Against all odds!

[Axxaer]

Originally posted by wattro
Since it is inevitable that 1 result out of an infinite # of samples will produce the desired outcome, we can guarantee a non-zero chance of each flip also creating the desired outcome (a re-ordered deck of cards)

Sorry, but if you're going to take this track, then I'll have to point out that as the theoretical concept of infinity is, well, infinite, and thus has no numerical value, any number divided by infinity will result in a zero probability because a sample space cannot (to human knowledge of the concepts of infinity and sample spaces) ever be infinite, and as Kataphraktoi rightly pointed out, any outcome which has a factor of 0 outcomes will also have a 0 probability of being a future outcome. 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. (E.g. Take a regular perfectly symmetrical coin. You currently have an absolute probability of 0.5 of landing on either side, but a mathematical probability of 0 of landing on either side. Flip it once. You still have the same absolute probability but now have a 1.0 mathematical probability of landing on one side and a 0.0 mathematical probability of landing on the 'flipside'. Each time you flip it, absolute probability says it is just as likely to land on either side, although mathematical probability tends to say one will be more likely than the other based on the gathered sample space. As the sample space grows, it is absolutely and mathematically probable that the mathematical probability will converge towards the absolute probability, although based on pure mathematical probability from the current sample space, this is generally not the predicted outcome. (I wonder why Douglas Adams didn't include that explanation in the Hitchhiker's Guide's explanation of why the universe's population is zero )

So to you people who disagreed with Kataphraktoi's (mathematically) correct statement that:

Originally posted by Kataphraktoi
...statistics represent what has already happaned and are attempting to forecast what will happan. Until it has happaned once, chances are 0%. Everytime you flip em out of the plane,its another +1 to your example size.

[The keeper]

Trying to get back on topic here a bit -----



Combat odds do not take into account first strikes. In a recent game of mine, I had a cat upgraded to drill 4. I had many many first strikes each time it engaged in a battle. On a couple of occasions, this cat took out opposing units without getting hit. Units being fortified pikemen, and knights. Even though I was able to overwhelmingly win these battles, the odds were still tilted in the favor of the ai when it gave the stats for the battle.


That is a possibility for the anomalies.


Also, I dont know this to be true, but I think that units are given a random roll, and they keep it through the turn. In my present game, the ai had a maceman that defeated 3 knights in one turn, while taking very little damage. I didn't have any more units in the area, so the next turn, I sent another knight in, and whipped him easily.

So it is possible that if a unit gets a good roll, it will continue with that good roll for the rest of the turn. So it looks like a long streak of really unlucky rolls, when in reality, it is just one unlucky roll used more than once.

[DeepO]

Originally posted by The keeper

Combat odds do not take into account first strikes.

Combat odds do take into account fs. It was one of the main points these new ods had to solve: first strikes don't change the ratio of strengths, so nobody had a good idea what first strikes did. Now, all you need to do is read the odds.

*****ing if you lost against a 99% odd is optional.

DeepO

[Diadem]

Originally posted by Kataphraktoi

No they cant. statistics represent what has already happaned and are attempting to forecast what will happan. Until it has happaned once, chances are 0%. Everytime you flip em out of the plane,its another +1 to your example size.

You made that up on the spot, didn't you? It's hilarious, I give you that. But it's nonsense as well.

Whoops, except the facts indicate it didnt happan. It hasnt been replicated, and many pro-evolutionary facts are completely made up. Including radiocarbon dating, which has been proven to give highly erronous readings. In fact, thats why ''scientists'' use it-it tells em what they want to hear. Not my kind of religion, thanks. i prefer facts over faith-based systems

You prefer facts over faith-based system. That's wise. However, I have to point out that evolution is a fact.

Your counter-arguments are pretty funny. It hasn't been replicated. Doh. Did you expect scientists to conjure a new planet out of thin air to replicate evolution? It has been observed though, and those observations have been replicated.

You seem to have misunderstood the meaning of the term 'made up'. Scientific facts are not 'made up'. Your post about statistics is. So is your argument against radiocarbon dating. There's a difference, you know.

