- Rewards work like drugs for ADHD - bbc online
- Hulu Selangor: Straight fight now! Zaid Ibrahim vs P Kamalanathan!
- TERKINI : Satu Lawan Satu Di Hulu Selangor
- Caesarrr the malamute!
- What lah!
- “Social trap” from Wikipedia
- “Tit for tat” from Wikipedia
- DAP kepada MCA: Tarik Diri Dari Berkempen!
- Datuk Jema Khan, Can we change?
- Star Awards + Weight Issues
- Prisoner’s dilemma from Wikipedia
- Game theory from Wikipedia
- A Dozen Red Roses
- Choon Kee Hakka Noodle At Jalan Sayur
- Kejadian Ribut di PJS 5 & 6
- Datangmu Tak Diundang, Pergimu Tak Dihalang
- Monty Hall problem from Wikipedia
- Calon Payung Terjun BN, Kamalanathan Tidak Ada Manifesto
- Personal attacks 'not cool' as campaign tool - Umno BANKRUPT of ideas
- Day 3 - Hulu Selangor LIVE - Malaysiakini - www.malaysiakini.com
Posted: 19 Apr 2010 09:00 AM PDT
Behavioural rewards 'work like drugs' for ADHD <!-- S BO --> <!-- S IIMA -->
Stimulant drugs, such as Ritalin, are given to some children with ADHD
<!-- E IIMA --> <!-- S SF -->The brains of children with attention-deficit disorders respond to on-the-spot rewards in the same way as they do to medication, say scientists.A Nottingham University team measured
Posted: 19 Apr 2010 08:59 AM PDT
UPDATED 11.17PM The remaining independent candidate for the by-election Johan Mohd Diah said he will withdraw his candidacy resulting a straight fight between BN and Pakatan.
The remaining independent candidate for the Hulu Selangor parliamentary by-election, Johan Mohd Diah, 31, withdrew his candidacy tonight, resulting in a straight fight between the Barisan Nasional (BN) and Pakatan Rakyat candidates. According to a Bernama report, he signed his withdrawal papers at Hulu Selangor Land and District Office at Kuala Kubu Baru at 9.05 pm. After that, he declined to speak to reporters and left immediately.
Breaking news at Malaysiakini first even though its source was from Bernama. Bernama only published the news at 23:44.
April 19, 2010 23:44 PM
Independent Candidate Johan Md Diah Withdraws
HULU SELANGOR, April 19 (Bernama) -- The by-election for the Hulu Selangor Parliamentary constituency on Sunday will now see a straight fight between the Barisan Nasional (BN) and the Parti Keadilan Rakyat (PKR) after both Independent candidates withdrew Monday.
In the latest development, Johan Md Diah, 31, signed the form to withdraw his candidacy at the Hulu Selangor District and Land Office in Kuala Kubu Baharu, at about 9.05 Monday night.
However, he declined further comment.
Late Monday afternoon, Johan, who is a member of the Shah Alam Umno Youth committee, held a media conference at the Felda Sungai Tengi, Hulu Bernam, near here to explain his willingness to contest in the by-election.
Earlier, Independent candidate V.S.Chandran had withdrawn as a candidate.
This means that P.Kamalanathan (BN) will face Datuk Zaid Ibrahim (PKR).
The by-election is being held following the death of the incumbent representative from the PKR, Datuk Dr Zainal Abidin Ahmad, due to brain cancer on March 25.
Posted: 19 Apr 2010 08:07 AM PDT
Pilihanraya kecil Hulu Selangor 25 April ini akan menyaksikan satu lawan satu, calon PKR, Datuk Zaid Ibrahim akan bertemu dengan Kamalanathan dari BN setelah dua orang calon bebas, VS Chandran dan Johan Mohd Diah telah menarik diri dari bertanding.
Penarikan diri kedua-dua calon itu telah disahkan oleh Timbalan Pengerusi Suruhanjaya Pilihan Raya (SPR), Datuk Wan Ahmad Wan Omar.
Calon Bebas V.S. Chandran menarik diri daripada persaingan pilihan raya kecil kerusi Parlimen Hulu Selangor setelah memfailkan keputusan menarik diri — pada hari ketiga kempen — kira-kira pukul 1 tengah hari ini.
Beliau hadir sendiri di bilik gerakan pilihan raya di Pejabat Daerah Hulu Selangor.
"Tiada kena-mengena dengan MIC tapi kerana BN, kepimpinan Najib," kata beliau sebelum menyerahkan surat menarik diri kepada SPR.
Selepas beberapa jam V.S Chandran, mengumunkan menarik diri daripada pilihan raya kecil Parlimen Hulu Selangor, seorang lagi calon Bebas, Johan Mohd Diah turut mengambil pendirian yang sama, lapor Mstar.
