Probability calculations for Words with Friends

In Words with Friends, sometimes it is helpful to know the probability of your opponent having a certain letter in his hand. While this may sound like a daunting task, it is actually quite simple and can be modelled with a hypergeometric distribution, which is most commonly used for sampling without replacements. The formula is given as:

where N refers to the population size, n the number of draws, m the number of 'successes' in the whole population, and k the number of successes that you want to calculate. The brackets relate to a binomial coefficient such that:

Let's use a simple example to test first. What is the probability that your opponent has a 'X' in the first round, assuming that you don't have one in your hand?

In this case:

n = 7, because each player starts with 7 tiles.

N = 97, because each player starts with 7 tiles and I don't have a 'X'. 

m = 1, because there is only one 'X' in the whole game.

N - m = 96, which refers to all the non 'X' tiles in the game.

k = 1, because you want to find the probability that your opponent has one 'X' in his hand.

P(X = 1) = [ 1! / ( 1! x 0! ) ]    x    [ 96! / ( 6! x 90! ) ]    /    [ 97! / ( 7! x 90! ) ]

= 7 / 97 

= 7.22%

Let's check this with just logic and simple probability instead of the formula. Your opponent has 7 tiles in his hand, so this is equivalent to 7 draws.

Probability that he draws a 'X' in his first attempt = 1 / 97

Probability that he draws a 'X' in his second attempt = 96 / 97  x  1 / 96  = 1 / 97

Probability that he draws a 'X' in his third attempt = 96 / 97  x  95 / 96  x  1 / 95 = 1 / 97

...and so on until the seventh attempt. Now, it is obvious that the probability is 1 / 97 for each attempt, so in total, the answer is 7 / 97, which is 7.22%. 

Of course, the hypergeometric distribution can be used to calculate more complicated scenarios, like for example, what is the probability that your opponent has 2 'S' in his first round, assuming you have none in your hand?

This time, m = 5 (there are 5 'S' in the game), and k = 2. The other variables remain the same.

P(X = 2) = [ 5! / ( 2! x 3!) ]   x   [ 92! / ( 5! x 87! ) ]   /   [ 97! / ( 7! x 90! ) ]

= 3.83%

However, it would be more apt to calculate the probability that your opponent has at least 2 'S' in his first round. This means we want to find P(X ≥ 2), which means P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5). Doing the calculations would give you an answer of 4.05%.

This distribution can be easily replicated on Microsoft Excel with the function FACT() for factorial (for the Binomial coefficient).

It should be noted that this method may not be 100% accurate due to the fact that you can use less than 7 tiles at one go. So it is likely that your opponent will hoard the better tiles like 'S' or blank and wait for an opportunity. Thus the calculations above can be thought of as 'the minimum probability' that your opponent has a particular letter.

Orchard Cafe @ Orchard Hotel

I went for breakfast with my mother at Orchard Cafe this morning, because we had a $50 voucher from à la carte. The breakfast dishes were not cheap - for example, a Japanese breakfast set, which consists of a bowl of rice, baked salmon, and miso soup, costs $28, while a plate of nasi lemak costs $15. The Orchard Cafe Breakfast comes with a choice of either two eggs or an omelette with various ingredients, bacon, chicken sausage, and a choice of juices and coffee or tea.

I checked with a waitress to see if we could use the voucher for the buffet, and was told that we couldn't - we could only select items from the menu. Since we also had the à la carte membership card, I suggested using it for the buffet instead (50% for 2 pax) and use the voucher another time. The waitress apologised and said that the card was not valid for the buffet too. Oh well.

In the end, we decided on the Orchard Cafe Breakfast ($32) and an Eggs Benedict ($15), and asked the same waitress over.

Me: Can we have one Orchard Cafe Breakfast and one Eggs Benedict?

Waitress: Oh, the Orchard Cafe Breakfast is actually the buffet, so you will have to take it yourself.

Me: Huh? So can we use the voucher for this then?

Waitress: Uhh... yes.

Me: What the hell?

Okay I didn't say the last part aloud, but that was what went through my mind. Firstly, the way the Orchard Cafe Breakfast was described in their menu made it seem like an à la carte order, because you had to choose between two eggs done in any style or an omelette. Secondly, the voucher isn't valid for the buffet because it can only be used for the menu items - but the buffet is on the menu so it's okay? Sounds like a circular reference error on Microsoft Excel!

