Wednesday, December 19, 2012

Win at Monopoly using Monte Carlo simulations

Now that we are experts at Risk, let's turn to Monopoly, the classic board game. In Monopoly, players determine whether to buy properties and build houses, so as to maximise rental yield. To some extent, one should gun for the most visited spaces, so that your opponents pay rent more often.

Which spaces are the most popular? Once again, drawing out the theoretical probabilities would be rather tedious, so we turn to Monopoly game simulations.

Tuesday, December 18, 2012

Win at Risk using Monte Carlo simulations

The objective in Risk is simple: world domination. In this board game, players attack each other's territories using dice. The attacker gets to roll three dice, and the defender two dice. The highest numbers are compared, and if the attacker has a larger number the defender loses one soldier (and vice versa). The same is done for the second highest numbers. For example, if the attacker rolls 6, 4, 2 and the defender rolls 5, 5, players loses one soldier each.

However, even though the attacker rolls an extra dice, the defender has an edge as well. In the event of a tie, the attacker will lose one soldier. Is this enough to offset the attacker's 3-dice advantage? What does this mean for rolling strategies?

Thursday, November 29, 2012

Singapore: rich, but emotionless

Singapore received some media attention recently for being the most emotionless country in the world. This stemmed from a Gallup study which interviewed residents in more than 150 countries, asking if they experienced five positive and five negative emotions the previous day:
  • Did you feel well-rested yesterday?
  • Were you treated with respect all day yesterday?
  • Did you smile or laugh a lot yesterday?
  • Did you learn or do something interesting yesterday?
  • Did you experience enjoyment, physical pain, worry, sadness, stress, and/or anger?
The "yes" responses were then averaged. Here only about a third (36% to be exact) of Singaporeans experienced one of these emotions the previous day, the lowest in the world. The global average was about half, and the most emotional country was Philippines, with a score of 60%.

This, ironically, led to some emotional responses from Singaporeans. For instance, one local politician rebutted the findings by listing a number of recent incidents which sparked public outrage and interest.

On the other hand, a Gallup partner commented that "if you measure Singapore by the traditional indicators, they look like one of the best-run countries in the world... but if you look at everything that makes life worth living, they're not doing so well".

Is Singapore really "not doing so well"? Is it because of our high GDP?

Wednesday, November 21, 2012

Are there really lucky numbers?

According to Chinese numerology, some numbers are considered lucky, and some unlucky. For example, the number "4" sounds like the Chinese word for "death", and is considered to be highly unlucky. "8", on the other hand, sounds like "wealth", so it is considered to be one of the luckiest numbers.

Such beliefs affect our actions in a tangible manner. When giving "red packets" of money to friends and relatives, for example as a gift during a wedding, it is considered rude to give amounts like $144. On the other hand, amounts like $128 and $188, are favoured, so it is good to keep some change handy.

Are such numbers really lucky? How can we test it out?

Tuesday, November 6, 2012

What are the odds that Obama will be re-elected?

As The Express Tribune puts it,

"Capping a long and bitter campaign, Americans began casting their votes at polling stations across the country on Tuesday, with many polls showing a statistical dead heat between President Barack Obama and his challenger Mitt Romney".

Yet, when forced to put money on the table, and forced to take sides, what are the odds of Obama or Romney winning?

Wednesday, October 17, 2012

Which is more like to win the Nobel Prize for Economics - Microeconomics or Macroeconomics?

The Nobel Prize was just awarded two days ago to two researchers in the field of Matching Theory, which has been used to match medical students to hospitals, and kidney patients to donors. Awesome stuff.

The most recent prize went to Microeconomics, then. However, Macroeconomics, historically, has had the largest haul, winning 43% of all Nobel Prizes since 1969. Microeconomics comes in at a close second, at 39%, while Econometrics and General Economics garnered a paltry 7% and 11% respectively. Should any aspiring Nobel Prize economist look towards Macroeconomics then?

Saturday, September 15, 2012

Does Economics Really Need Maths?

Economics has an incredible amount of mathematics. In fact, you wouldn't be too far off the mark if you were to rename it as Applied Mathematics (economy). Take the following model below, from my school notes, which describe how firms collude to set high prices.

Because of this, LSE economics students undergo a gruelling one-month math course before the start of their Masters programme. At the end of it, they take mathematics exams. It is hardly any fun, but does it really help with economics?

Sunday, August 26, 2012

The Economics of Kua Simi Kua

Staring incidents can be nasty. Just a few months back, one such incident sparked off a fight, and  a 17-year old boy suffered stab wounds in his back. Ouch. Despite this, Game Theory, a branch of economics applied to competition between firms, suggests that fights should never happen. I know it doesn't make sense, but let's run through the logic and see what we can learn from it.

