Instance dungeon

2008-06-03T05:54:53Z

85.164.207.5:

{{Unreferenced|date= May 2007}}
In [[MMORPG]]s, an '''instance dungeon''' is a special area, typically a [[dungeon (games)|dungeon]], that generates a new copy, or instance, of the dungeon map for each group that enters the area. This saves server work and ensures that there will never be competition ([[kill stealing]], [[spawn camping]]) over resources such as [[mob (computer gaming)|mobs]] within the instance and that [[player character]]s experience minimum [[lag]].

This also preserves the gaming experience, since some gaming scenarios do not work if the player is continually surrounded by other players, as in a multiplayer setting. Instance dungeons may contain stronger than usual mobs and rare, sought-after equipment. They also may include level restrictions and/or restrict the number of players allowed in each instance to balance gameplay.

Instances were first proposed by [[Richard Garriott]] in the late 1990's as a way to solve a set of related problems which had become obvious in [[Ultima Online]]. The problem is simple to state: everyone wants to be "A Hero" and slay "The Monster", rescue "The Princess" and obtain "The Magic Sword". When there are 2,000 and more players all playing the same game, clearly not everyone can be a hero. The problem of everyone wanting to kill the same monster and gain the best treasure was terribly obvious in the game [[EverQuest]]. The creation of instances largely solves this set of problems. There are few examples of boss camping and kill stealing in [[World of Warcraft]] - because a copy of the dungeon (instance) is always created on demand for you or your party.

Games that have been known to use instancing include:
*''[[Age of Conan]]''
*''[[Anarchy Online]]''
*''[[City of Heroes]]''/''[[City of Villains]]''
*''[[Dark Age of Camelot]]''
*''[[Dungeons & Dragons Online: Stormreach]]''
*''[[Dungeon Runners]]''
*''[[Runescape]]''
*''[[EverQuest]]'' (Instances added with the Lost Dungeons of Norrath expansion)
*''[[EverQuest 2]]''
*''[[Final Fantasy XI]]'' (instances added with the Treasures of Aht Urghan expansion)
*''[[Granado Espada]]''
*''[[Guild Wars]]''
*''[[Myst Online: Uru Live]]''
*''[[The Realm Online]]''
*''[[World of Warcraft]]''
*''[[Star Wars Galaxies]]''
*''[[The Lord of the Rings Online: Shadows of Angmar]]''
*''[[Tabula Rasa (computer game)|Tabula Rasa]]''
*''[[Auto Assault]]''
*''[[Phantasy Star Online]]''

One game known for not using instance dungeons is ''[[EVE Online]]''. Because of the vast amount of space available in the EVE universe, missions for players are created in real space, which any other player could in theory travel to. This allows multiple players to perform the same mission at the same time (in the same manner as an instanced dungeon) but also allows other players to view or participate in the mission, if they discover the location, or if invited to assist by the player who was initially given the mission.

[[Guild Wars]] takes almost the opposite approach, with every combat area in the game being instanced; the game world is strictly divided into Town / Outpost areas (Where you can meet other players) and Explorable / Mission areas, which are all instanced. Even Town / Outpost areas are themselves created on demand, with a new "district" of that town being created for every 100 players in it; players can move between these at will. This system provides the advantages for players of being able to play with players across the globe, as in EVE, along with the advantages in load scaling and resources of a traditional multiple server model for [[ArenaNet|the developers]].

''[[Vanguard: Saga of Heroes]]'' is another game that does not use instance dungeons. However, it is envisioned that, through the Advanced Encounter System (AES), certain "boss" NPCs can be triggered when a group enters an area; this NPC would then be "tagged" to that group, meaning no other players could attack or interact with it. AES was not implemented in the commercial release of ''V:SoH'', but Sigil programmers are reportedly working on it and are planning to release it in a future patch.

In [[RuneScape]], instances are used mostly in quests, so that other players cannot interfere with the player who is doing the quest, such as battling boss [[Non-player character|NPC]]'s or having to accomplish a special task. They are also used in certain 'minigames'.

Several games use instancing to scale the [[mob (computer gaming)|mobs]] to the players' levels, and/or the number of players present.