Food-wise, nothing really stood out from the buffet. The fried eggs, chicken sausages, ham slices, and nasi lemak were decent, the lamb sausages and 油条 were not good, while the chawanmushi was downright horrible - easily the worst chawanmushi I have ever eaten in my life. It was too hard, had no taste, and the crab stick and mushrooms inside were hard, stale, and tasteless. Thumbs-down for the buffet. Not going to come here for breakfast anymore.

Immortals

I caught Immortals today, being someone who loves Greek mythology and has read such stories since I was young. (NOTE: Spoilers below.)

Here is the synopsis from Rotten Tomatoes:

The brutal and bloodthirsty King Hyperion (Mickey Rourke) and his murderous Heraklion army are rampaging across Greece in search of the long lost Bow of Epirus. With the invincible Bow, the king will be able to overthrow the Gods of Olympus and become the undisputed master of his world. With ruthless efficiency, Hyperion and his legions destroy everything in their wake, and it seems nothing will stop the evil king's mission. As village after village is obliterated, a stonemason named Theseus (Henry Cavill) vows to avenge the death of his mother in one of Hyperion's raids. When Theseus meets the Sybelline Oracle, Phaedra (Freida Pinto), her disturbing visions of the young man's future convince her that he is the key to stopping the destruction. With her help, Theseus assembles a small band of followers and embraces his destiny in a final desperate battle for the future of humanity. 

The show was a total let down. Other than the whole plot not staying true to the original Greek mythology at all (really, not at all!), it was also filled with holes and gaps that are so big that it couldn't even hold rocks.

The movie seemed to revolve around the Bow of Epirus, which is supposedly so powerful that its wielder can conquer the world and defeat Gods. In the end, King Hyperion only used it once - to destroy the gates of a fortress. After the gates fell, he had the chance to send several more arrows in (yes, ammo is unlimited) to wreak more destruction. But he didn't. Hmm. Other usages of this legendary bow were minor and hardly worth mentioning.

When the fortress was breached, the soldiers panicked and tried to flee. Theseus managed to hold them together with a speech in a lacklustre tone that was barely audible. In just a few seconds, all of them had such a huge morale boost that they were banging their shields and pumping their spears in the air. Nice. Obama could learn a thing from two from Theseus, man.

Also, this is a Greek movie, dammit. Why is the oracle so obviously Indian? She looked so out of place, and as one movie reviewer said, she has to be "the loosest virgin in the Peloponnese". Her reason for sleeping with Theseus? "I want to see the world with my own eyes." (if she loses her virginity, her oracle powers would be lost as well) Oh my god. I didn't need extra cheese to go with this.

I thought Titans are supposed to be big. Huge. Enormous. Gigantic. The movie's Titans were human sized, and the way they were imprisoned in a cage with long bars across their mouths made them perfect for table soccer.

The caged Titans, from Immortals. Table soccer, anyone? Source: Latinoreview.com

I should have checked Rotten Tomatoes first before watching (they gave it a score of 38%). When King Hyperion said, "His pain has just began", I think he was referring to some of the audience.

Heng Kee @ Hong Lim Food Centre

I was a 'late learner' when it comes to curry chicken noodles, because since young, I have been eating curry chicken only with rice. So the notion of eating it with noodles seemed rather foreign to me. However, the first curry chicken noodles I tried at Heng Kee in 2006 converted me totally.

Heng Kee curry chicken noodles, $6.50

Their curry tastes very unique, with a very slight tinge of sweetness. As someone who doesn't really have a liking for sweet stuff, I should emphasise that this sweetness is really very slight, in case some people get turned off by a sweet curry. The tao pok and potatoes have been immersed in the curry for a long time, so what you get is very soft tao pok and a potato that crumbles easily. Strangely, the chicken is not stewed together with the curry; it is just normal steamed chicken that is added into your bowl after you order it. But it still tastes perfect when combined together, and you won't feel that the chicken is a separate part of the dish. 

When the noodles are ready, the uncle would actually add scoop some oil from his curry pot and drizzle it into the bowl. After painstakingly removing the oil several times, I finally remembered to ask the uncle not to add any oil. 

When I first tried it in 2006, their curry chicken noodles came in three prices - $3 / $4 / $5. It then became $4 / $5 / $6, and not long after, $4 / $5 / $6.50. $4 gives you a small bowl with no choice of chicken parts. $5 gives you a bigger bowl with a choice of chicken parts, but no chicken drumstick or thigh. $6.50 obviously offers the biggest bowl with chicken drumstick and thigh. Unsurprisingly, there is always a long queue and each bowl takes quite some time to prepare, so to make my time more worth it, I will always order the $6.50 bowl. Their chilli is actually more salty than spicy, and also with a slight tinge of sweetness. It is a must-have with the chicken!

