Review: Dragon Age (Origins)

This is the first time I played a party RPG. And it was awesome.

You arrive at Lothering

It took me a while to get into the interface. When it started (I chose a human mage) the movement controls (ADSW) felt awkward - different from other first person games, even though the scene was drawn at first person. It didn't take long though to get used to it. But before even I got used to it, the story had already began. I met the mouse and the bear in the Fade. Was already curious to see how (and if) I will escape Fade (which is sort of the dreamworld in the game, also where spirits reside) to pass the test posed to me. I think there is something in the storytelling which makes you get addicted to it from the start. I encountered the Fade demon and defeated him - was surprised by who he was and how I could defeat him without using any offensive abilities. Immediately I got hooked.

Though started out smoothly (where in the first encounter you don't even have to fight to win), the fighting in the game paces up surprisingly fast. I soon found out that the game is not like taking a walk in the park - at times, the combat needs to be carefully planned making full use of the "pause and strategise" feature.

Meanwhile the story continued on. There are some rather surprising turns that happened in the first part of the game, and after that you get a kind of free roaming ability - i.e. you can choose which area (and hence quest) to cover next. When you have covered all the primary quests, you then get to continue the main storyline to the end of the game. It takes a hell lot of time to reach that stage, and it never gets boring. That's because all the primary quests are crafted with lots of details, characters, locations, environments - and a very long story unique to them. Each one of them seems like a game on its own. I am pretty sure, looking at the vast variety and spectacular difference in all angles between the primary quests, that BioWare had different teams working on separate primary quests.

Despite the length of the game, it never feels dull. There are a lot of satisfying turns and twists to keep you fully engaged in the story. And in the course of the game you will meet some very memorable characters. Some of them will join your cause and fight with you - depending on your actions. Most of the companions also have their own side quest. You will need to unlock the side quests through the course of the game - mostly by gaining their appreciation towards you by giving them gifts, or doing things that they respect.

The game also has multiple endings depending on what you choose. Perhaps because my character died at the end of the game saving the world, it was a rather emotionally charged ending for my story. And after it ends, there is a treat - which took me by surprise. It has a slide show which details the impact of your actions on Ferelden for years to come. Since most of these are tied to specific choices you made over the course of the entire game, it is quite a feast.

The "Landsmeet"

The game offers many addons, of which two add new capabilities (along with small a quest each) which you can spend your money on. One is Warden's Keep, which adds a tash for storing your equipments - otherwise you will have to sell your stuff to make space for new items, as you cannot carry unlimited amount of them. The second is The Stone Prisoner, which unlocks the most unique companion - a golem called Shale. He is very well integrated in the rest of the game's stotyline - so once you unlock him, you will never feel that he is a companion that comes from an addon.

Let me pause here and mention something, rather an alert if you have not played the game yet so that you don't miss out on content. [Spoiler Alert] There is a character called Leliana in the game. I was aware of this since the game advertises an add on campaign called "Leliana's Song", though I wasn't sure exactly at which point she would join the game. After a lot of the story passed, I became suspicious and one day read more on her. And to my dismay I found that she is supposed to join in a scene that is only triggered if you visit a particular pub in Lothering, a village which gets obliterated early in the game. And once it is gone, there is no way to get her there in your group (unless you'd like to download dev-tools and use a crude hack to modify your save file, which I didn't want to do). So if you play the game, visit all houses in Lothering till you find Leliana, before Lothering becomes inaccessible!

Pros -
+ Engaging story
+ Your actions can change the course of the missions
+ Challenging fight system
+ Lot's of spells and abilities, but smooth learning curve
+ Very long game which never became dull
+ Companion characters are good, you are bound to take liking to some of them

Cons -
- Graphics is solid and nice, but not spectacular
- Sometimes certain important items are not clearly marked, which can cause you to miss certain experiences, as serious as a companion in your quest. It may be impossible to fix later on if you don't want to start from a previous save, which may not be a great option considering the length of the game.
- Party stash needs to be unlocked by buying Warden's Keep, this should have been a native feature in the game

Overall, this is an excellent single player game - definitely one of the best that I have played. You are bound to have hours of fun playing it - in fact I will be surprised if you don't loose couple of day's sleep due to this game. Excellent and recommended.

