus contradicts the first premise.

Quantum mechanics: Does not the experimentor's act of examination of the experiment (pertaining to statistics in this case) will affect the outcome?

The Universe with a conscious is embodied within your Quantum Mechanic's Theory. We are proof. I think therfore I am.

And this begs the Ultimate question...what we are...do we have a purpose...why are you here and now and in your particular body...and you have self consciouness.

If we are just a product of evolution and chance, we are the universe, and we have a consciousness which does effect the world.

Has thoust Man become God?

[Kataphraktoi]

Sample size, not example size. I refuse to believe that you know what you are talking about if continually make a mistake like that (sorry).

i mentioned un-edited,no? i do mean sample size.

but that is far from this discussion - we are talking about a unit winning or losing a battle.

and i thought we were talking about a deck of cards...whoops.

Posts like this just demonstrate a lack of understanding of the basic concepts. The universe does not "like" doing anything at all, as it's not a conscious entity. Is there anything that "wants" the cards back together? Nope. Is there anything that "wants" the cards apart? Nope.

By like, i mean the events that are favoured to happan, such as a rock 'liking' to fall. excuse my bad english.

My main point is: All factors that i know of involved in this are heading towards the cards being spread out, not falling back together.

[Mujadaddy]

Excuse me for a second...uh... I like the new "Odds generator" but I was ok with the old Strength vs. Strength numbers...

Originally posted by Xerxes712

If the end result that created humans is via the linear probability mutations; We have a conscious, thus the Universe (which is us in its basic essence) is self aware of itself and thus contradicts the first premise.

Ok, we have a failure to communicate on this one. My instinct is to reply, "tautology,' but I can't be sure if you mean what I think you mean here.

Quantum mechanics: Does not the experimentor's act of examination of the experiment (pertaining to statistics in this case) will affect the outcome?

Not exactly... quantum mechanics says that, at a certain point, the act of observation of certain physical phenomena introduces energy into the system to be observed and therefore disrupts the resultant measuring. Nothing metaphysical about that---just like counting roaches with a flashlight...

The Universe with a conscious is embodied within your Quantum Mechanic's Theory. We are proof. I think therfore I am.

"Fuzzy Logic" embodied in the structure of the universe does not alone prove the Universe has a conscious component. 6 Billion organisms who define a concept in their own culture do not impose this concept upon the universe -- they develop their theories to fit the observable facts.

And this begs the Ultimate question...what we are...do we have a purpose...why are you here and now and in your particular body...and you have self consciouness.

If you say so I'm just here to talk about Civ in the OffTopic and OffTopic in the Civ forums.

If we are just a product of evolution and chance, we are the universe, and we have a consciousness which does effect the world.

This effect wouldn't be, by any strange coincidence, measurable, repeatable, and self-consistent, would it? You're not talking about praying for your football team to win, are you?

Has thoust Man become God?

Was it ever not so?

[wattro]

Originally posted by Kataphraktoi
i mentioned un-edited,no? i do mean sample size.

Right you are, my mistake.

Originally posted by Kataphraktoi
and i thought we were talking about a deck of cards...whoops.

No, that is a byproduct of the discussion of the odds that an AI unit could consistently win an improbable combat. The deck of cards is an analogy that was introduced help understand how probability factored into the the discussion.

Originally posted by Kataphraktoi
My main point is: All factors that i know of involved in this are heading towards the cards being spread out, not falling back together.

Thank you for proving my point. Though you might not see it, I'll try to explain. You said it yourself - '...heading towards...' ABSOLUTELY -- they are HEADING TOWARDS spreading out because it is extremely probably that they WILL spread out, but it is not guaranteed. Heading towards spreading out is not the same as spreading out.

There are factors at play which might determine that not all cards are at all times spreading out from each other. In fact, I almost guarantee that at some points, some cards will cross X, Y, and/or Z planes located at each of the other cards.

Perhaps two of the fifty-two cards are blown out of the plane and separated - each card now will follow a different path to the earth, flipping, spinning and falling independendtly. What if, for just one moment, those two card's (which were originally in sequence) paths meet during the descent so that the cards are in fact resequenced. Extremely unlikely, but entirely plausible.


I don't know what the other two crackpots are going on about...

[Bhruic]

The problem with numbers is that the human mind doesn't comprehend them well. For example, let's assume that you have a 99% chance of winning a particular combat. Almost everyone reading this forum would likely do that combat, fully expecting to win.

But if there are 100 people reading this forum, then there is a 63.4% chance (roughly) that someone is going to lose that battle. If there are 1000 people reading this forum, then there is a 99.996% chance that someone is going to lose that battle. And yet, all things being equal, we still would all expect that we would win.

The problem is, of course, that the 999 people who won the battle don't come to the forum to complain about winning it, but the 1 person who loses does.

Bh