Pemerhati politik berpendapat UMNO BN telah berusaha untuk memastikan kedua-dua calon Bebas menarik diri kerana kedua-dua calon Bebas itu adalah masing-masing ahli MIC dan UMNO di mana undi BN akan berpecah jika mereka teruskan hasrat mereka untuk bertanding di dialam PRK berkenaan.
Selain dari itu, pihak UMNO BN juga telah cuba mendapatkan beberapa orang pemimpin PKR, kecil dan bbesar untuk mengisytiharkan keluar parti.
Taktik-taktik UMNO BN itu, selain dari memperkudakan SPR, adalah diantara taktik kotor dan terdesak UMNO BN bagi memenangi PRK Hulu Selangor ini "at all cost" (dengan apa cara sekalipun) sepertimana taktik mereka merampas kuasa kerajaan Pakatan Rakyat Perak.
Usaha UMNO BN ini dipercayai dilakukan oleh Perdana Menteri sendiri, Najib Tun Razak namun tidak pernah akan mengakui melakukannya.
Posted: 19 Apr 2010 07:45 AM PDT
Posted: 19 Apr 2010 07:39 AM PDT
When I went to visit Ijam at the hospital last week, the nurses seemed to be treating both Ijam and Fuzi well. When one of Fuzi's neighbors came to visit a nephew at the same ward and bumped into Fuzi, Fuzi slowly whispered to the nurse begging her not to tell the neighbor of Ijam's HIV. Fuzi no longer cares that the whole neighborhood knows of her HIV, but she couldn't bear the thought of Ijam's HIV status being known to all and sundry. The nurse assured her that they would never give such info to others. So the neighbor was only told that Ijam was warded because of dengue.
However, when Ijam was transfered to the end room, a single room, I did suspect that they used the room as an isolation room due to Ijam's HIV. Oh well, in a way it was a blessing… I had more privacy to chat with Fuzi when I visited.
Ijam was discharged on Sunday, and so I went to fetch them at the hospital to send them home. It was then that I learnt from Fuzi that other than the isolation room, Ijam was indeed treated differently than the other kids at the pediatric ward.
A few things mentioned by Fuzi caught my attention.
1. While the other kids were served their food in trays, Ijam on the other hand was given "nasi bungkus". In other words, no need to wash the trays he would have been using if his food was served just like the rest.
2. When changing the bed sheets of the pediatric patients in the ward, bare hands were used EXCEPT for Ijam's bed. Before coming in to Ijam's room, they made sure they put on gloves just to change the bed sheet.
3. The nurses advised Fuzi that all the utensils used by Ijam at home be separated from the ones used by his siblings!
Fuzi ended up more confused than ever before! When she and Ijam were initially diagnosed HIV+, the doctors told her not to worry about sharing utensils at home. Now, after she had been mixing all the utensils at home for more than 4 years after diagnosed, they tell her a different story?
"Macam mana ni kak? Betul ke saya kena asingkan pinggan, cawan, semua? Selama ni saya tak pernah asingkan pun! Cakap siapa saya nak ikut ni?!"
"Ikut je cakap doktor!"
Thank goodness the doctors had explained to her earlier about the do's and don'ts. Otherwise, Fuzi would probably panic and send all her children for testing again in case they got infected due to sharing of household utensils! Imagine how Ijam would feel if everything his has to be kept separately, when all his siblings share things at home.
If something is medical-related, people would generally believe the nurses more than they would believe someone like me! Imagine the wrong perceptions they are giving to the public!
And I have been giving talks to the public when the hospital staff themselves need to be given more awareness on HIV!
Posted: 19 Apr 2010 06:40 AM PDT
Social trap is a term used by psychologists to describe a situation in which a group of people act to obtain short-term individual gains, which in the long run leads to a loss for the group as a whole. Examples of social traps include overfishing, the near-extinction of the American bison, energy "brownout" and "blackout" power outages during periods of extreme temperatures, the overgrazing of cattle on the Sahelian Desert, and the destruction of the rainforest by logging interests and agriculture.
Read all here in "Social trap" from Wikipedia
Many economic situations are not zero-sum, since valuable goods and services can be created, destroyed, or badly allocated, and any of these will create a net gain or loss. Assuming the counterparties are acting rationally, any commercial exchange is a non-zero-sum activity, because each party must consider the goods it is receiving as being at least fractionally more valuable than the goods it is delivering. Economic exchanges must benefit both parties enough above the zero-sum such that each party can overcome its transaction costs.
Posted: 19 Apr 2010 06:35 AM PDT
Tit for tat is an English saying meaning "equivalent retaliation". It is also a highly effective strategy in game theory for the iterated prisoner's dilemma. It was first introduced by Anatol Rapoport in Robert Axelrod's two tournaments, held around 1980. An agent using this strategy will initially cooperate, then respond in kind to an opponent's previous action. If the opponent previously was cooperative, the agent is cooperative. If not, the agent is not. This is similar to superrationality and reciprocal altruism in biology.