Till now, it is still the best curry chicken noodles I have ever tried. There is another outlet directly above, but Heng Kee wins it easily. Recently, after Hong Lim Food Centre was renovated, a third outlet opened upstairs too, but I didn't bother to try. Some of my friends said that the curry chicken noodles at May Hua Food Court (near Golden Shoe Car Park) is good, but one sip of the curry proved otherwise.

One thing to note - remember to bring tissue paper. The bowl is served with the spoon inside, and very often, the spoon is 90% immersed in the curry (look carefully at the spoon in the picture), so you would need to clean the spoon first before eating.

'Cheapskate' motorists? No, dumb writer

In today's Straits Times Forum:

"THE public carpark behind Far East Shopping Centre is popular because it provides cheaper parking for the Orchard Road area. Unfortunately, there are motorists who exploit this by waiting for their friends or family members in their cars, without displaying carpark coupons.

I had an unpleasant experience there on Monday about 11.30am while trying to find a parking space. The driver of a Mercedes-Benz was reading newspapers at the wheel, without coupons being displayed on the dashboard.

I approached her to check if she intended to park her car. She said she was waiting for her daughter but did not intend to use a parking coupon.

That driver was not alone. Other motorists were also occupying parking spaces without paying for them.

The carpark was full and there were many motorists queuing for parking spaces.

How does the Urban Redevelopment Authority (URA) deal with such motorists who prevent others from legitimate use of parking spaces?"

Jeyarani Anita Henry (Ms)

Is there anything wrong with someone parking their car in a parking slot while sitting inside the car at the same time? So what does the writer want?

1) To ban people from remaining in their cars when they park their car in a public car park?

2) Force them to put coupons even though they are sitting inside?

Does it mean that if the driver waits inside the car but also displays a parking coupon, the writer will be satisfied?  The driver wastes one parking coupon, the writer still does not get a slot. So who wins? The government, of course. The revenue of one parking coupon is earned for nothing. 

Why I don't want kids

Among my friends and family, I am rather well known for detesting kids. So a natural by-product of this is that I don't want any kids, even after I get married. I see parents at NTUC Fairprice with screaming and running kids, and it certainly helps to reaffirm my views (while trying to suppress the urge to knee one in the face).

Reasons? Plentiful.

1) They are expensive. I don't need to elaborate on how expensive living in Singapore is. Having a kid on top of that? Diapers, milk powder, clothes, textbooks, school fees, toys, repairing the furniture, unclogging the toilet bowl? I would rather spend the money on figurines or vacations.

2) They are troublesome. You need to spend an obscene amount of time on them and yet still suffer a lot of headaches. And when they become teenagers, multiply the headaches by ten.

3) Because they require so much time and money, you can't do what you want. You can't just go out for a dinner and movie without ensuring that someone can take care of them. While having a maid is an option, I don't trust maids (my family has had more than eight maids) and most of them are either dishonest, lazy, or take you for granted when you treat them well.

4) To me, the most irritating sound in the world is a kid's wailing or screaming. If only someone can invent some sound-proof mask for kids... 

5) Being a parent is a thankless job (just like being the government). They do not know how much you have sacrificed for them. And even if they do, they may not appreciate it. 

6) You can't control what kind of person your kid will turn out to be. While good parental guidance can help, it may not overcome traits which the child is born with. Even if you treat them well and bring them up well, they may not be filial. Two people especially stand out in my mind. Let's call them A and B.

A's parents are not well-to-do, but in order to send A to the US for his university education, they scrimped and saved. But when A was at the US, he told his friends (with no remorse) that he doesn't care what his parents have done for him. In fact, he even used his parents' hard-earned money to buy an expensive car, and thinks that there is nothing wrong with it. 

B is someone who has no qualms about leeching off his parents, despite his parents not being especially wealthy too. He thinks that spending other people's money (including his parents) is an especially wonderful feeling, and if he had his parents' credit card, he will "swipe-swipe-swipe" and buy a house, a car, everything. When I remarked that that seems to be a life of a parasite, he responded defiantly "And what's wrong with that?"

I don't know A personally. He was just someone my friend knew, and my friend was so upset with him that she stopped talking to him ever. But I know B personally, and from what I know, his parents have not done anything to betray him or insist that he send money home to Malaysia. (Then again, I do know that he doesn't send any money home) So what led to him developing such a character?

So in choosing not to have a kid, I am actually following the best risk management approach - risk avoidance. I think there are other better things I can do with my life. However, I acknowledge that this is only how I feel currently, and that it may change with time. 