All about "Information Value"

In statistical data mining, sometimes we need to determine out of a set of variables which ones are best in capturing a desired behavior. For example, let's say you have a pool of customers for your credit card company, and you want to determine who out of them are about to default (i.e. refuse to pay up after possibly making a huge expense). You need to then identify which of the attributes you have on the customer can potentially identify and alert you of such behavior. One of the popular ways in which this is done by analysts is by looking at something called 'Information Value'. In the context of data mining is also sometimes referred to by the short form - InfoVal.

Definition
Information Value of \(x\) for measuring \(y\) is a number that attempts to quantify the predictive power of \(x\) in capturing \(y\). Let's assume the target variable \(y\) which we are interested in being able to measure, is a 0-1 variable (or an indicator). Let's also further assume that it is the number of accounts who will go bad in the immediate future. Let's now divide our population in 10 equal parts after sorting the entire pool by \(x\), and create the deciles. Now we are all set to define Information Value -
$$IV_x = \sum_{i=1}^{10}{\left(bad_i-good_i\right)\ln\frac{bad_i}{good_i}}$$
Here,
\(i\) runs from 1 to 10 deciles in which we have divided the data,
\(bad_i\) is the proportion of bad accounts captured in \(i\)th decile out of all bad accounts in the population,
\(good_i\) similarly is proportion of good (i.e. not bad) accounts in \(i\)th decile.

Note that the variable whose effectiveness you want to measure is getting used since it is the variable by which the entire data is sorted and divided into deciles.

How does it work?
But why does it work? You can check that if \(x\) has no information on \(y\) at all, then the \(IV\) turns will trun out to be zero. That's because when you sort by \(x\) and create deciles, the deciles are as good as random with respect to \(y\). Hence, each decile should capture 10% of total bads and 10% of total goods. So \(bad_i-good_i=0\) and \(\ln\frac{bad_i}{good_i}=0\). So the \(IV\) turns out to be zero.

On the other hand if after sorting by \(x\) some decile has higher or lower concentration of bad's than good's, then that would mean that that particular decile is different from the overall population, and \(x\) lets us create it. The decile will contribute a positive value to the summation which defines \(IV\) in the equation above. So it is clear that for a good \(x\) variable, there will be more of such deciles where the proportion of goods and bads differ - and by a larger margin as your \(x\) is more effective in capturing \(y\) - hence \(IV\) indeed gives a measure of predictive power of \(x\).

Issues
However, there is something artificial in the definition of \(IV\) above - it is the functional form. Indeed there can be many different ways to create the functional form that is being summed up.

To give some examples - \(\sum_{i=1}^{10}{\left(bad_i-good_i\right)^2}\), \(\sum_{i=1}^{10}{\left|bad_i-good_i\right|\frac{n_i}{n}}\), etc. all should be equally good candidates.

The last one in particular is interesting - because it has the proportion in the equation, making it a consistent measure. That is, if you decide to divide the data into 20 parts or 30 parts and so on, you will go closer and closer to a limit. Incidentally, the limit to which it converges is essentially gini/2 under some assumptions. For \(IV\) on the other hand, this leads to a problem - you cannot divide the data indefinitely - as you may hit segments which have no good (or no bad) accounts at all - in which case taking the \(ln\) will bomb.

Also for the same reason, it will be inaccurate and unfair to compare two variables when one of them has ties - which makes it impossible to unambiguously divide the population into 10 equal parts. (This is cautionary since it is a mistake that I have seen many analysts make, even when drawing Lorenz curves for example where the inequality of deciles can and should always be taken into account. For IV, to stress, it however cannot be taken into account.)

Origin
If \(IV\) has these problems, how did the definition come about in the first place? Also should you use it?