This strategy is dependent on four conditions that has allowed it to become the most prevalent strategy for the prisoner's dilemma:
In the last condition, the definition of "good chance" depends on the payoff matrix of the prisoner's dilemma. The important thing is that the competition continues long enough for repeated punishment and forgiveness to generate a long-term payoff higher than the possible loss from cooperating initially.
A fifth condition applies to make the competition meaningful: if an agent knows that the next play will be the last, it should naturally defect for a higher score. Similarly if it knows that the next two plays will be the last, it should defect twice, and so on. Therefore the number of competitions must not be known in advance to the agents.
Against a variety of alternative strategies, tit for tat was the most effective, winning in several annual automated tournaments against (generally far more complex) strategies created by teams of computer scientists, economists, and psychologists. Game theorists informally believed the strategy to be optimal (although no proof was presented).
It is important to know that tit for tat still is the most effective strategy if the average performance of each competing team is compared. The team which recently won over a pure tit for tat team only outperformed it with some of their algorithms because they submitted multiple algorithms which would recognize each other and assume a master and slave relationship (one algorithm would "sacrifice" itself and obtain a very poor result for the other algorithm to be able to outperform Tit for Tat on an individual basis, but not as a pair or group). Still, this "group" victory illustrates an important limitation of the Prisoner's Dilemma in representing social reality, namely, that it does not include any natural equivalent for friendship or alliances. The advantage of "tit for tat" thus pertains only to a Hobbesian world of rational solutions, not to a world in which humans are inherently social. However, the fact that this solution does not work effectively against groups of agents running tit-for-tat does illustrate the strengths of tit-for-tat when employed in a team (that the team does better overall, and all the agents on the team do well individually, when every agent cooperates).
READ ALL HERE IN THE, Tit for tat from Wikipedia
Posted: 19 Apr 2010 06:20 AM PDT
Naib Setiausaha Penerangan DAP, Teo Nie Ching (gambar kiri) meminta agar MCA memberi penjelasan - Mengapa menyokong Zaid Ibrahim untuk memansuhkan Akta Keselamatan Dalam Negeri (ISA) pada seketika dahulu, tetapi kini pula berhempas pulas untuk menyingkirkan suara hati dalam arena politik ini?
Pada 12 September 2008, ketika Teresa Kok (EXCO Senior Selangor), Raja Petra Kamaruddin (blogger) dan Tan Hoon Cheng (wartawan Sin Chew Daily) ditangkap di bawah ISA, pimpinan MCA ketika itu seperti Chua Soi Lek (kini Presiden), Donald Lim Siang Chai (kini Naib Presiden), Gan Peng Sieu (kini Naib Presiden) telah tampil ke depan, dan dengan lantangnya bersuara untuk keadilan, menyatakan sokongan kepada pendirian Zaid Ibrahim untuk memansuhkan ISA.
Menurut laporan media, tiga orang pemimpin ini menyatakan pendirian untuk berganding bahu bersama Zaid Ibrahim pada 16 September 2008:
"Keadilan itu melewati kepartian, penahanan tanpa bicara adalah tidak adil, BN harus mengarahkan agar ISA dimansuhkan." (Blog peribadi Chua Soi Lek pada 16 September 2008)
"Saya menggesa agar kerajaan mengkaji dan memansuhkan ISA dengan segera, malah saya menyokong dan memuji pendirian Menteri Jabatan Perdana Menteri, Zaid Ibrahim, iaitu menggesa agar kerajaan membebaskan Teresa Kok dan Raja Petra Kamaruddin, dan menggunakan saluran perundangan yang lain untuk menyelesaikan kes ini. (Donald Lim, laporan Malaysiakini, 16 September 2008)
"Pemuda MCA akan menyokong sepenuhnya pendirian Zaid Ibrahim dalam isu ISA, malah menyeru agar pihak berkenaan mengkaji semua undang-undang preemption." (Gan Peng Sieu, laporan Sinchew Daily, 16 September 2008)
Teo Nie Ching menggesa agar pemimpin MCA memberi penjelasan dalam tempoh 48 jam - Mengapa mereka menyokong sepenuhnya Zaid Ibrahim pada ketika itu, namun kini pula mengerah tenaga ahli MCA di Hulu Selangor, untuk menyokong calon MIC yang mengangguk kepada ISA, dan bermusuhan dengan Zaid Ibrahim?
Teo Nie Ching menegaskan, seandainya Chua Soi Lek, Donald Lim dan Gan Ping Sieu gagal memberi penjelasan dalam masa 48 jam, maka MCA seharusnya menarik diri tanpa syarat dari kempen untuk BN, keluar dari Hulu Selangor, untuk membuktikan bahawa pendirian MCA dalam pemansuhan ISA dan sokongan terhadap Zaid Ibrahim berkekalan!