[[Category:Video game gameplay]]
[[Category:Massively multiplayer online role-playing games]]
[[Category:Competitive video gaming]]

[[cs:Instance (MMORPG)]]
[[de:Instanz (Computerspiel)]]
[[fr:Donjon instancié]]
[[fi:Instanssi (World of Warcraft)]]
[[zh:副本 (魔獸世界)]]

Introduction to Statistics

2006-04-20T11:51:38Z

85.164.251.17: /* Experiments, Outcomes and Events */

{{nav3|Wikiversity|Wikiversity:School of Mathematics|School of Mathematics:Statistics}}

== Preamble ==
Statistics is permeated by probability. An understanding of basic probability is critical for the understanding of the basic mathematical underpining of statistics.

Most statistical procedures use probability to make a statement about the relationship between the independent variables and the dependent variables. Typically, the question one attempts to answer using statistics is that there is a relationship between two variables. To demonstrate that there is a relationship the experimenter must show that when one variable changes the second variable changes and that the amount of change is more than would be likely from mere chance alone.

There are two ways to figure the probability of an event. The first is to do a mathematical calculation to determine how oftern the event can happen. The second is to observe how often the event happens by counting the number of times the event could happen and also counting the number of times the event actually does happen.

The use of a mathematical calculation is when a person can say that the chance of the event rolling a one on a six sided die is one in six. The probability is figured by figuring the number of ways the event can happen and divide that number by the total number of possible outcomes. Another example is in a well shuffled deck of cards, what is the probability of the event of drawing a three. The answer is four in fifty two since there are four cards numbered three and there are a total of fifty two cards in a deck. The chance of the event of drawing a card in the suite of diamonds is thirteen in fifty two (there are thirteen cards of each of the four suites). The chance the event of drawing the three of diamonds is one in fifty two.

Sometimes, the size of the total event space, the number of different possible events, is not known. In that case, you will need to observe the event system and count the number of times the event actually happens versus the number of times it could happen but doesn't.

For instance, a warranty for a coffee maker is a probability statement. The manufacturer calculates that probablity that the coffee maker will stop working before the warranty period ends is low. The way such a warranty is calculated involves testing the coffee maker to calculate how long the typical coffee maker continues to function. Then the manufacturer uses this calculation to specify a warranty period for the device. The actual calculation of the coffee maker's life span is made by testing coffee makers and the parts that make up a coffee maker and then using probability to calculate the warranty period.

== Experiments, Outcomes and Events ==

The easiest way to think of probability is in terms of experiments and their potential outcomes. Many examples can be drawn from everyday experience: On the drive home from work, you can encounter a flat tire, or have an uneventful drive; the outcome of an election can include either a win by candidate A, B, or C, or a runoff.

'''Definition:''' The entire collection of possible outcomes from an experiment is termed the ''sample space'', indicated as '''<math>\Omega</math>'''

The simplest (albeit uninteresting) example would be an experiment with only one possible outcome, say <math>A</math>. If we remember our set theory from elementary school, we can express the sample space as follows:

<math>\Omega = \{ A \} </math>

A more interesting example is the result of rolling a six sided dice. The sample space for this experiment is:

<math>\Omega = \{ 1,2,3,4,5,6 \}</math>

We may be interested in ''events'' in an experiment.

'''Definition:''' An ''event'' is some subset of outcomes from the ''sample space''

In the dice example, events of interest might include 
a) the outcome is an even number 
b) the outcome is less than three 

These events can be expressed in terms of the possible outcomes from the experiment: 
a) : <math> \{2,4,6\} </math> b) : <math> \{ 1,2 \}</math>