I can only guess how such a metric came into being, and became popular over that despite having drawbacks. The concept of information actually arises in several other branches of mathematics, eg. Information Theory where you measure a very interesting quantity called entropy (which vaguely resembles \(IV\)), and Fisher's Information of a variable (which deals with how much information a statistic contains about a particular parameter of a distribution). I think someone was aware of these concepts, and wanted to create something similar for the corporate world to measure "information captured in a variable". In the corporate world how things work in most places, is that you show something works, and it becomes de-facto unless someone else challenges it and shows something else works better. Somehow the challenges are rare to come by in most places, which is why at senior leadership there needs to be a conscious effort into engaging the employees into thinking rather than following tradition. For \(IV\), this was pretty much the case. We have already seen that it works, and after it was shown to work it became a standard - without proper math/statistical backing to explore pros and cons and to see if it can be bettered. And once something becomes a standard, it gains inertia and becomes legacy - which propels it through 'common wisdom'. The employees of that particular organization learned about it (they learned the formula, understood what it tries to measure, learned the SAS codes or SQL queries required to compute it). When they migrated, the knowledge migrated with them.

Recommendation
The only reason you might want to use \(IV\) is because of legacy - you may have worked on a bank which used it, and may have developed some reference points (i.e. thumb rules like "if \(IV\) is more than \(abc\) then the variable is good, otherwise it is bad") of good or bad \(IV\) values.Even if you have used \(IV\) before, it should not take a very long time to develop experience on reference points for gini - you will be able to do that through a course of one or two projects. I will in general though recommend not to use IV, in favor of other more intuitive measures - roc, gini, KS to name some. I personally prefer gini - it is easy to understand, is consistent, and is very robust in measuring power of a variable.

To conclude, though \(IV\) is still popular in some places of the banking world, I would recommend not using it in favor of gini/ROC which measures the same thing while being more intuitive and without the flaws of \(IV\).

How real are you?

Are we real? Of course we are. How much real are we, say when compared to characters of a story, movie, or a video game? You might think that's an odd question - reality is reality, fiction is fiction! It may be so, but let's pause and think for a moment.

What differentiates reality and fiction? We can imagine a huge moon overlooking shores of an urban city surrounded by water - but that won't be real. Or will it? For an event to be real, you need real humans (supposing it involves humans) who have a mind governed by psychology - who think, feel reason like we do. We need real environment, made of billions of atoms so that the repercussion of every action is calculated with the greatest scrutiny. Merely outlining the large scale effects of an event (as is done in a fiction) is not enough to make it real. In short we should have an Universe where all the laws of physics are followed just as in ours, and we should be in it.

Before we go further into it, I would like to propose a thought experiment. Let's take a living human brain, and let's scan the configuration of the brain as precisely as possible. Fear not - since due to recent advances in modern physiology, this can be done without harming the person at all. Let's say we scan every neuron and the state of it - in the sense which other neurons is it connected to, and where is it currently sending any electric impulse. Then in principle, one can sit down and using pen and paper simulate the brain - by writing down its current state and slowly evolving it following the right biological course of the neurons. Using more sophisticated science, infact one may be able to code questions posed to the brain in terms of sound waves - interpreted into electric signals by the relevant portion of the brain. And once the computation has taken its course, following the same biological simulation one may carry out the necessary recoding and end up with the exact vibration of the larynx, from which sound waves can be deduced - pretty much the same sound waves which a real mouth will speak if a real brain is asked a real question. (You can find a variant of this experiment here in Wikipedia.)


However note that the person who is carrying out these computations, does not need to at all 'understand' the question that was posed in form of sound waves. The scanned brain may even belong to Stephen Hawking - and the question a deep one in astrophysics - and the person who is simulating this may not even understand English - but at the end of calculations he will still come out with exactly the same answer that a real Stephen Hawking would have given. Just as in real world, the consciousness and understanding that a brain possesses may be an emergent phenomenon, so can it be for a person meticulously simulating it on pen and paper.

So if the brain of a living person is scanned, and then tediously simulated by following mathematical equation on pen and paper, will give rise to exact same answers that the real brain will give (provided no mistakes are made). This is just like you can predict where Jupiter will be on this day next year - even though you of course cannot see it in the next year in our reality at this moment.

Do you think then the simulated brain is 'real'? Let's see. Let's suppose we note down the configuration of a real brain for simulation, and then destroy the real brain. (Well that's a rather inhuman thing to do, but it is only a thought experiment.)

Will the thought, feeling, knowledge, experience be preserved as the brain is simulated? Yes.

