An Indepth Decision Making Guide

[Sharpeyex]

Today I saw someone alching at GE. A slightly lower levelled player went and asked what he's alching.

 

"I make 1gp profit each alch."

"How?"

"By making my own nats."

 

Seeing this fundamental mistake of disregarding time, I feel that it is essential to get the idea of decision making across the players, in which the overall efficiency of activities can be improved without additional effort.

 

This guide is divided up to three parts. Part one will explain the foundations of what this guide will be based on, Part two will explain the fundamentals of decision making, and finally part three will explain some applications of this guide so that you know where this is heading to. If you are not particularly interested in decision making and efficiency guides, please only read Part One, as further readings may cause extreme boredom and even slight brain hemorrhage if emotions get a chance to take over rationality.

 

Hopefully by the end of reading this guide, you will not only become much more efficient in playing RS, and also make better decisions for the remainder of your life.

 

Part One: Foundations

 

1. A Short Introduction

2. Opportunity Cost

3. Utility Theory

 

Part Two: Fundamentals of Decision Making

 

4. Basics of Game Theory

5. Behavioural Economics (Under Construction)

6. Descriptive and Mathematical Statistics (Coming Soon...)

 

Part Three: Applications (Also Coming soon...)

 

7. Analysis of recent debates

8. Case Studies

 

Credits and Closing Words (Will be done after the completion of this guide)

9. Credits and Closing words

 

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Part One: Foundations

 

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1. A short introduction

[hide=]So, let's start with a question: "What is the most valuable thing on RS?"

 

Some of you may say it's gold pieces, while others may refer to expensive items or experience in a skill. While they may be true on the first sight, consider that all of the above could only be obtained by using your own time. Yes, TIME. Time is the most valuable thing on RS.

 

"For one hour you are making nats, but for the same amount of time you can go kill some green drags, and you will have money to buy that much nats while having a lot of left overs."

 

When making decisions, it is essential to consider all alternatives that could possibly provide better returns for the same time invested in. The concept of having time as base of measurement in RS could include every single action that is to be considered in decision making. Having gold as base of measurement would not take into account of experience gained and psychological satisfaction of socialising around. A game's objective after all, is to entertain the player.

 

Therefore in this guide, time will be used as a base of measurement of Opportunity Cost, which will be discussed later on.

 

Then following Opportunity Cost, this guide will take you further into the theory of Utility to discover the true reasons behind every rational choices of an individual.

 

Further on, this guide will talk about decision making against other players, known as Game Theory, which would assist you in making decisions at the times of competitive play.

 

Finally, for those that are interested, some behavioural factors will be discussed at the near-end of this guide.

 

I hope that you take time and learn those things carefully, as the concepts here can be applied not only to RS, but most likely, to our everyday lives.[/hide]

 

2. Opportunity Cost

[hide=]Opportunity Cost is the fundamental concept of decision making. If you have 1k gold, you can spend it on either Construction OR Prayer, but not the same amount to both. When you have only 1 hour of play time, you can choose a mixture of either to train or to pvp, and they will add up to 1 hour, but no more.

What this means is that if you choose to do something, you must give up is something else you might want to do. Specifically, you give up the best alternative option you can choose.

 

This cost of not choosing the best alternative option is called Opportunity Cost.

 

If I can make 300k per hour at green dragons, then should I stand around GE and talk to random people for 1 hour? To answer this question, apply the concept of opportunity cost. If you talk around for 1 hour, then your cost of talking is the best alternative you must give up, which in this case, is 300k gold. So, talking around at GE for 1 hour will cost you 300k gold.

 

And also, if I can also choose to make 200k per hour with WC, should I go cutting wood? If you consider this without taking into the account of experience gained from WC or combat, then the cost of going WC and gaining 200k for one hour is the cost of 300k-200k=100k. So if you choose to WC, you will lose 100k gold per hour.

 

When considering what to buy with your 10m gold or what to do with your 3 hours of free time, make sure that you consider every single alternative, in comparason to opportunity cost. This way, it will make sure that you will always choose the most efficient or psychologically satisfying action that you can do, given a limited amount of time. Or gold, if you want to think that way.[/hide]

 

3. Utility Theory

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In economics, Utility is a measure of the relative satisfaction from, or desirability of, consumption of various goods and services. In the context of RS, Utility is simply a term measuring how satisfied or how entertained you are from doing something.