We can borrow definitions from set theory to express events in terms of outcomes. Here is a refresher of some terminology, and some new terms that will be important later: 
<math> \cup </math> represents the Union of two events 
[[Image:[http://en.wikipedia.org/wiki/Image:Venn_A_union_B.png]]] 
<math> \cap </math> represents the Intersection of two events 
[[Image:[http://en.wikipedia.org/wiki/Image:Venn_A_intersect_B.png]]] 
<math>\{\cdots\}^{c}</math> represents the complement of an event. For instance, "the outcome is an even number" is the complement of "the outcome is an odd number" in the dice example. 
<math> A \backslash B </math> represents ''difference'', that is, <math>A</math> ''but not'' <math>B</math>. For example, we may be interested in the event of drawing the queen of spades from a deck of cards. This can be expressed as the event of drawing a queen, but not drawing a queen of hearts, diamonds or clubs. 
<math>\varnothing</math> or <math>\{\}</math> represent an ''impossible event'' 
<math>\Omega</math> represents a ''certain event'' 
<math>A</math> and <math>B</math> are called ''disjoint events'' if <math>A\cap B = \varnothing</math>

== Probability ==
Now that we know what events are, we should think a bit about a way to express the likelihood of an event occuring. The classical definition of probability comes from the following. If we can perform our experiment over and over in a way that is repeatable, we can count the number of times that the experiment gives rise to event <math>A</math>. We also keep track of the number of times that we perform the same experiment. If we repeat the experiment a large enough number of times, we can express the probability of event <math>A</math> as follows: 
<math>P(A) = \frac{N_{A}}{N} </math> 
where <math>N_{A}</math> is the number of times event <math>A</math> occurred, and <math>N</math> is the number of times the experiment was repeated. As <math>N</math> approaches infinity, the fraction above approaches the true probability of the event <math>A</math>. The value of <math>P(A)</math> is clearly between 0 and 1. If our event is the ''certain event'' <math>\Omega</math>, then for each time we perform the experiment, the event <math>\Omega</math> is observed; <math>N_{\Omega} = N</math> and <math>P(\Omega)=1</math>. If our event is the ''impossible event'' <math>\varnothing</math>, we know <math>N_{\varnothing}=0</math> and <math> P(\varnothing) = 0</math>.

If <math>A</math> and <math>B</math> are ''disjoint events'', then whenever event <math>A</math> is observed, then it is impossible for event <math>B</math> to be observed simultaneously. Then 
<math>N(A\cup B) = N(A) + N(B)</math> 
Given our definition of probability, we can arrive at the following: 
<math>P(A\cup B) = P(A) + P(B)</math> 

At this point it's worth remembering that all events are not disjoint events. I was originally confused by events and outcomes, and this was the source of many misunderstandings. For events that are not disjoint, we end up with the following probability definition. 
<math> P(A\cup B) = P(A) + P(B) - P(A\cap B)</math> 
How can we see this from example? Well, let's consider drawing from a deck of cards. I'll define two ''events'': "drawing a Queen", and "drawing a Spade". We can tell off the bat that these are not disjoint events, because you can draw a queen that is also a spade. There are four queens in the deck, so if we perform the experiment of drawing a card, putting it back in the deck and shuffling (what statisticians refer to as ''sampling with replacement'', we will end up with a probability of <math>\frac{1}{13}</math> for a queen draw. By the same argument, we obtain a probability for drawing a spade as <math>\frac{1}{4}</math>. The expression <math>P(A\cup B)</math> here can be translated as "the chance of drawing a queen or a spade". If we assume naively (as I used to) that for this case <math>P(A\cup B) = P(A) + P(B)</math>, we can simply add our probabilities together for "the chance of drawing a queen or a spade" as <math>\frac{1}{13}+\frac{1}{4}</math>. If we were to gather some data experimentally, we would find that our results would differ from the prediction -- the probability observed would be slightly less than <math>\frac{1}{13}+\frac{1}{4}</math>. Why? Because we're counting the queen of spades twice in our expression, once as a spade, and again as a queen. We need to count it only once, as it can only be drawn with probability of <math>\frac{1}{52}</math>. [[Still confused?]] 

'''Proof:''' If <math>A</math> and <math>B</math> are not disjoint, we have to avoid the double counting problem by exactly specifying their union. 
<math>A \cup B = A \cup (B \backslash A) </math> so 
<math>P(A \cup B) = P(A \cup (B \backslash A)) </math> 
<math>A</math> and <math>B \backslash A</math> are disjoint sets. We can then use the definition of disjoint events from above to express our desired result: 
<math>P(A \cup B) = P(A) + P(B \backslash A)</math> 
We also know that 
<math>P(B \backslash A) = P(B) - P(B\cap A)</math> 
so 
<math> P(A \cup B) = P(A) + P(B) - P(B\cap A)</math> 
Whew! Our first proof. I hope that wasn't too [[dry]].