The common arguments people give me when they hear that I don't want kids. 

1) What about when you grow old? Aren't you afraid of ending up being old and lonely?

Come on, there is no guarantee that your kids will visit you after they grow up and start their own families. Also, like what I mentioned earlier, even if you bring them up the proper manner, they may not grow up to be filial. 

People without children also spend their lives differently, and this may include forging more social ties with friends, colleagues, pets, and so on. 

2) But kids are so cute!

"Cute" is subjective. You may think that a kid is the cutest thing ever in the whole world, but in my eyes he is just a rascal that sucks your time, money and energy away and uses them to produce noise, tears, and shit.

Q3: Wait till you grow older. You may change your mind by then.

This is the only argument that I acknowledge and agree with. But I do know for certain that for now - and in the near future - no kids for me. 

Seng Kee Minced Pork Noodles @ Changi

I don't usually travel to the eastern part of Singapore, but Seng Kee Minced Pork Noodles is a place which is definitely worth my time (and petrol). Located at 316 Changi Road, it stands out because the whole place belongs to them, unlike the usual standalone stall in a hawker centre. 

I arrived here at 520pm on a Saturday, and was greeted (pleasantly) with an almost-empty restaurant. 

Braised pork ribs, $5

The pork ribs were obviously braised for quite some time, because even the soft bones can be eaten easily. The flavouring had also seeped into the meat totally, so what you get is a plate of very delicious and soft pork ribs.

Bak chor mee, $4.50

This is their standard bak chor mee. On its own, it was already very good, until I tried their special version with egg and mushroom sauce...

滑蛋肉挫面 - Bak chor mee with mushroom and egg sauce, $6

This is definitely one of the best bak chor mee I have ever eaten. Of course, with its thick sauce, it is rather different from the traditional bak chor mee, so a comparison may not be fair. The sauce was so rich, thick and delicious that every mouthful was (almost) greeted with a contented sigh. In fact, thinking about it when I am writing this makes me feel hungry again!

Fish maw soup with pork tendons, $12

A huge bowl of soup which is practically saturated with ingredients - fish maw, minced pork, mushrooms, pig liver, sliced pork, black fungus, and pork tendons. Unsurprisingly, this soup was extremely sweet and tasty. However, I think the pork tendons were quite unnecessary, so the standard fish maw soup ($8) should suffice.

After I finished my dinner here, I was already making plans to bring my whole family here soon. I am actually very surprised that there is no long queue at a restaurant that serves such fantastic food! Since the restaurant opens from 8am to 10pm, I figured that the crowds would come more often on weekdays for dinner and weekends for breakfast or late dinner.

Deceptive Advertising #2

While having breakfast at Serangoon Garden this morning, someone gave me a brochure for an upcoming condominium near my place - Cardiff Residence, which is located along Lorong Chuan. Since I was very familiar with this area, I looked at the condo location more carefully and was rather appalled by how misleading the brochure is.

This is a picture of the brochure.

Stamford American International School and Australian International School are actually located further down Lorong Chuan road, but this was still acceptable. What I couldn't accept is where they placed Serangoon MRT station and NEX Shopping Mall. Google Maps shall be our judge for reality in this post.

Google Maps. Green circle = original location of Serangoon MRT and NEX. Red circle = developer/agent's location of Serangoon MRT and NEX

So according to the brochure, Serangoon MRT station and NEX have been transported around 1km away from their original location at Upper Serangoon Road to along Serangoon Avenue 2 and Boundary Road. While they did include a disclaimer - "This artist's impression is preliminary only and should not be considered as representation of facts" - this is just too blatantly wrong and false. 

Uncle, take it easy lah

I used to see this irritating uncle in the morning when I take the Circle Line MRT to work. He is perpetually in a rush, and when the train arrives at Lorong Chuan, he would get off the cabin and move to the head of the train - so that he is closest to the escalator at the next stop, Bishan. And he would time himself such that he goes into the cabin last. Why? So that he can be the first to get off. 

After not seeing him for several months, I met him again this morning. This time, he was already at the train head, standing right in front of the train doors. When the train doors opened, he grudgingly moved aside slightly to let people in. I happened to be the last, so I (purposely) took his original spot. I could tell that he was a bit flustered and irritated as he kept on throwing quick glances at me. A few seconds later, he even tried to inch towards me in an attempt to position himself better to be the first one out. But I stood my ground and even put my paper-bag strategically beside me to fend him off. All this while I had my eyes fixed on my PSP.