 

Let's start with an example. Considering all other factors constant, if you can wc for 150k/hr and RC for 50k/hr, which one would you choose?

 

First of all, consider all net returns an action can provide you with.

 

Gains from 1 hour of WC: 150k + 40k WC exp

Gains from 1 hour of RC: 50k + 20k RC exp

 

To make the decision, consider which combination of exp and gold would be more satisfying to you. If the WC package is more satisfying than the RC package, then it would be better to choose to do some woodcutting, and vice versa.

 

In other words, a rational person will perform whichever activity that is more satisfying.

 

Mathematically, that is:

Let Gold be g, experience gained from WC be x, Experience gained from RC = y,

 

Choose WC if and only if:

u(150000g + 40000x) > u(50000g + 20000y)

 

Choose RC if and only if:

u(150000g + 40000x) < u(50000g + 20000y)

 

Indifferent if and only if:

u(150000g + 40000x) = u(50000g + 20000y)

 

Where u stands for the utility that you will get from the actions done in the brackets.

 

Utility can depend on a lot of things. Some people value RS more than WC so their utility of RC might be higher, while others value gold a lot more than exp so their utility of having gold is higher. Therefore, the correct choice will vary from player to player.

 

3.1 Practical example: training range from lvl 95 to 99, to red chin or not to red chin

 

[hide]First consider all alternatives and all possible payoffs

 

Red chin from 95 to 99: approx 4.3m exp. For the purpose of this case study, the following assumptions apply:

That you red chin undead monkeys at Ape Atoll dungeon;

That you can gain 350k exp per hour.

That you use 1500 red chins per hour

That your full inventory load of prayer pots (total of 20) can last you one trip

That it takes you a total of 1 hour to prepare all of the trips (including the bank access and the walk)

 

Total amount of time needed: 4.3m / 350k = 12.28 hours,

Total amount of trips: 12.28/1.5 = 8.18 trips

 

Total Amount of prayer pots needed: 8.18 x 20 = 163.6 (approx 164)

Total amount of red chins needed: 12.28 * 1500 = 18420

Total Cost: 808 x 18420 + 11900 x 164 + 12.28h + 1h = 14883360 + 1951600 + 13.28h = 16834960(approx 16.8m) + 13.28 hours

Now the cost of training from 95 to 99 traditionally: bronze knives + yaks

Assumptions:

That it you gain 60k exp per hour

That it takes around 15 minutes to prepare and get to destination

That you use up around 500 projectiles per hour

 

Total amount of time needed: 4.3m / 60k = 71.67 (approx 72 hours)

Total amount of projectiles needed: 71.67 x 500 = 35835

 

Total Cost = 35835 x 14 + 72 hours = 501690 + 72 hours

 

Now the analysis: Red Chin cost 16.8m + 13.28 hours, while yaks cost 0.5m + 72 hours.

So they are: (Let hours be h)

u(-16834960 - 13.28h)

and

u(-501690 - 72h)

 

Solve for h to see how much each hour should worth in coins

u(-16834960 - 13.28h) = u(-501690 - 72h)

Assume that your utility for every coin and every hour on both side are equvalent for the purpose of this analysis

-16834960 - 13.28h = -501690 - 72h

16834960 + 13.28h = 501690 + 72h

16834960 - 501690 = 72h - 13.28h

16333270 = 58.72h

h = 278155 (approx 278k)

 

So back to our question, should you red chin to 99 range?

The answer is, according to the above data, If you can make more than 278155 per hour then yes you should, otherwise no, stick with the yaks.

 

The above data and the assumptions can change whenever needed to fit a better model for yourself. I hope that this example illustrated how best make decisions through mathematical means.

 

Please remember to change the values in this model to the most up-to-date price information if you are going to use it for your own analysis.

 

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Part Two: Fundamentals of Decision Making

 

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4. Game Theory

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Here's a definition from the internet of Game Theory: "A branch of applied mathematics that studies strategic situations in which individuals or organisations choose various actions in an attempt to maximize their returns"

 

In this thread we will only be talking about the basic aspects of Game Theory, the maths shouldn't get difficult.