Will the brain answer to any question asked exactly the same way the 'real' person would have answered? Yes.

In general will the brain react in exactly the same way in which the real brain will react, when posed with the same (simulated) conditions? Yes.

So by all accounts the simulated brain's actions will match with the real brain - it will even have a (simulated) consciousness corresponding to the real brain.

The only fact which makes it not real, is that you are not there - you cannot directly see or talk to it or interact with it. What if your brain scan is also taken and is simulated alongside the other brain? Your simulated brain will have no doubt that the other brain is real. For them, since there is no way to detect the real you, your world will be as fictitious - just a 'what if we are being simulated' hypothesis.

Is there any way for the simulated brains to figure out that their world is merely simulated - and is not 'real'? The answer seems no (unless we choose to give them hints - eg. suddenly make a paper appear which has answers to their key scientific questions - which let's say we do not want to). They will see, feel, smell, touch their simulated world just as we do. They will have their own (simulated) thoughts, feelings, experiences, memories. They will experience (simulated) happiness, fear, joy, anger, peace just as we do. For them their (simulated) world is as real as we feel ours is.

It is a slightly disturbing conclusion that there is no way for them to detect they are being simulated, since it means that we could be living in a world which is entirely being simulated, and we would have no way to know about it. But it gets worse.
That's all my schedule permits me to write in the real (or simulated?) world where I live - we will continue the exploration next week. Update: Continued here.

Review of Race Driver GRID coming from NFSMW

I have had Need for Speed: Most Wanted for a long time in my computer, and I recently installed GRID. I will jot down couple of observations that I can make when I compare the two.

+ GRID has two features which are sorely missing in NFSMW, namely ability to replay your race, and damage your car. Both features were there in some other even earlier versions of NFS, but somehow did not make it through to Most Wanted.

In GRID, the replay is shown in a computer controlled camera (you can change it to one of the standard ones if you want), and as the rest of the game is very polished in visual quality. It really makes you look good!

The damage model is good, though coming from NFS where there is no damage, it takes a little time to adopt yourself for handling it. However it does not get too much in the way - as long as you avoid high speed crashes. Your car is immobilized immediately (and the race is over) if you hit the wall at 170mph. The dashboard shows which part of the car is damaged while you are driving. The only other effect I have seen is that if you badly damage one of your wheels, the car will be disbalanced and will have a tendency to automatically steer to one side which you will have to constantly counter throughout the remaining part of the race.

- There is no civilian vehicles and no cops. All the races are pure races, with closed tracks walled off with concrete blocks or blocks of car tires. The tires (as well as parts of your car) get scattered if you bump into them slow enough not to total your car. They will then remain on the track till the end of the race.

- There is no nitro boost. This makes winning more a matter of control.

+/- The difficulty is notched up, partly because of the damage model mentioned above. Also unlike NFS, the competitors here are all more serious in all levels - it is unlikely that you will find someone driving at a slower speed than yours in a long road without turns. Also it will take some time to get used to the controls and the cars, the physics is slightly different from NFSMW. Apparently it's a little more 'realistic' or 'sim' like. However after a bit of practice, you will start winning some of the races. The increased difficulty provides a sense of accomplishment when you win.

+ The game has a feature called 'flashback' which you can use a limited number of times (maximum 5) depending on your difficulty. This lets you rewind time to correct your mistakes (much like Prince of Persia series) and works beautifully in the game. This helps countering the difficulty and balance the game a bit more.

+ The graphics is just a treat for the eyes. The cars and the tracks are gorgeous, they make you want to play on just for the looks. I ended up 'test driving' the cars I own for adapting to the controls, and it was really nice. The menu system is very nice too, it's never static. You will feel that you are almost setting something into motion when you navigate through it.

+ The cars and the race types all have a different feel. It's like multiple racing games in one. You can drive 'Pro Muscle' through the city, or professional motor racing cars in 'Pro Tuned'. The cars for 'Drift' racing have a different weight setting which makes them more susceptible to drifting when you turn.