So when the train reached Bishan, I was the one first out. Unsurprisingly, he quickly overtook me and half-ran up the escalator to catch the North-South train. I looked at the sign - 'Train Arriving' (which actually means Train Arrived) - and from the number of people who were walking in my opposite direction, I figured that the train would be leaving soon and I wouldn't make it. So I took it easy. 

Uncle didn't, however. When I reached the North-South train, the train had just left and he was nowhere in sight. Evidently, he had managed to catch the train. Damn it.

The 30s syndrome

Today, I had lunch with an old friend I have known since JC. So this makes 2011 the 14th year I have known him.

He said that he is feeling old, now that he is 30 years old. He used to go clubbing almost every weekend, drink till 3 to 4am and go home roaring drunk, and spend hundreds of dollars in the process without batting an eyelid. But now, he prefers to stay at home or to spend more time with his girlfriend. He used to drink iced water whenever possible; now he drinks warm water. It's the thirties-syndrome, he claims. 

If this is the case, it seems that I have reached 30 years old at least 4 to 5 years ago. If I get requests to go clubbing on a Friday or Saturday night, I would decline them 90% of the time. To me, such activities are a waste of time and money, and I would need to spend the whole weekend recuperating. I would rather do what I do every weekend - having breakfast with my mother and my dog, swimming, practising the piano or cello, going out with my girlfriend, and clearing some work so that I don't have to work too late on weekdays. 

Such activities give me a strong sense of self-satisfaction and fulfillment, and I would feel that my weekend has been utilised fully and not wasted on sleeping.

On the issue of drinking warm water, I used to drink cold water all the time too, including early in the morning. If there was no cold water available, I would even add ice (an ex-colleague looked aghast when she saw me do that at 830 in the morning). Now, it's room temperature water for me most of the time.

iPhone 4S?

When the iPhone 4S was announced several weeks ago, I greeted the news with a distinct lack of enthusiasm. There weren't any truly exciting features. Well, maybe Siri. But I doubt if many of us will use Siri on a very regular basis - after the novelty wears off, Siri will probably be kept in the closet most of the time. Besides, my contract wasn't up yet, so getting a new phone was not really a viable option. 

However, recently I am getting really tempted to buy the iPhone 4S.

Firstly, my iPhone 4 now lags like hell - coincidentally after I installed iOS5. Words with Friends lags so much that sometimes I need to wait for more than a minute for the game to load. It may be because Zynga hasn't released an update for it yet, so I am crossing my fingers. But other apps are also more laggy now - for example, Safari. And when unlocking my phone, the phone now seems to be a bit less responsive, so when I key in my 4-digit passcode, it tends to miss out one digit quite often. 

Of course, my home button is another issue. It is extremely unresponsive, and I would need to press it very hard for it to work. Assistive touches do help to get around this, but it does have its own fair share of problems - coupled with laggy apps, assistive touches only make things worse.

Even if I decide not to get it, can my current iPhone 4 last me for one more year till the iPhone 5 comes out? I am not so hopeful about that.

No Name Hainanese Curry Rice @ Beo Crescent

Before I came here, I was actually trying out Meng Kee Char Kway Teow (refer to my previous post), because it was just a three-minute walk away from here (Blk 40 Beo Crescent). But this stall was much tougher to find, which makes its name especially apt. I actually walked past this stall twice without realising it.

No Name Hainanese Curry Rice, with fried pork, chup chye, and minced pork. $3.70

The queuing was tortuous to me. Not because the queue was long - there were only eight to ten people in front of me, and the queue was clearing quite quickly. Rather, it was due to the stuffiness of the coffee shop. Ventilation was very poor, and coupled with the sweltering mid noon heat, I could feel the beads of sweat trickling down my back as I queued. This had better be worth it, I told myself. 

Well, it turned out to be pretty good, fortunately. The fried pork was excellent! It was crispy, succulent, and yet not oily. A quick look around confirmed that seriously everyone ordered the fried pork. Another look at how much fried pork the stall has further affirmed its popularity.

The rice, curry gravy (which is totally not spicy) and chup chye form the basic core of Hainanese curry rice, and theirs was delicious. The minced pork was also pretty good.

This is really cheap and good! Now, I find this much more worth travelling from home (I stay near Bishan) for instead of Meng Kee Char Kway Teow.

Meng Kee Char Kway Teow @ Havelock

Another place recommended by ieatishootipost, located at 22 Havelock Road. I went there at around 1130am yesterday (it was a Saturday) and there was no queue at all, to my surprise.