 

The previous part of this guide explained the basic calculations on opportunity cost. Game Theory, in plain English, can be understood as the competition between opportunity costs of different individuals.

 

4.1 Pure Strategy Nash Equilibrium

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This part of the guide will begin with the concept of "Dominant Strategy" and "Dominated Strategy"

 

For example, we all know that there are two black dragon spots inside the member's dungeon. It usually gets crowded very easily, so people started to bring air strikes to 1 click the dragons in order to "get ahead" of other players in the timing. An easy explaination of game theory here is that the opponent is using air strike; you can either use it or not use it. If you use it, consider everything else as constant, then you both have an even chance of getting it. If you do not bring air strike, your chance of getting the black dragon is almost none.

 

Your Opportunity of bringing is 1/2 chance to get a dragon, not bringing is close to 0% chance of getting a dragon.

 

Your competitor's opportunity cost is the same. But now, there's a problem. Extra air and mind runes will annoy you, and you prefer not to bring it if it's not necessary. Then, there's another problem, you don't know if your opponent will bring air strike or not. So how to analyse this situation?

 

First of all, let us define the outcomes.

 

If you bring air strike, and your opponent does not bring air strike: you get 100% dragons, and your opponent get 0%, and vice versa.

If you both do not bring air strike, or if you both do bring air strikes, both of you have 50% chance of getting the dragon.

 

The meaning of this description is very simple. If you choose to bring air strike, two outcomes will occur. If your opponent does not bring air strike you get 100%; if your opponent does bring air strike, you get 50%. Alternatively, if you do not bring air strike, and your opponent also does not bring, it's 50%, otherwise 0%. So if you bring air strike, you will beat the action of not bringing air strike, because 100% is better than 50%, and 50% is better than 0%.

 

In this case, choosing to bring air strikes is better than not bringing air strikes in all situations. Thus, the best method, regardless of what your opponent does, is to bring air strikes. This "best move" is called Dominant Strategy; and choosing not to bring air strike is the worst of all situations, which is called Dominated Strategy. Therefore, to best gain utility for yourself, one should use dominant strategy, if it's available.

 

If you have been following this guide closely, you might have guessed that it's possible to predict outcomes based on given information about the utility of both players in the strategic situation. The following of this guide will explain what is known as Pure Stragegy Nash Equilibrium.

 

Based on the above information, we all know that it's best to bring air strikes to black dragons. Your opponents ofcourse, if rational, will always bring air strikes with them too, because they will be well aware of this above analysis. Therefore, since both you and your opponent will always choose to bring air strikes, the best you can do under a competitive situation is to get 50% of the dragons.

 

Therefore, based on the assumption that everyone is clever and thinks before doing, the predicted outcome will be that both of you to bring air strikes, and both of you gain a dragon with even probability. I see people rage over this too many times, so for those with anger control problems, there's no need to be angry when you are not getting a dragon, the process itself could be stochastic in nature, which means that it's normal for you to get a dragon, and it's also normal if you don't get one.

 

Anyway, the predicted outcome is known as the Pure Strategy Nash Equilibrium, where a Nash Equilibrium is a state where every player's action is optimal given every other player's action, and that both player's decision will form a steady state where there are no incentives for the predicted outcome to move anywhere else.

 

If you are still following this guide well, then please read on, as it contains a very important aspect, if not the most important, about game theory in general.

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4.2 Mixed Strategy Nash Equilibrium

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Sometimes, you will end up in situations where no pure strategy Nash Equilibrium exists. For example, you may play a game of rock,paper and scissors with a friend, and as well all know, one strategy will beat another and it's a never-ending loop. If you list out the possibilities and analyse them, you will find that there is no single best strategy in the set.

 

Instead, we will use the idea that one may randomly choose a strategy according to a distribution of probabilities. This is known as the Mixed Strategy Nash Equilibrium, where for every possible strategy of a player, there is a certain probability which will bring the best results, similar to that of a pure strategy Nash Equilibrium. Since RS itself is highly stochastic, the methods that involve Mixed Strategy may well be much better off for analysis of this kind. J

Again, we will start by a case study. Suppose that you are playing a game of Castle Wars. You are chasing down a flag bearer who have just entered the dungeon in the middle of the map. When you have entered the dungeon a few seconds later, the flag bearer has disappeared off your minimap. You now have two choices: Going to your castle, or go the opponent's castle.