Memorable quotes from Portal

Memorable quotes from Portal depicting the characteristic humor –

Once the tests are complete – and the AI plans to kill you –

(GLaDOS): [near the end of the nineteenth and final test chamber] "Congratulations. The test is now over. All Aperture technologies remain safely operational up to 4000 degrees Kelvin. Rest assured that there is absolutely no chance of a dangerous equipment malfunction prior to your victory candescence. [the moving platform the player is standing on is sinking into a fire pit] Thank you for participating in this Aperture Science computer-aided enrichment activity. Goodbye."

Once you figured your way into the main chamber of the AI, and attempt to shut it down by destroying parts of it –

(GLaDOS): Have I lied to you? [pause] I mean, in this room? Trust me, leave that thing alone.

Portal 2 –

(GLaDOS): Okay look, we both said a lot of things that you are going to regret. (Combined with the characteristic evil and pseudo-cheerful voice in which it is said, this one is a gem!)

(GLaDOS): This next test involves the Aperture Science Aerial Faith Plate. It was part of an initiative to investigate how well test subjects could solve problems when they were catapulted into space. Results were highly informative: They could not. Good luck!

(Wheatley): Most test subjects do experience some cognitive deterioration after a few months in suspension. Now, you've been under for... quite a bit longer, and it's not completely out of the question that you might have a very minor case of serious brain damage. But don't be alarmed, all right? Although, if you do feel alarm, try to hold onto that feeling, because that is the proper reaction to being told you have brain damage.

(Wheatley): They say the old caretaker of this place went absolutely crazy. Chopped up his entire staff... of robots; all of them robots. They say at night you can still hear the screams... of their replicas; all of them functionally indistinguishable from the originals. No memory of the incident. Nobody knows what they're screaming about. Absolutely terrifying. Though obviously not paranormal in any meaningful way.

(Wheatley): You two are going to love this big surprise. In fact, you might say that you're both going to love it... to death. Love it until it kill- until you're dead. [chuckles] All right? I don't know whether you're picking up on what I'm saying here, but …

(GLaDOS): Yes, thanks. We get it. [Chell and GLaDOS enter a elevator] All right, he's not even trying to be subtle any more. Or maybe he still is, in which case: wow, that's kind of sad.

Inception movie review

Rating: 60/100

TLDR: Nice but too many inconsistencies in the script spoil the fun.

Nice idea (though not original, there have been other pieces with main plot revolving around people sharing dream), and fast paced. The movie keeps you engaged throughout. It also succeeds in making you talk about it while you are leaving the hall, but mostly because of questions that were left open.

The script has many holes however, which result in many inconsistencies throughout the movie -
1. Why does the effect of gravity not flow through levels of dreams?
2. How come the infinite staircase sometimes suddenly become disconnected? (This was probably thrown in just to show how a staircase may look infinite from a certain angle in real world - but is completely inconsistent with the storyline.)
3. Fine, they have invented a machine through which you can connect people together in a dream. How come the dreamed 'dream sharing machine' works, when you are already in a dream?
4. How does the 'limbo' retain what was built there before, may be by a different person?? (Cobb's creations are there in dream initiated by someone else.)
5. Why does the top fall when the old man spins it when the movie begins?
6. Why couldn't Cobb's wife simply spin her top to test if it is real life or a dream?
7. How did Cobb wake up from limbo?
8. Why does Arthur not wake up by the Van's freefall (the 'kick') but instead simply start experiencing zero gravity in the dream?

The movie also seems to throw a lot of ideas just for the effect, most of which are irrelevant or have no consequence to the story. Eg. Penrose staircase, and bending of the road in the constructed dream world by the student.

I liked a few of them though - for example the puzzle of creating a maze in two minutes that cannot be solved in one minute, or the idea that someone thinks the real life is a dream and wants to wake up from it.

Lots of room for improvement. At most this is comparable to Matrix 2, but not anywhere near as perfect as Matrix 1. With the concept, I feel they could have done a better job if they thought it through.

Addendum:
Leo's role was pretty much the same as Shutter Island. For others too, there was hardly any scope of showing acting in the movie, as it was mostly a chase.

I was actually debating whether to rate it 50% or 60%. I decided with 60% since it atleast kept me engaged, and the acting did not completely suck.