*Teo Nie Ching ialah Naib Setiausaha Penerangan DAP merangkap ahli parlimen Serdang. Diterjemah dari kenyataan asal dalam bahasa Cina. -MR
Posted: 19 Apr 2010 05:10 AM PDT
Malaysian Insider ; Datuk Jema Khan, "Can we change? "
Imagine you are in a game show. The game show host asks you as a contestant to pick one of three doors to win the prize which is a new Mercedes Benz. Behind two of the three doors are goats which you do not want to win: only one door has the Mercedes. The game show hosts knows where the goats and the Mercedes are.
You pick door A. The game show hosts opens door C and shows you a goat behind it. The host then asks you if you want to change your choice to door B. You reason that your chances of getting the Mercedes was one in three before and since he has opened the door C to show you a goat, your chances are now 1 in 2 to win the Mercedes. The host maybe trying to trick you to change so you decide you will stick with door A since the probability of winning the Mercedes is the same with either door A or B.
In my experience in posing the above question to friends (which incidentally is called "The Monty Hall Paradox"), the vast majority would stick with their initial pick and would not change.
It occurred to me that having made a choice, we human beings are reluctant to change our initial guess. In fact we will try to stick to our initial choice if we surmise that the probability of success is the same either way. It seems to be hardwired into our psyche.
It is the same with supporters of football clubs: the supporters will support their club of choice regardless. It is as though loyalty is prized over all else in respect of supporters of football clubs.
I even have friends in London who will bring their young children to support Arsenal and try to ensure that their offspring will be Arsenal supporters for life as they have been. It is as though if you are from North London, it is practically frowned upon to support any other football club.
Personally, I don't subscribe to this type of blind loyalty in sports. After all if I am a spectator, it is for the players to entertain me and not for me to commit to them. However I suppose I would miss out on all the camaraderie that goes with blind loyalty to a team.
There are similar elements at play in politics too. The established political parties will espouse loyalty of their party members as a virtue second to none. If you are a member of a party, it is expected that you, at least, will vote for it.
It is not an unreasonable assumption under normal conditions but the last general election showed that in a number of areas, the votes obtained by a party were less than its registered members in that area. It was seen as a change in the political dynamics in Malaysia.
I believe the next general election will be determined very much by the young and new voters. It is not so much that die hard supporters of the various parties change allegiances as who the new voters will vote for as their party of choice. I don't believe that the older voters will be a significant influence on the new voters. In fact I think most of the established parties are all trying to figure out what appeals to these new voters who are influenced by the internet age of the 21st century.
The new voters will find it increasingly difficult to swallow the various dictates of the established parties.
In respect of the original question of the game show, you should always change your initial choice because the probability is not the same.
If you chose door A and never changed your choice after being shown door C with a goat,
Posted: 19 Apr 2010 05:07 AM PDT
By chance, do anyone think that Felicia Chin's shoulders/arms looks too skinny?
She seems to have my ideal shoulders and arms that I would like.
Hmmm.. now… how should I about achieving that?
I know I'm not supposed to reproduce the above picture. But I want to share with everyone about the above picture.
Nicky says she's too skinny, malnutrition-ed. People MY size is then the "better" choice. AH.
I STILL LIKE HER SHOULDERS LEH!
But, Jacqueline can't resist food! She gets so easily tempted by foood! I bet you could bribe her next time just with her favourite food!
Well, Joanna is finally back from her "Chicken Pox" vacation. 2 weeks leh! SHIOK NOT?! Then I commented that she look like she lost weight after the 2 weeks. And we went on and on.. to talk about weight.
Primary 1. I was 123cm and weighs 23kg.
Next stage to secondary school!
Next my polytechnic years! No PE lessons to measure. We shall take the last measurement.
And Joanna was like saying there's a pattern to my weight!
And Shelin told me, weight taken right when you wake up is the most accurate! And that means, I AM ONLY 52KG LEH! (Breakfast makes me fatter by 3kg!)
Which is true! Secondary school, I was 48kg. I skipped breakfast and recess. I went home weighing a mere 45kg!
Previously I was soon-to-be underweight now I am HEALTHY range okay!
Filed under: Daily Reports, Entertainment, School Days, The Man She Loved
Posted: 19 Apr 2010 03:16 AM PDT
The prisoner's dilemma is a fundamental problem in game theory that demonstrates why two people might not cooperate even if it is in both their best interests to do so. It was originally framed by Merrill Flood and Melvin Dresher working at RAND in 1950. Albert W. Tucker formalized the game with prison sentence payoffs and gave it the "prisoner's dilemma" name (Poundstone, 1992).
A classic example of the prisoner's dilemma ("PD") is presented as follows:
If we assume that each player cares only about minimizing his or her own time in jail, then the prisoner's dilemma forms a non-zero-sum game in which two players may each cooperate with or defect from (betray) the other player. In this game, as in most game theory, the only concern of each individual player (prisoner) is maximizing his or her own payoff, without any concern for the other player's payoff. The unique equilibrium for this game is a Pareto-suboptimal solution, that is, rational choice leads the two players to both play defect, even though each player's individual reward would be greater if they both played cooperatively.