Consider the diagram below. First a challenger decides whether to challenge an Ah Beng*, maybe by staring his girlfriend. If he decides not to stare, he does not win anything, and gets a 0 payoff. Subsequently, the Ah Beng happily hangs out with his girlfriend, and gets a payoff of 5.

*"Ah Beng" eludes simple definitions. Try Wiki for more.

However, suppose a challenge is made. The Ah Beng now has to decide whether to fight. However, nobody wins in a fight. If you don't get injured, you'll probably end up arrested. Even if neither happens, life goes on and you are no better off. As a result, payoffs are negative for both parties, at -5.

Lastly, if the Ah Beng doesn't fight, his payoff is 0. This is smaller than the "status quo" payoff of 5 - his might "lose face", and even his girlfriend. Even so, this is better than getting arrested for assault. In turn, the Challenger gets a payoff of 5 from looking at the Ah Beng's girlfriend.

From what I've said so far, I think it should be clear that the Ah Beng will never fight when challenged. Working backwards, the Challenger will find it better to challenge than not challenge. If this were true, why do we still see staring incidents, and why do we not see guys openly ogling at Ah Bengs' girlfriends?

Saturday, August 4, 2012

Does the Chinese Zodiac affect when people marry?

In an earlier post, I wrote about how births go up during dragon years, an auspicious year for having children. Because of this, Chinese couples might like to get married in the rabbit year, the year before the dragon year, to have a dragon baby. This, at least, is what I heard from a friend who had trouble booking a wedding venue in the rabbit year. Does this bear out in the data?

Wednesday, August 1, 2012

Do Olympics host countries have a home ground advantage?

Olympics host countries not only enjoy an influx of tourists and global attention, but their athletes benefit from, as the Metro puts it, "stadiums full of supportive fans cheering them on... There is no question that the home advantage will have an influence on performance".

Besides supportive fans, host athletes also compete in familiar environments. For instance, conditions in Weymouth Bay, the London Olympics sailing venue, are unique and hence challenging. British sailors will no doubt have an edge navigating local waters. Lastly, home teams don't have to battle jet lag and referee bias.

Do these really matter that much? At the end of the day, we want to find out if host countries haul in more medals.

Monday, July 30, 2012

Do people buy more clothes & shoes during the Great Singapore Sale?

Singaporeans love shopping, and that is a fact that needs no proving here.

It comes to no surprise, then, that sales of shoes and clothes shot up 13-15% during the 2011 Great Singapore Sale, compared to the two months before and after.

Does the Great Singapore Sale (henceforth termed "GSS") really boost sales, or is it school holidays or mid-year bonuses driving purchases?

Friday, June 29, 2012

What is the happiest day of the week?

Life can be tough at the start of the week. You've had lots of fun over the weekend, but now it's time to wake up early, and drag yourself to work or school. But is it really that bad? Surely after more than 10 years of schooling, you should get used to it, and adapt psychologically. As I mentioned in this post, the adaptation theory suggests that happiness levels revert back to some constant level over time. Hence, do people get happier as the weekend approaches, or have they adapted and are unfazed by the work-weekend cycle?x

Tuesday, June 26, 2012

If money can't buy happiness, what can?

In an earlier post about economics and ministerial salaries, I said that at the end of the day economics is about happiness. In fact, thousands of academic papers have been published on the subject. Furthermore, this isn't something just for the academics - the Bhutan government has a Gross National Happiness index which is also being replicated by some groups in the US.

Happiness is important stuff, then, and everyone should have some inkling of the subject, if only for water cooler ammoA good place to start is "Happiness, Economics, and Public Policy": it gives a concise summary of findings, balanced with problems like "why measuring happiness is tricky". If you have the time, read the file in it's entirety, but I suspect most would just be interested what affect happiness (chapter 3). Here's a summary.

Saturday, June 16, 2012

Are motorists in Singapore becoming more careless?

In the middle of May, a man driving a Ferrari ran a red light and drove straight into a cab, leaving himself and 2 others dead. Video footage from an adjacent car surfaced on the internet, and many viewers were horrified by the speed and recklessness of the Ferrari driver. One viewer felt that the accident "actually makes me upset and feel sick to my stomach". The picture below, taken from the video footage, shows just how fast the man was driving (the red blur moving into a cab on the right):

Source: Channel NewsAsia

Given that road accidents increased over 20% from about 7,100 in 2001 to 8,600 in 2010, is this incident symptomatic of greater carelessness on the part of motorists?