 

If you both go to the same place, you will win because you will be able to catch the flag bearer and re-gain the flag; if you split up the flag bearer will win because he/she will be able to hold the flag for much longer. This is precisely a situation where no single direction is the best strategy, and we will have to analyse it stochastically.

 

First, we can say that if both of you choose your castle (Y for short) and your opponent's castle (O for short), you will be happy for killing the flag bearer, and gain a utility of 1. If you both go to different directions (Y, O or O, Y), you will be dissatisfied for not catching the flag bearer, and will yield a negative utility of -1. The Same applies for the flag bearer, where getting caught will yield a utility of -1, and getting away will grant a utility of 1.

 

To find the best mixed strategy, we will need some help from mathematics.

 

Let U1 be your utility, and U2 be your opponent's utility.

Let P1 be your probability of choosing direction Y, and P2 be the probability of your opponent choosing the direction Y.

Let (1 - P1) be the probability of you choosing direction O (probability add to 1, so the left overs from choosing Y is O), and let (1 - P2) be the probability of your opponent choosing direction O.

 

The probability of you both moving to the same direction is P1 x P2 for your side, and (1 - P1) x (1 - P2) for the opponent's side;

The probability of you both moving to different directions is P1 x (1 - P2) for your side, and (1 - P1) x P2 for the opponent's side.

 

Therefore, the total utility of you moving to Y is as follows: (When P1 becomes 1 where you are already moving to Y as a certainty)

 

U1 = (1 x P1 x P2) + (-1 x P1 x (1 - P2) )

 

Substitute P1 = 1 and simplify:

 

U1 = (1 x 1 x P2) + (-1 x 1 x (1 - P2) )

U1 = 2P2 - 1

 

And symmetrically for moving off to O:

 

U1 = (1 x (1 - P1) x (1 - P2) ) + (-1 x (1 - P1) x P2)

 

Substitute P1 = 0 and simplify:

 

U1 = (1 x 1 x (1 - P2) ) + (-1 x 1 x P2)

U1 = 1 - 2P2

 

Now, if the probability of your opponent run to the direction Y is greater than probability of O, it means that

 

P2 > 1 - P2

2P2 > 1

P2 > 0.5

 

which when substituted into the previous equations, you will have a higher chance to move to direction Y, because

 

2P2 - 1 > 1 - 2P2

 

Therefore you will always choose to go to the direction Y, yielding higher utility, which mean a decrease in your opponent's utility.

 

Vice versa, if your opponent tend to run to direction O with a higher chance, you will best off running to O all the time, which ends up beating your opponent more often than not.

 

Thus, I argue that if both players are rational, the best way to run is to randomly select a direction, both with even probability such that you will end up maximising your probability to win, which is also 50%. Any other combination of probability which are not evenly distributed will cause you to win less than 50% of the time, which implies that if you run with this set of probability allocation, the best your opponent can do is to beat you 50% of the time. This allocation is an example of Mixed Strategy Nash Equilibrium.

 

By changing variables and adding further players, this model will be fit to provide guidance in other similar strategic situations, such as whether or not should you hop world if a resource spot is taken, and whether or not should you switch armor, eat and use prayer in a pvp battle.

 

It's a hard topic, but the fruits are very rewarding should you gain the insight of this fundamental idea of game theory. This idea provides the foundation of what modern businesses use to maximise their profits.

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5. Behavioural and Psychological Sides of the story

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All that explained, here's some interesting facts from recent psychological research. The branch of Psychological economics is mainly concerned with how people will react, under the theory of utility, with psychological factors being taken into consideration.

 

Reference-Dependent Decision Making

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This entire sub-topic is based on a simple idea. This is that all human perceptions, such as feeling, taste, touch and etc, are all significantly affected by the current state of the individual. More precisely, the "current state" of the individual is known as Reference Points. When people make their decisions and judgements, what they think and see are based on such points. It is like a frame of reference in physics, where the speed of everything is relative to what you compare at.

 

For example, vast majority of us will not be able to live without electricty. However, historically people have lived without electricty for a length of time beyond human feelings can express. This is because we are used to the comfort that electricty brings to us, and it feels painful suddenly having to stop using it; back a few hundreds of years ago, people do not know how much comfort electricty can bring, so that they can live happily without it.