In the classic form of this game, cooperating is strictly dominated by defecting, so that the only possible equilibrium for the game is for all players to defect. No matter what the other player does, one player will always gain a greater payoff by playing defect. Since in any situation playing defect is more beneficial than cooperating, all rational players will play defect, all things being equal.
In the iterated prisoner's dilemma, the game is played repeatedly. Thus each player has an opportunity to punish the other player for previous non-cooperative play. If the number of steps is known by both players in advance, economic theory says that the two players should defect again and again, no matter how many times the game is played. However, this analysis fails to predict the behavior of human players in a real iterated prisoners dilemma situation, and it also fails to predict the optimum algorithm when computer programs play in a tournament. Only when the players play an indefinite or random number of times can cooperation be an equilibrium, technically a subgame perfect equilibrium meaning that both players defecting always remains an equilibrium and there are many other equilibrium outcomes. In this case, the incentive to defect can be overcome by the threat of punishment.
In casual usage, the label "prisoner's dilemma" may be applied to situations not strictly matching the formal criteria of the classic or iterative games, for instance, those in which two entities could gain important benefits from cooperating or suffer from the failure to do so, but find it merely difficult or expensive, not necessarily impossible, to coordinate their activities to achieve cooperation.
These particular examples, involving prisoners and bag switching and so forth, may seem contrived, but there are in fact many examples in human interaction as well as interactions in nature that have the same payoff matrix. The prisoner's dilemma is therefore of interest to the social sciences such as economics, politics and sociology, as well as to the biological sciences such as ethology and evolutionary biology. Many natural processes have been abstracted into models in which living beings are engaged in endless games of prisoner's dilemma. This wide applicability of the PD gives the game its substantial importance.
In political science, for instance, the PD scenario is often used to illustrate the problem of two states engaged in an arms race. Both will reason that they have two options, either to increase military expenditure or to make an agreement to reduce weapons. Either state will benefit from military expansion regardless of what the other state does; therefore, they both incline towards military expansion. The paradox is that both states are acting rationally, but producing an apparently irrational result. This could be considered a corollary to deterrence theory.
In environmental studies, the PD is evident in crises such as global climate change. All countries will benefit from a stable climate, but any single country is often hesitant to curb CO2 emissions. The benefit to an individual country to maintain current behavior is greater than the benefit to all countries if behavior was changed, therefore explaining the current impasse concerning climate change.
In program management and technology development, the PD applies to the relationship between the customer and the developer. Capt Dan Ward, an officer in the US Air Force, examined The Program Manager's Dilemma in an article published in Defense AT&L, a defense technology journal.
In social science
In sociology or criminology, the PD may be applied to an actual dilemma facing two inmates. The game theorist Marek Kaminski, a former political prisoner, analysed the factors contributing to payoffs in the game set up by a prosecutor for arrested defendants (see references below). He concluded that while the PD is the ideal game of a prosecutor, numerous factors may strongly affect the payoffs and potentially change the properties of the game.
The prisoner's dilemma applies to the decision whether or not to use performance enhancing drugs in athletics. Given that the drugs have an approximately equal impact on each athlete, it is to all athletes' advantage that no athlete take the drugs (because of the side effects). However, if any one athlete takes the drugs, they will gain an advantage unless all the other athletes do the same. In that case, the advantage of taking the drugs is removed, but the disadvantages (side effects) remain.
Advertising is sometimes cited as a real life example of the prisoner's dilemma. When cigarette advertising was legal in the United States, competing cigarette manufacturers had to decide how much money to spend on advertising. The effectiveness of Firm A's advertising was partially determined by the advertising conducted by Firm B. Likewise, the profit derived from advertising for Firm B is affected by the advertising conducted by Firm A. If both Firm A and Firm B chose to advertise during a given period the advertising cancels out, receipts remain constant, and expenses increase due to the cost of advertising. Both firms would benefit from a reduction in advertising. However, should Firm B choose not to advertise, Firm A could benefit greatly by advertising. Nevertheless, the optimal amount of advertising by one firm depends on how much advertising the other undertakes. As the best strategy is dependent on what the other firm chooses there is no dominant strategy and this is not a prisoner's dilemma but rather is an example of a stag hunt. The outcome is similar, though, in that both firms would be better off were they to advertise less than in the equilibrium. Sometimes cooperative behaviors do emerge in business situations. For instance, cigarette manufacturers endorsed the creation of laws banning cigarette advertising, understanding that this would reduce costs and increase profits across the industry. This analysis is likely to be pertinent in many other business situations involving advertising.