== Conditional Probability ==
Many events are conditional on the occurance of other events. Sometimes this coupling is weak. One event may become more or less probable depending on our knowledge that another event has occured. For instance, the probability that your friends and relatives will call asking for money is likely to be higher if you win the lottery. In my case, I don't think this probability would change.

Let's get formal for a second and remember our original definition of probability. 
<math>P(A) = \frac{N_{A}}{N}</math>
Consider an additional event <math>B</math>, and a situation where we are only interested in the probability of the occurance of <math>A</math> when <math>B</math> occurs. A way at this probability is to perform a set of experiments (''trials'') and only record our results when the event <math>B</math> occurs. In other words 
<math> \frac{N_{A\cap B}}{N_{B}} </math> 
We can divide through on top and bottom by <math>N</math> the total number of trials to get <math>P(A\cap B)/P(B)</math>. We define this as ''''conditional probability'''': 
<math>P(A|B) = \frac{P(A\cap B)}{P(B)}</math> 
which when spoken, takes the sound "probability of <math>A</math> given <math>B</math>."

[[/A Totally Confusing Problem that Shows how Difficult it is to Conquer Intuition/]]

=== Bayes' Law ===

An important theorem in statistics is '''Bayes' Law''', which states that 
<math> P(B|A) = \frac{P(A|B)P(A)}{P(B)}</math>, 
It is easy to prove. We start with identical expressions for <math>P(A\cap B)</math>. 
We know that: <math> P(A\cap B) = P(B\cap A) </math>, 
<math> P(A\cap B) = \frac{P(A|B)}{P(B)}</math>, and 
<math> P(B\cap A) = \frac{P(B|A)}{P(A)}</math>. 
Since <math> P(A\cap B) = P(B\cap A) </math>, 
<math>\frac{P(A|B)}{P(B)} = \frac{P(B|A)}{P(A)}</math>. 
A Simple rearrangement of above line gives us '''Bayes' Law'''.

== Independence ==

Two events <math>A</math> and <math>B</math> are called ''independent'' if the occurence of one has absolutely no effect on the probability of the occurence of the other. Mathematically, this is expressed as: 
<math>P(A\cap B) = P(A)P(B)</math>. 

== Random Variables ==

It's usually possible to represent the outcome of experiments in terms of integers or real numbers. For instance, in the case of conducting a poll, it becomes a little cumbersome to present the outcomes of each individual respondant. Let's say we poll ten people for their voting preferences (Republican - R, or Democrat - D) in two different electorial districts. Our results might look like this: 
<math>\{RRRDRRDRRR\}</math> and <math>\{DDDDDRDDDD\}</math> 
But we're probably only interested in the overall breakdown in voting preference for each district. If we assign an integer value to each outcome, say 0 for Democrat and 1 for Republican, we can obtain a concise summary of voting preference by district simply by adding the results together.

== Discrete and Continuous Random Variables ==
There are two important subclasses of random variables: discrete random variable (DRV) and continuous random variable (CRV).
Discrete random variables take only countably many values. It means that we can list the set of all posible values that a discrete random variable can takes, or in other words, the number of posible values in the set that the variable can take is finite. If the posible values that a DRV X can take are a0,a1,a2,...an, the probability that X takes each is p0=P(X=a0), p1=P(X=a1), p2=P(X=a2),...pn=P(X=an). All these probabilites are greater than or equal zero.

For continuous random variables, we cannot list all posible values that a continuous variable can take because the number of values it can take is extremely large. It means that there is no use to calculate the probability of each value seperately because the probability that the variable takes a particular value is extremely small and can be considered zero P(X=x)=0).

== Distribution Functions ==

== Expectation Values ==

[[Category:School of Mathematics]]

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Instance dungeon

Introduction to Statistics