Meng Kee char kway teow, $3

ieat gave it 4.5/5, which is one of the highest scores for char kway teow (his top score of 4.75 is for Hillstreet Char Kway Teow, at Bedok South Road) so I had rather high expectations. It was fried in a different way, with lots of sweet sauce added, so the plate turned out to be sweeter than your usual char kway teow. It was also quite moist (which I like) and smooth, and came with bits of pork lard and hum. 

On its own, the dish was a bit too sweet for my liking, but it was still not bad. I very much prefer Hong Lim's char kway teow (Outram Park Fried Kway Teow Mee). Till now, it is still the best I have ever eaten. I wouldn't mind eating here again, but I wouldn't make a trip down specifically for this.

Charly T @ The Cathay

Charly T is a small diner situated at The Cathay. It's specialty is its roast chicken, and in a way it is very much like Kenny Rogers Roasters. 

I baulked when I first heard how much their whole chickens cost - $42? True, it comes with four sides, but still... I can buy a whole chicken from NTUC for less than $7 and roast it myself! 

So the real reason why I came here was because I had two BigDeal vouchers ($15 for $30 each). 

Deep fried calamari rings, $9

A decent dish you can do with or without. I don't know what the sauce is, but it was slightly sour, which I felt wasn't really suitable for the calamari.

Charly T half chicken - $24, with 3 sides

The chicken was not bad, but for this price, it was definitely not worth it. At least it wasn't too dry, especially the breast. I do recall Kenny Rogers Roasters' chicken breast being so dry that I would need to eat it with some of their macoroni cheese.

The chicken also comes with 3 sauces, which was also one of their so-called selling points. While the sauces tasted quite special and good, I didn't think they were really necessary.

Macoroni and cheese, coleslaw, butter garlic rice

The macoroni cheese was quite poor; it tasted bland and a bit artificial. Kenny Rogers Roasters' macoroni cheese is still my favourite. The coleslaw was average, but the butter garlic rice was not bad.

Moroccan beef sticks with roasted potatoes, $16

The beef was nicely medium, so it was still quite juicy. This helped to cover up the slight lack of beef flavour. I guess they use New Zealand beef, which is cheaper but not as flavourful as Australian beef.

CT Fries, $8

I found the fries to be the best of all. Deliciously hot and slightly crispy, I had to refrain from finishing the whole bowl, if not I wouldn't have enough space in my stomach for the chicken and beef. 

So would I come here again if I didn't have any vouchers? Well, I would consider it only on Mondays, when they have their whole chicken promotion - $30 for one whole chicken with 4 sides (normal price is $42). Other than that, I wouldn't even step one foot in.

Tonkotsu King @ Orchid Hotel

It seems that Singaporeans are really crazy over their ramen. Over the past few years, ramen shops have been sprouting like mushrooms, and being a ramen-lover myself, I have nothing to complain. Today, I tried another ramen restaurant - Tonkotsu King, at Orchid Hotel (Tanjong Pagar). My friend told me repeatedly to arrive by around 1130am to 1140am, because the shop is tiny and a queue forms outside very quickly. A quick count yielded only around 18 seats (including counter seats) for the whole shop.

The inside of the tiny Tonkotsu King

As the name suggests, only tonkotsu (pork bones) soup is served here. While this may hint at a lack of variety, you get a choice of tonkotsu, black spicy tonkotsu, and red spicy tonkotsu. The base is essentially the same; they simply add a thick black pepper sauce (black spicy) or some red chilli powder and chilli oil (red spicy) for the latter two dishes. 

After you have chosen your soup base, you get to customise your ramen in three other ways - oil, noodles, and soup. 

Oil = Less oil, normal, more oil

Noodles = Soft, normal, hard

Soup = Light, normal, rich

Wanting to try something different, I ordered the black spicy version with less oil, normal noodles, and rich soup. While waiting, we were treated to a free flow of marinated beansprouts and hard boiled eggs. I love beansprouts, so I helped myself to a generous serving of beansprouts. As for the hard boiled egg, it was done very well in the sense that it was not too cooked - the egg white was still quite soft, and the egg yolk was slightly liquid and not rock-hard.

Black spicy tonkotsu with egg, $13.80

When my ramen came, I tried the soup first without mixing the black spicy sauce. It was quite good, albeit a bit too salty - but then again, I did opt for the rich base. Then I mixed the black spicy sauce in and immediately regretted it. I found that the black pepper did not really go very well with the soup and having it in its original form would be better. This doesn't mean that the soup tasted horrible after mixing - it was still good, just that it would have been better without the black pepper. It was also a good thing that I requested for less oil - to me, there were already too many pieces of chicken oil floating around in the soup, and I removed them as soon as I could.