Without enforceable agreements, members of a cartel are also involved in a (multi-player) prisoners' dilemma. 'Cooperating' typically means keeping prices at a pre-agreed minimum level. 'Defecting' means selling under this minimum level, instantly stealing business (and profits) from other cartel members. Anti-trust authorities want potential cartel members to mutually defect, ensuring the lowest possible prices for consumers.
The theoretical conclusion of PD is one reason why, in many countries, plea bargaining is forbidden. Often, precisely the PD scenario applies: it is in the interest of both suspects to confess and testify against the other prisoner/suspect, even if each is innocent of the alleged crime. Arguably, the worst case is when only one party is guilty — here, the innocent one is unlikely to confess, while the guilty one is likely to confess and testify against the innocent.
Many real-life dilemmas involve multiple players. Although metaphorical, Hardin's tragedy of the commons may be viewed as an example of a multi-player generalization of the PD: Each villager makes a choice for personal gain or restraint. The collective reward for unanimous (or even frequent) defection is very low payoffs (representing the destruction of the "commons"). Such multi-player PDs are not formal as they can always be decomposed into a set of classical two-player games. The commons are not always exploited: William Poundstone, in a book about the prisoner's dilemma (see References below), describes a situation in New Zealand where newspaper boxes are left unlocked. It is possible for people to take a paper without paying (defecting) but very few do, feeling that if they do not pay then neither will others, destroying the system.
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Posted: 19 Apr 2010 03:09 AM PDT
Game theory is a branch of applied mathematics that is used in the social sciences, most notably in economics, as well as in biology (most notably evolutionary biology and ecology), engineering, political science, international relations, computer science, and philosophy. Game theory attempts to mathematically capture behavior in strategic situations, in which an individual's success in making choices depends on the choices of others. While initially developed to analyze competitions in which one individual does better at another's expense (zero sum games), it has been expanded to treat a wide class of interactions, which are classified according to several criteria. Today, "game theory is a sort of umbrella or 'unified field' theory for the rational side of social science, where 'social' is interpreted broadly, to include human as well as non-human players (computers, animals, plants)" (Aumann 1987).
Traditional applications of game theory attempt to find equilibria in these games. In an equilibrium, each player of the game has adopted a strategy that they are unlikely to change. Many equilibrium concepts have been developed (most famously the Nash equilibrium) in an attempt to capture this idea. These equilibrium concepts are motivated differently depending on the field of application, although they often overlap or coincide. This methodology is not without criticism, and debates continue over the appropriateness of particular equilibrium concepts, the appropriateness of equilibria altogether, and the usefulness of mathematical models more generally.
Although some developments occurred before it, the field of game theory came into being with the 1944 book Theory of Games and Economic Behavior by John von Neumann and Oskar Morgenstern. This theory was developed extensively in the 1950s by many scholars. Game theory was later explicitly applied to biology in the 1970s, although similar developments go back at least as far as the 1930s. Game theory has been widely recognized as an important tool in many fields. Eight game theorists have won the Nobel Memorial Prize in Economic Sciences, and John Maynard Smith was awarded the Crafoord Prize for his application of game theory to biology.
4. See also 2
Posted: 19 Apr 2010 02:53 AM PDT
One thing that can always make a lady smile. One thing that can always make her spirits high. Is something so pure and strictly simple. They are the marvel from our nature, the splendor of magic in a thing called flowers.
Be it a bouquet of exotic orchids, which is glorious and cost a fortune, or a garland of lilies, that is so delicate and yet so stunning, or a single hibiscus that her son picks from the garden, soon wither and fade but never in her heart. A flower gathers happiness around. Its bloom brings joy and spread love like petals in the wind.
Today I receive a dozen roses. So beautiful they are, so red with passion. You might not know what it meant to me, but these roses fill my heart with so much glee.
Thank you, Azman.. I am so happy!
Posted: 19 Apr 2010 02:40 AM PDT
Choon Kee Hakka noodle at Jalan Sayur, Pudu.
I woke up early last Saturday. Well, waking up at 9 am is early for me on weekends. Wuan was about to go to the Pudu market to buy shrimps for the arowana. Since I was already awake, I offered to drive her. As we circled around to look for parking, we got hungry. Wuan suggested that we check out the hakka noodle at Jalan Sayur. I readily agreed since I did not get to taste the noodle from this seemingly popular stall the last time we were there.
The stall shares the end lot with a few other stalls in a row of zinc roofed shops by the junction of Jalan Sayur and Jalan Pudu. These shops must have been there for as long as anyone can remember. They are what food courts are like 80 years ago. Two banners, one in Chinese the other English, hanging from the roof inform customers that they are opened from 6 am to 10 pm and tells a brief history of the stall. They have been selling hakka noodle since 1931 and that the fourth generation is running the business now.
While it is popularly known as hakka noodle, the yellow-coloured signboard at the shop says "Da Pu Mian". The Chinese characters on the glass surface of the stall says "Chun Ji Da Pu Mian". "Chun" is the name of the stall, usually the owner's. The suffix "ji" denotes that it is an eatery. "Da Pu" is a town in the Guandong Province in China with a predominant Hakka population. "Mian" means noodle. This place is so rich in heritage that its history is worth chronicling, especially the stalls that have been operating in the same location for nearly one century already.