Friday, June 15, 2012

The shrinking Singapore household

In November 2011, HDB chief executive Cheong Koon Hean stated that while HDB flats have become smaller in size, the average household size has likewise fallen. As a result, the amount of space enjoyed by each person has increased, and each individual is better off despite living in smaller homes. This got me curious - while it comes to no surprise that households today are shrinking, does this trend differ across house sizes?

Are commuters happy about public transport?

Commuters can be quite vocal about public transport in Singapore. For example, Occupy Bishan MRT, a Facebook group, was set up for people to discuss (or mostly complain about) public transport issues.

While such groups help people let off some steam, they can also feedback to official channels through the Land Transport Authority's annual Public Transportation Customer Survey. The survey asks commuters if they were satisfied with eight bus and train attributes, a simple “yes” or “no” question.

The survey is hence a barometer of satisfaction levels. For example, 60% of commuters were satisfied with how long they had to wait for a bus in 2009. This proportion dropped to 56% in 2011, and hence more people have become unhappy about the wait. Have satisfaction levels fallen for other attributes too?

Thursday, June 14, 2012

Why are the trains and buses so crowded?

Photo from Hardwarezone
Singapore's buses and trains are pretty crowded - the crowds at Bishan station in the photo above depicts a typical weekday morning rush hour. Some blame the rising number of foreigners. For instance, one felt that "Singapore is definitely getting more and more crowded with more foreigners coming here. Travelling on the MRT during rush hour has become quite an uncomfortable experience."

While it is true that Singapore's population has grown - the number of people on our island grew 20% in the past 5 years - something deeper is at work here.

Wednesday, June 13, 2012

How big is the "Dragon baby" boom?

A "Dragon baby" is a child born under the Dragon sign of the Chinese Zodiac. Arriving every 12 years, the Dragon year is considered auspicious by many Chinese, and children born that year are believed to be blessed with strength and luck. The New York Times reports that mainland Chinese flock to Hong Kong to escape China's one-child policy, and have Dragon children in Hong Kong. 

This birth spike is not without its problems. BBC News highlights that this creates problems as schools and hospitals are strained to accommodate the birth spike. With fewer places in hospitals, schools and jobs to go around, Dragon children look to face a lifetime of intense competition. Given this, surely some parents would opt to avoid the Dragon year. Is this enough to offset the birth spike?

Tuesday, June 5, 2012

Does economics justify high ministerial salaries?

Singapore ministers are known for drawing the largest salaries amongst politicians around the world - its Prime Minister earns US$1.7m a year, more than four times higher than Barack Obama's relatively paltry US$400,000. One reason, amongst others, is that without high pay, “corruption will set in, and we will become like many other countries, and face the problems that many other countries face,” then Defense Minister Teo Chee Hean told the press in 2007.

This is a contentious issue in Singapore. Opposition member of parliament Low Thia Kiang, in the same year, argued that Finland, Denmark and Switzerland managed to have less corruption with lower pay. Other opinions on the net range from outright disagreement - "you don’t need a ridiculous pay to prevent corruption" - to contemplative acceptance: "the only empirical study of the issue [...] concluded that higher pay was associated with less corruption".

Can economics contribute anything of value to this debate?

Tuesday, May 29, 2012

Cinemas: more crowded, more expensive?

As a student, I used to walk up to the box office with my friends to buy tickets 30-60 minutes before the movie started. These days, I book my tickets hours in advance on the internet, or even a day or two. Is this a matter of cinemas becoming more crowded?

Monday, May 28, 2012

How many Singaporeans spend beyond their means?

In 2008, PM Lee Hsien Loong said that MPs often "see families who have over-committed themselves financially’ – for instance those who have been ‘extravagant in doing up their homes using renovation loans’, or ‘bought expensive furniture or large screen TV sets on hire purchase". He added that some have bought houses that they could not afford as well. Can we put some numbers to this?

Saturday, May 26, 2012

A smaller win for WP: is PAP gaining ground?

Yaw Shin Leong from the Worker's Party (WP) won the Hougang seat during the Singapore General Elections in 2011, but was expelled following reports of personal indiscretions early this year. As a result, a by-election was recently completed, again won by the WP.

However, it is not only about winning or losing, but how the margins have changed for the WP. This year, the WP received 62% of the vote, down from 65% just a year earlier. The PAP candidate, Desmond Choo,   commenting on his 2.7 percentage-point increase in votes, felt that "the process of change has started".

Is this a sign that voter preferences have shifted in favour of the People's Action Party (PAP)?

Wednesday, May 23, 2012

Are Singaporeans paid enough?

For Singaporeans, job satisfaction is not so much about making clients happy or contributing to society than it is about pay, according to the Mercer "Inside Employees' Minds" survey. Since pay matters so much, it is worth asking "are you satisfied with what you're getting?".