The ramen also came with black fungus and char siew. Both were decent - nothing extraordinary. But the flavoured soft boiled egg was the best I have ever tasted. The egg white was so soft that it was almost runny, and whatever seasoning they used in the soup to boil the egg had fully permeated into the egg. And the egg yolk was also delicious and half-runny. At $2 more just for an egg, it may seem expensive, but it was worth every cent.

Tonkotsu King is definitely a good place for ramen, and I will probably visit it again in the near future. But next time, I am just getting the original tonkotsu soup with no black or red spicy seasonings. And perhaps I will add my own option on the order form - "no oil".

The Internal Security Act and Hypothesis Testing

According to our Minister for Home Affairs, Teo Chee Hean, "more than 800 people were arrested under the Internal Security Act (ISA) in the 1970s of whom 235 were issued with Orders of Detention." 

While there have been many people speaking up against the ISA, I am more neutral on this. I understand why the ISA is necessary - to enable the Government to act quickly to preserve public order without the hassle of going through a trial. Lee Kuan Yew pointed out before that the absence of the ISA is akin to "go(ing) through the motions of a trial and let a guilty man off to continue his damage to society". Of course, in the hands of the wrong person (or Government), this could lead to a potential abuse of power where innocents can be seized just for opposing the Government.

It is interesting to note that such a large number of people were detained without trial. It is safe to assume that a percentage of these people are actually innocent, which, in statistics, is indicative of a Type I error. In this case, we can actually set up a hypothesis with H₀ being the null (or default) hypothesis and H₁ being the alternative hypothesis.

H₀: The person is innocent.

H₁: The person is guilty.

This is where statistical error comes in - a Type I or Type II error. A Type I error is when H₀ is rejected when it is actually true - i.e, the person is innocent but still convicted, whereas a Type II error occurs when H₀ is accepted when it is false - i.e, the person is declared innocent but is actually guilty. In this case, a Type I error is the most applicable, because it is quite possible that a significant number of the people seized are, in reality, innocent. An example would be the people closely related to the suspects that were seized simply because, well, they are closed related.

The level of significance, usually denoted by the symbol alpha (α), refers to the probability of a Type I error. In statistical problems involving hypothesis testing, the student is usually given the level of significance (which is usually 1% or 5%) and asked to test if H₀ should be rejected or not.

Of course, if we were to use the above situation in hypothesis testing, I think the level of significance would be significantly higher than 5%.

Buying life insurance

Today, a friend messaged me this:

"Hi, want to check with you. Any good life insurance product in the market to recommend?"

This unsurprisingly-common question is actually rather impossible to answer. Firstly, life insurance covers a whole span of products, including whole life, endowments, term, and so on. Each product caters to different needs, and a proper needs analysis would not be possible without some of the person's key information like age, income, number of dependents, financial circumstances, etc. 

Secondly, even if the question is zoomed into a particular product category, say, whole life, there is still no simple answer. This is because premiums are not everything. A product may cost the cheapest, but if it also offers the least benefits, is it necessarily the best value for money? 

Thirdly, there usually isn't a product that is uniformly cheaper than all the other insurers' products across different ages, gender, smoking status, and sum assureds. Insurer A may have the cheapest term plan for younger males and for larger sum assureds, but for older females and smaller sum assureds, Insurer B may be cheaper. This happens because each insurer has its own mortality curves, morbidity curves, surrender rates, claims experience, and profit margins, which they use to price their products. 

Life insurance is much more different compared to other financial products because each product costs differently for each individual (varying ages, gender, smoker status, sum assureds) and also caters to specific needs. Thus, it is always advisable to do a proper fact find with an insurance agent or financial adviser before purchasing life insurance.

Virtual spring cleaning

I had three external 3.5" HDD with capacities of 1.5TB, 1.0TB, and 0.75TB respectively. The 1.5TB HDD was filling up and it was starting to show erratic behaviour, like disconnecting by itself when I am transferring animes in halfway, so I decided to quickly get a new HDD before something happens and I regret it for the rest of my life. Well, at least for a few weeks of my life. 

So a few days ago, I got a 3TB Western Digital external HDD at Challenger for $207. Hmm, this HDD alone is already the equivalent of all my current HDDs combined. I sat down and started transferring animes to my new HDD, and after a few hours, it... disconnected by itself. 