The yellow signboard and the red Chinese words on the stall says "Chun Ji Da Pu Mian".
There were several groups of young people mingling around the stall. I thought they were waiting in queue. I did not fancy waiting for thirty minutes again. It turned out that there was a tuition centre nearby and the group of teenagers were waiting for their classes to begin. Wuan spotted an empty table right beside the stall and we quickly made our way there.
While I settled down, Wuan went to stand in line to order. One of the helpers told Wuan that he would come to the table to take our orders. Anticipating a long wait, Wuan went off to the market to buy the shrimps. From where I was, I could observe the activity of the middle-aged couple manning the stall. The man cooked the noodles while the woman added minced meat, char siu and vegetables to complete the orders.
I was impressed with the couple's memory as they both could remember at least ten orders in succession and prepare them accordingly. First, one could order small, medium or large portions of either noodles or lou shi fun. Some of the customers wanted extra mince meat while others wanted extra wantans. All those they could remember. While they were taking orders, their hands never stopped working.
Choon Kee Hakka noodle at Jalan Sayur, Pudu.
There was an unending stream of customers queuing up for take-away and a similar queue of customers waiting for tables. After a twenty-minute wait, the man cooking the noodles asked for my order. Five minutes later, our two small portions came with a bowl of three wantan dumplings each. Minced pork and char siu were piled on top of the noodles together with choy sum and garnished with spring onion. It was a pleasant surprise when I found some bak eu pok (crispy pork lard) together with the minced meat. The little bits of crispy pork lard enhanced the taste and aroma of the noodle.
A small portion of noodle costs RM4.00, medium RM4.40 and large RM4.60. I would say the price is reasonable. Wuan and I were pretty full afterwards. The half-hour wait was worth it. The noodle, minced pork, char siu and wantan dumplings were all nicely done. The plus point is that the place is accessible by wheelchair from the car park although there is no accessible parking. By the way, parking at Jalan Sayur costs RM2 per entry. I am definitely going back for seconds and thirds and more. No doubt about that.
Choon Kee Hakka Noodle at Jalan Sayur, Pudu.
Hakka noodle topped with minced pork, char siu, choy sum and spring onion at Choon Kee.
The bowl of wantan dumplings that came with the Hakka noodle at Choon Kee.
Posted: 19 Apr 2010 02:24 AM PDT
Pada Sabtu lepas beberapa kawasan di Petaling Jaya dilanda ribut yang agak dasyat, termasuk di PJS 5 dan PJS 6 Desa Mentari.
Saya sempat menziarah tapak kejadian bersama Sdr Halimey Abu Bakar Ahli Majlis MBPJ serta anggota MPP sebaik sahaja selepas ribut melanda. Saya turun ke Blok 2, Blok 3 dan Blok 8 Desa Mentari serta Kg. Lindungan (termasuk Masjid Kg. Lindungan) sekitar jam 6.15 petang.
Saya terus menelefon Dato' Zulkepli Ahmad, Pegawai Daerah Petaling selaku Pengerusi Jawatankuasa Bencana Daerah dan Tengku Nazaruddin Tengku Zainuddin, Pegawai Biro Aduan MBPJ. Tidak lama kemudian pasukan Quick Response Team MBPJ turun ke tapak kejadian.
Kesan ribut tersebut pokok, papan iklan dan khemah tumbang manakala bumbung terbang. Beberapa kereta ditimpa pokok. Cermin kereta pecah akibat bumbung terbang.
Saya beredar menjelang waktu Isyak. Tuan Syed Shahir Mohamud, Ketua Cabang Keadilan Kelana Jaya pula menziarah tapak kejadian.
Semalam Sdr Halimey mengadakan majlis dialog dengan mangsa kejadian bersama-sama Pejabat ADUN, Pejabat Daerah Petaling, Jabatan Kebajikan Masyarakat, Majlis Bandaraya Petaling Jaya, Mentari Corporation dan PKNS.
Saya baru sahaja mengadakan mesyuarat bagi menyelaraskan tindakan sebentar tadi bersama semua badan-badan tersebut. Saya meminta agar tindakan segera diambil bagi meringankan sedikit bebanan mangsa.
Penduduk boleh menghubungi Sdr. Suhaimi Mohd Khairi, Pembantu Khas Kawasan saya di 0122180590 untuk mendapat maklumat lanjut.
Gambar-gambar boleh dilihat di sini.
Posted: 19 Apr 2010 06:16 AM PDT
Kami telah jangkakan beliau keluar parti, sebab itu kami tidak memilihnya sebagai calon".