[Diadem]

Originally posted by Axxaer

Sorry, but if you're going to take this track, then I'll have to point out that as the theoretical concept of infinity is, well, infinite, and thus has no numerical value, any number divided by infinity will result in a zero probability because a sample space cannot (to human knowledge of the concepts of infinity and sample spaces) ever be infinite

In mathematics, having an infinite sample space is no problem. Infinity is, mathematicly, a rigorously defined concept, and using it in calculations is not a problem at all. Of course, a physical sample space can never be infinite. But that just means that you can not test predicted probabilities of outcomes of a certain test to a perfect accuracy. That's nothing new. Perfect accuracy, does not exist it physics, and it never will.

, and as Kataphraktoi rightly pointed out, any outcome which has a factor of 0 outcomes will also have a 0 probability of being a future outcome.

Tell that to Dauphin, who is now homeless because of Kataphraktoi's theory

You are basicly saying that something that hasn't happened before can never happen. So before 1969, going to the moon was absolute impossible, and the NASA mission was, according to you, complete suicide. And since I've never had a car accident, I'll be perfectly save doing 200 mph on a sidewalk.

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.

Predictions are always based on current / prior knowledge. If you don't know anything about a problem, you can't predict possible outcomes. It's impossible to test probabilities, as we already established (remember, physical infinite sample spaces do not exist), so you always need mathematics to calculate them. In fact the concept of 'probability' does not make sense outside mathematics.

The distinction between 'absolute' and 'mathematical' probability you are making, sounds nonsensical to me. If there is a distinction between 'physical' and 'mathematical' probability, it is that the latter deals with idealized situations. If you flip a perfect coin, the probability of getting heads is exactly 0.5. But if you flip a real coin, it is not. A coin is never perfectly symmetrical. And also, there is a small chance of the coin landing on its side (this actually happened to me once).

You could call that a difference between 'mathematical' and 'physical' probability. However the difference lies not in your theory of probability, but rather in your experiment.

E.g. Take a regular perfectly symmetrical coin. You currently have an absolute probability of 0.5 of landing on either side, but a mathematical probability of 0 of landing on either side. Flip it once. You still have the same absolute probability but now have a 1.0 mathematical probability of landing on one side and a 0.0 mathematical probability of landing on the 'flipside'. Each time you flip it, absolute probability says it is just as likely to land on either side, although mathematical probability tends to say one will be more likely than the other based on the gathered sample space.

Allow me to give you some advice: Don't talk about things you don't have a clue about, okay? You are making a fool of yourself...

[Kataphraktoi]

Your counter-arguments are pretty funny. It hasn't been replicated. Doh. Did you expect scientists to conjure a new planet out of thin air to replicate evolution? It has been observed though, and those observations have been replicated.

We are going to be warned for OTing here evolution is real, however, the kind of evolution i refer to cannot provide a starting point for life-only its continuation. selective breeding among nature and animals ''adapting'' to their enviroment are good examples of evolution in progress today. However,the fact is,those genes already existed and are simply more prevalent, due to the animals without the needed genes dying. so the different birds depicted in Darwin's origin(thats your bible isnt it? if not, say so ) with different sized beaks depending on what nuts they have available, and its not a magical transformation at all.

You are basicly saying that something that hasn't happened before can never happen. So before 1969, going to the moon was absolute impossible, and the NASA mission was, according to you, complete suicide. And since I've never had a car accident, I'll be perfectly save doing 200 mph on a sidewalk.

How are you going to know that though? going to the moon is impossible, and driving 200 mph is ok, until you know its not actually safe or going to the moon. of course, anyone could do some calculations on being able to control that car or fly to the moon, and decide without trying it is not,in fact,safe or the moontrip is infact possible. the same laws you use to determine this could also show that a deck of cards or a pile of goo cant come together as thats not how things work.

all matter is trying to get to a state of no energy\most base form, and the only way to make cars,cities,etc, is for humans to take large amounts of energy and force things together. only sentient beings can actually start anything. so saying a car could just somehow poof into existance, would be crazy talk. but a organism 10000 times as complex is rational and factbased? theres no 1 in 10000000 chance it could happan. it just cant and wont happan. fact is, we cant observe these things being created today, because all the creating got done with a long time ago.