 

We will be discussing four main areas under this topic.

 

1. Loss Aversion

 

Consider the following situation. Take the most expensive item you have, regardless it being a godsword or a whip, or maybe a dragon med helm for the unfortunate few. Imagine that now, an offer is being made to you. The offer is that you have a 60% chance to gain another one of the identical item, but there is also 40% chance that you will lose yours permanently. Will you choose to accept the offer?

 

Statistically, accepting the offer is the correct option, as it will give you a positive expected return. However, majority will not choose to accept the offer. The most expensive item is most likely the most valued item by the player, which are most likely being held by the player for a long time. The player have become "used to", or attached to, the item existing on the account, and although a second one is even better, the demise of the first set will ultimately be unacceptable, regardless the smaller probability of it occuring.

 

Summarised in one sentence, going lower than one's reference point is more painful than receiving the same or slightly more benefit of taking the risk. It is why in the real world insurance premiums would work, because people rather pay what can sometimes be triple of their expected loss just to be certain that they will not lose whatever they may value greatly.

 

2. Endowment Effect

 

Now let us venture to the G.E. and investigate a very obvious fact which people tend to ignore. Suppose that you see someone with an item that you do not have. Ask yourself this question: If the trade limit does not exist, then how much are you willing to pay to buy it off the person? Now imagine that you already have the item for yourself, then how much are you willing to accept if someone offers to buy it?

 

Endowment Effect basically states that once a person is "endowed", that is, given, something, his/her valuation of it will increase. This is why people rush to buy newly released items, such as the armadyl armor set, and refuse to sell them when they know that the price is obviously going down and will not come back up.

 

This is actually an extension on the topic Loss Aversion, which focused on the singular fact of owners valuing their items higher than buyers.

 

3. Diminishing Senstivity

 

Once again, let us open with a question. Which one of the following is more painful? Sudden market shift causing you to lose 10mil gold, or slow market change that cause you to lose 1m gold per day over a period of 10 days?

 

Or a more easier question, which one is more painful, getting killed in 1 hit by a dragonfire, or being ripped apart in the darkness of a cave without light source over the period of a minute?

 

For both questions, the latter optoin is obviously more painful than the initial option. When losses become quite great, it is easy to become numb at it, which means further loss are not feeling as bad as the initial loss. Almost all of us have played Castle Wars before. We try not to die for the first death, but after the first death, we can die as many time as we want, without feeling any difference than not dying at all. In terms of decision making, know that the first move of all things are the most difficult; after you start, it becomes so easy as you no longer care about, well deaths, in our example.

 

4. Non-linear Probability Weighting

 

Imagine that Jagex has just released an attachment made to your favourite weapon, the godsword, giving it a 1% chance to cause an extra immediate hit. Now consider the following two situations. First, Jagex have decided that 1% is not enough, and have increased it to 2%. The second case is that the game already have a godsword attachment that give you 50% chance to cause an extra immediate hit, but Jagex decided to increase it to 51%. In both situations, the increase is 1%, but which one is more important to you, as a hardcore meleer, 0% to 1% or 50% to 51%?

 

Statistically, the increase in damage are equal. Both give you on average a 1% increase of your damage. However, needless to say, there will be more people raging on the forums about going from 1% to 2% than 50% to 51%. In fact, I personally suspect that no one will even care about the increase from 50% to 51%, but a whole bunch of discussion will appear about the 1% to 2%.

 

This is precisely the first characteristic of non-linear probability weighting: Overweighting of small probabilities. It happens a lot in the real world, such as people afraid of being on the airplane as it may crash. It happens even more in runescape, as when people blindly make complaints about something that they don't even have the right idea about, the biggest one being all the complaints about different weapons being over/underpowered. This discussion will continue at later stages of this guide.

 

The second characteristic of non-linear probability weighting: Certianty Effect. Consider the previous godsword case. Which one will worth more to you, an increase of the effect from 50% to 75%, or 75% to 100%?

 

If I am to answer it for you, it would be the second option to boost it to 100%, which is also known as being certain of the occurance. Of course, my answer is statistically meaningless, as both options weight excatly same in terms of expected value and probability. This occurs because people value something that is "certain to happen" more than something that happens with a certain chance, despite ideantical derived mathematical results.