This time, I had my suspicions. My 0.75TB HDD had showed the same symptoms before, although at a much lower frequency. So I guessed that the culprit is the USB hub I used to connect these HDDs, and after removing it and plugging my HDDs to my iMac directly, voila - they all worked perfectly fine. *touch wood*

After copying all my animes into the new HDD, I realised that I still had a lot of space. So I selected some anime series to backup into the 1.5TB HDD (My anime library is actually 1.86TB, so if I were to back it up entirely, I would need to buy another HDD), transferred my photos and some other files into my iMac directly (instead of keeping them in one of the HDD), and did some basic spring cleaning, deleting files I would not be using. 

This resulted in freeing up the 0.75TB and 1.0TB HDD, so I am going to try and sell them for a quick buck. My desk now looks less cluttered too. 

With so much extra space, I decided to try out the Time Machine, a backup utility by Apple. What Time Machine does is that it captures the most recent state of your data. This allows you to restore any file, or even the whole system, across various time periods. For the past 24 hours, Time Machine makes hourly backups. For the past month, it stores daily backups. And for anything beyond that, it saves weekly backups until the HDD runs out of space. 

The size of my system backup is around 326GB. My backup HDD still has almost 800GB available, so it's not an issue. Along with the 700+GB of space available in my iMac and another 1.2TB of free space combined across the two external HDDs, I hope I won't need to buy a new HDD anytime soon.

Youmenya Goemon @ 313

A colleague recommended this place for "good and cheap Japanese pasta", so I visited the outlet at 313 with three other colleagues. Despite his warning to go early to get seats, we reached at 1215pm and were greeted with a 75%-empty restaurant. It's all because of its location - this outlet is located at a corner of 313 where traffic is very low.

A look at their lunch menu confirmed that prices were still quite reasonable, with pastas costing mainly around the $12 to $13 range. I selected their Lunch Set A, which consists of a regular pasta, soup and salad at $14.

Salad and soup

 I thought that the soup would be miso soup, but it turned out to be a clear and light soup. I would very much prefer miso soup though. The salad was quite good - their Japanese salad sauce was quite tasty and appetite-stimulating, and the vegetables were fresh. 

Crab, shrimp and scallop pasta in cream sauce

This is only a regular portion, but it's already big enough for most people. Shredded crab meat and dried scallops were used, so the flavour is more uniform throughout the pasta, but I think they could still add a little bit more. The prawns were the highlight though - they were very fresh and crunchy. Overall, I found this lunch set quite a good value for money indeed. Their pastas cost more than Pasta de Waraku's, but definitely taste better as they also use better quality ingredients.

Note that their main outlet is actually at Marina Bay Link Mall, and the prices are different from 313's. For example, a Lunch Set B (regular pasta + salad + soup + drink) costs $15 at 313 but costs $18.50 at Marina Bay Link Mall. And I remember my pasta costing $12+ at 313, but their website states that it costs $13.50.

Update as of 8th Nov 2011:
I visited their Marina Bay Link Mall outlet today and confirmed that the prices were indeed different from 313's. The main reason was because of the salad - over here, you can help yourself to one serving of salad at the salad bar. And the salad is really much fresher and comes with several salad dressings, which were all very good. On its own, a small bowl of salad already costs $5.80 here, so this justifies the price difference between the two outlets.

Keep your investments simple

Having a lot of funds in your portfolio doesn't necessarily mean that your portfolio is more diversified. And it certainly doesn't mean that it will perform better either. Sometimes, keeping your portfolio simple is the best way to invest. And monitoring it will be less of a hassle too.

1) Get exposure to the key regions

The key regions are Asia ex Japan, Japan, Europe, US, and emerging markets. These regions should form the core of your portfolio. There is actually no need for thematic funds like climate change, agribusiness etc unless your portfolio is big enough, or if you are a more experienced investor. 

To a certain extent, even single country funds can be excluded from a portfolio, especially if your portfolio size is small. For very small portfolios, investing into a global equity or global balanced fund is the fastest and easiest way to diversify your portfolio and gain exposure globally.

2) Diversify

Many investors think that fixed income funds are boring and leave them out of their portfolios. While their lower returns are nowhere as exciting as equity funds, they actually help to reduce the overall volatility of your portfolio. Fixed income funds are liquid and offer returns that are higher than bank savings deposits or fixed deposits, but with an acceptable increase in risk. If you have short term goals approaching, invest more into fixed income funds.

3) Invest regularly

Committing a fixed amount into your portfolio every month via a RSP (Regular Savings Plan) is a good way of maintaining discipline. The benefits of Dollar Cost Averaging have already been stated time and time again, so I won't repeat them here. 

If you have a longer time horizon, it is better to invest your RSP into an equity fund. If you have a shorter time horizon or if you are unsure about which equity funds to go into, there is no harm committing to a bond fund for your RSP too.