Allow me to give you some advice: Don't talk about things you don't have a clue about, okay? You are making a fool of yourself...

Discarding arguments with petty insults. you must be getting desperate

[Dauphin]

Originally posted by Axxaer
So to you people who disagreed with Kataphraktoi's (mathematically) correct statement that:

It can be considered correct depending on your stance and the specific meanings that you wish to apply to terms - fair enough if you want to get into a detailed, and I would say philosophical, debate about the definition of probablity. However, I found that the basic assertion stated above so grossly misrepresented itself that it rapidly lead to absurd conclusions, and for that I had to remonstrate.

[DeepO]

You guys are something... in all the years I studied statistics, I never came across such colorful definitions of statistics... these are great!

Clearly there is some terminology problem here, in that everyone is talking about different things. So let me add more confusion to the stack:

Statistics is a purely mathematical concept, without any physical meaning. Which means "physical statistics" can't exist. Now you can have al kinds of nice little theories on how to derive one from the other, but it simply won't work. Monte Carlo simulations to calculate probabilities is not 100% correct, nor are hypothesis tests or other 'prediction' methods... on the mathemical side of things, you will always have e.g. a 99% of being correct.

But that 99%... what does it really mean? No matter how small or large it is, it will forever stay a mathematical concept, with no true physical meaning. You can improve on your theory (Newtonian --> quantum physics, for instance), which means you can make the mathematical 'error' smaller. That doesn't mean you get more 'physical certainty', as you don't know the connection between the physical and mathematical errors.

Of course, this doesn't correspond with intuition. If my unit has a 99.1% of winning, I expect it to win the battle more easily than a unit which has a 1% chance of winning. I can never prove it, though, as it would require a mathematical (=statistical) description of the physical concept of luck. And that description doesn't exist for single occurences. At least not without making mathematical assumptions.

So, you can't proof anything in the physical world using statistics, and discussions like the cards falling from the airplane can always be debated with both sides having a good point and no clear winner.

This doesn't mean that statistics applied to physical things doesn't have its purpose, only that you have to be careful when drawing conclusions. In CIV speak, you can plan battles using the combat odds calculator, as long as you are willing to 'take a risk', or accept that sometimes, the outcome is not like you predicted. I found that to be working better than just go in blindly, and have faith that I'll be lucky enough to win against all (statistical, so useless) odds.

DeepO

[Dauphin]

Lies! Damn lies!

[/obligatory old joke]

[Blake]

all matter is trying to get to a state of no energy\most base form, and the only way to make cars,cities,etc, is for humans to take large amounts of energy and force things together. only sentient beings can actually start anything.

You seem to be assuming that evolution is/was a process that didn't "use" energy, it was powered by the sun.

[Mujadaddy]

Originally posted by Kataphraktoi all matter is trying to get to a state of no energy\most base form, and the only way to make cars,cities,etc, is for humans to take large amounts of energy and force things together. only sentient beings can actually start anything. so saying a car could just somehow poof into existance, would be crazy talk. but a organism 10000 times as complex is rational and factbased? theres no 1 in 10000000 chance it could happan. it just cant and wont happan. fact is, we cant observe these things being created today, because all the creating got done with a long time ago.

People who pick organisms as the "ooooo complicated" feature of nature crack me up completely.

You betray a complete ignorance of microbiology, organic chemistry and physics.

I'm not telling you what to believe; I'm telling you that you're ignoring facts.

[Enigma_Nova]

I go with the idea that if evolution didn't happen, then we wouldn't be around to talk about the probability of evolution happening, so therefore the condition that we are talking about evolution makes the probability of evolution happening equal to one.


P.S. When I reformatted my hard-drive, I lost the dancing lock. Please pretend I have attached it, in celebration of this thread being off topic.

[Axxaer]

Originally posted by Enigma_Nova
P.S. When I reformatted my hard-drive, I lost the dancing lock. Please pretend I have attached it, in celebration of this thread being off topic.

[Aro]

Yep. I just love it.

[Mujadaddy]

So, yeah, combat odds... those are great