 

This as well, happens very often in both worlds we are familiar with. In the real world, this contributes to why people would pay more to buy certainty with insurance companies, whereas in RS it is why people value Dark Bow more than other weapons, which can be seen in ranging/pvp guides that the authors are clearly in favour of choosing Dark Bow over other weapons for their intended purposes.

 

There are other theories out there about this topic; the four listed here is merely an entry point for further discussions which involve complex mathematical analysis that becomes less necessary for our purposes here. Feel free to have a go at it, as they are freely available on the internet.

 

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Part Three: Applications (Coming Soon!)

 

 

 

 

To be continued... soon...

Edited February 12, 2010 by Sharpeyex

[Youmu]

That's a nice start to a guide. I always choose the best things that I want to do so that I can get the best out of Runescape.

 

Good luck to your guide completion! :thumbsup:

[Returnofmic]

Looks extremely promising.

 

I will certainly keep an eye on this topic (:

[Sentry_Wolf]

Very good and interesting guide, keep it up. :)

[Draconic]

Error-

 

. . . If you can make more than 278155k per hour. . .

 

:wink:

[Ambler]

not bad a guide, and I have an addition:

 

Is it worth completeing the summer quests to access the corporeal beast? The quests take about 2-3 hours to complete (not including getting the levels!) then you have access to the corporeal beast! here is my theory:

if you kill the corp in a coinshare trip, where you avrage lets say (for the sake of this) 20 kill an hour kills an hour (we will call this X ), and the chance of a sigil drop is Y so it takes Y divided by X hours to get a Sigil drop. (correct me if im wrong) and the profit made by this is Z, but can you earn Z coins in the time it takes to complete the quest and recive the drops?

 

You can use this if you like!

[Shangdi]

Very promising. I shall keep track of this.

 

Should help me get some things done better.

 

 

And wow, turns out I could save money by chinning even at my meager income level. :-o

[Grimy_Bunyip]

I'm always a huge supporter of efficiency guides

 

but mind if i ask a quick question. Utility is just a coefficient you multiply to the time and costs depending on how much you like it? or am i misinterpreting this?

[0p3r4tor]

I dont like to go too much into the details like this, though it does give a helpful insight into the decisions we make.

[AlexRose]

The main point of this thread? Time is quite litterally money, and can therefore be converted from two seemingly irrevelant skills or time-comsuming efforts and measure the true profits of each.

[kdtaereo]

Great work out here my friend. But don't forget this is a game, i prefer something fun than something rewarding. So many people think only on their RS account and forget about their real life, i don't recommend this.

 

:thumbsup:

[yuyu13]

Great work out here my friend. But don't forget this is a game, i prefer something fun than something rewarding. So many people think only on their RS account and forget about their real life, i don't recommend this.

 

:thumbsup:

whome?

[santa_hat_man]

Very nice guide, ill be waiting for an update.

 

A few errors that I found:

-An extra "is" in the first paragraph of "Opprotunity Cost".

 

-You put RS instead of RC in "Utility Theory" second last paragraph.

 

Unless you meant to put them there, in that case ingnore me. Lol.

[All_Is_Great]

The whole thing makes sense, except for the fact that games are meant to be fun, not to do everything in the most efficient way or you lose. So keep that in mind.

[Bladewing]

^ Fun has utility value, too.

[Sharpeyex]

Thanks for the replies guys, sorry I've been away for a while. I will continue to work on this guide from now on, and hopefully to see it done in the next week or so.

 

To Sonic3190, returnofmic, Sentry_Wolf, Davidyang200, and Op3r4tor: Thanks for your interest in this guide! I will definitely write more of this sort in the future.

 

To kdtaereo, allisgreat, and bladewing: Thanks for your support, and yes you are right, fun does have utility value too, which is why most of examples here use the unit of measure with utility, rather than money itself.

 

To Draconic and Santa_hat_man: Points taken, corrections made. Thanks for pointing it out!

 

To Morionic: You are on the right track. Utility itself is the amount of satisfaction you receive. You must give up things to gain utility, or satisfaction, which is most commonly time and its derivatives such as money and etc.

 

To AlxeRose: Quite right! your response very well covers what opportunity cost basically is. Nice one =)