The movie was essentially a bunch of things thrown together to confuse people. This serves two purposes - people talk about it, and also people may watch it again in case they missed something, in the hope of some getting answers (which are not there).

Chris Nolan's imagination falls plain short of the idea of a dreamworld. If I were to implement it, it would not be lucid and perfect world with guns, explosions and zero gravity etc - it should be more like something that makes you feel you are dreaming. May be with a lot of computer generated images, imaginative creatures.

The reason it is being compared to Matrix is that clearly the intention was to copy Matrix. And it manages to fail in all levels in doing so.

Do you have a son born in a Tuesday?

Here's a very nice probability puzzler -

For a scientific experiment, I walk upto a random person in a mall. I ask, "Do you have exactly two children, and one of them is a boy who was born in Tuesday?" The person answers "Yes". Assuming that he is telling the truth, what is the chance that he has two boys?

Assume all necessary clauses, eg. I don’t know the person, I can’t see his children, etc. Also note that exactly two "one of them" here means "atleast one of them", just as in normal English.

In so many ways the solution conflicts with intuition, that I can’t help feeling that this question has been designed to show that our intuitive ability fails when it comes to conditional probabilities.

If there was nothing mentioned about Tuesday

The first thought that comes to mind is that if one is a boy, surely we must find the probability of the remaining one being a boy - so the answer must be half. Well that’s simply not true, even forgetting the ‘Tuesday’ condition, the chance of both being boys is 1/3. It’s because we have 3 equally likely cases given there is atleast 1 boy –

BG, GB, BB

Hence P(2 boys | atleast 1 boy) = 1/3, simply by counting cases.
Note however, this would change, and intuition would be right, and the probability will be half, if the question was framed in slightly different manner – “Do you have exactly two children? If so, if you choose any one of them at random, is he a boy?”

The original problem with one boy on Tuesday

We have to find P(both boys | atleast one boy on Tuesday).

Again intuition says, being born on Tuesday doesn’t change the question – atleast one is still a boy, and given that, the chance of both being boys is still 1/3. Wrong again – Tuesday is very relevant to the problem in an interesting way. It makes the boy being asked about special, and almost identifies him. Solution is given below .

By enumerating all equally likely cases

There are in total 196 cases, which are all equally likely. The table below lists them all.


The answer can be simply counted off the table, it’s 13/27.

Using conditional probability

The solution above is fine, but the approach breaks down if the problem was complicated – by increasing the number of children to 3 or 4. We then wouldn’t have the luxury to visualize the sample space (i.e. all possible outcomes) easily. Fortunately, another way of solving it which does not depend on a table exists, which is in nature and so will still carry forward in more complicated cases with ease. For the mathematically inclined, the solution using laws of conditional probability is given below.

We will use some abbreviations to remove the clutter -

BT = Boy born on Tuesday
BnT = Boy not born on Tuesday
G = Girl

So for example, (BT,BnT) means first child is a boy born on Tuesday, second is a boy not born on Tuesday.

P(both are boys, and atleast one boy on Tuesday) = P(BnT,BT) + P(BT,BnT) + P(BT,BT) = 1/2*6/7*1/2*1/7 + 1/2*1/7*1/2*6/7 + 1/2*1/7*1/2*1/7 = 13/196

P(atleast one boy on Tuesday) = P(BnT,BT) + P(BT,BnT) + P(BT,BT) + P(BT,G) + P(G,BT) = 1/2*6/7*1/2*1/7 + 1/2*1/7*1/2*6/7 + 1/2*1/7*1/2*1/7 + 1/2*1/7*1/2 + 1/2*1/2*1/7 = 27/196

So P(both are boys | atleast one boy on Tuesday) = P(both are boys and atleast one boy on Tuesday) / P(atleast one boy on Tuesday) = 13/27.

General case

Here the added condition was of being born in Tuesday. It can be seen that if we replace this with any other random condition (e.g. “Is his name Jacob?”), having probability p, the answer will turn out to be (2-p)/(4-p). This can be worked out easily if you replace all 1/7 with p, and all 6/7 with (1-p) in the solution given above.

Wikipedia has some more on this:
http://en.wikipedia.org/wiki/Boy_or_Girl_paradox#Third_question