Ia adalah reaksi spontan dari Parti Keadilan Rakyat (PKR) selepas Bendahari PKR Hulu Selangor, Dr Halili Rahmat (gambar) mengumumkan keluar daripada parti itu dan menyertai Umno.
"Kami telah menjalankan kaji selidik mengenai latar belakang dan kami dapati beliau bukan seorang calon yang baik. Kenapa bukan calon yang baik? ..saya tidak bercadang mendedahkannya. Sebab itu kenapa kami tidak memilihnya," kata ketua penerangan PKR, Latheefa Koya.
Latheefa berkata, mereka sudah mendengar khabar angin bahawa pakar bedah itu mahu keluar daripada parti itu apabila bekas Menteri di Jabatan Perdana Menteri, Datuk Zaid Ibrahim diumumkan sebagai calon parti bagi pilihan raya kecil ini Selasa lalu.
"Kami tidak terkejut. Jadi kami telah membuat keputusan yang tepat untuk tidak memilih beliau," katanya di Kuala Kubu Baru di sini hari ini.
Dr Halili, anak jati Hulu Yam di sini dan pernah menjadi doktor peribadi kepada Penasihat PKR, Datuk Seri Anwar Ibrahim, berhasrat untuk bertanding dalam pilihan raya kecil tetapi sebaliknya kepimpinan parti itu memilih Zaid.
Keputusan Dr Halili itu adalah perkembangan terbaru dalam rentetan tindakan pemimpin bahagian dan wakil rakyat PKR untuk keluar parti itu tahun ini.
Bagaimanapun, Latheefa berkata, tindakan keluar parti itu tidak memberi sebarang kesan kepada PKR dalam menghadapi pilihan raya kecil Hulu Selangor. - Bernama
Posted: 19 Apr 2010 01:26 AM PDT
The Monty Hall problem is a probability puzzle based on the American television game show Let's Make a Deal. The name comes from the show's host, Monty Hall. The problem is also called the Monty Hall paradox, as it is a veridical paradox in that the result appears absurd but is demonstrably true.
A well-known statement of the problem was published in Parade magazine:
As the player cannot be certain which of the two remaining unopened doors is the winning door, most people assume that each of these doors has an equal probability and conclude that switching does not matter. In fact, in the usual interpretation of the problem the player should switch—doing so doubles the probability of winning the car, from 1/3 to 2/3.
When the above statement of the problem and the solution appeared in Parade, approximately 10,000 readers, including nearly 1,000 with PhDs, wrote to the magazine claiming the published solution was wrong. Some critics pointed out that the Parade version of the problem leaves certain aspects of the host's behavior unstated, for example, whether the host must open a door and must make the offer to switch. However, such possible behaviors had little or nothing to do with the controversy that arose (vos Savant 1990), and the intended behavior was clearly implied by the author (Seymann 1991). More general interpretations of the problem in which, for example, the host may sometimes reveal the car, have been discussed in mathematical literature.
The Monty Hall problem, in one of its common formulations, is mathematically equivalent to the earlier Three Prisoners problem, and both bear some similarity to the much older Bertrand's box paradox. These and other problems involving unequal distributions of probability are notoriously difficult for people to solve correctly, and have led to numerous psychological studies that address how the problems are perceived. Even when given a completely unambiguous statement of the Monty Hall problem, explanations, simulations, and formal mathematical proofs, many people still meet the correct answer with disbelief.
Steve Selvin wrote a letter to the American Statistician in 1975 describing a problem loosely based on the game show Let's Make a Deal (Selvin 1975a). In a subsequent letter he dubbed it the "Monty Hall problem" (Selvin 1975b). In one of its mathematical formulations (the so-called conditional version, see below), the problem is mathematically equivalent (Morgan et al., 1991) to the Three Prisoners Problem described in Martin Gardner's Mathematical Games column in Scientific American in 1959 (Gardner 1959a).
There are certain ambiguities in this formulation of the problem: it is unclear whether or not the host would always open another door, always offer a choice to switch, or even whether he would ever open the door revealing the car (Mueser and Granberg 1999). However, the common interpretation is to suppose that the host is constrained always to open a door revealing a goat and always to make the offer to switch, and that the initial choice of the player is correct with probability 1/3. It is common to suppose that the host opens one of the remaining two doors perfectly randomly (i.e., with equal probabilities) if the player initially picked the car (Barbeau 2000:87).
Without a clear understanding of the precise intent of the questioner, there can be no single correct solution to any problem (Seymann 1991). The following unambiguous formulation represents what, according to Krauss and Wang (2003:10), people generally assume the mathematically explicit question to be:
We also need to assume that winning a car is preferable to winning a goat for the contestant.
The player, having chosen a door, has a 1/3 chance of having the car behind the chosen door and a 2/3 chance that it's behind one of the other doors. As the host opening a door to reveal a goat gives the player no new information about what is behind the door he has chosen, the probability of there being a car remains 1/3. The new information from the host tell us only that there is a 0/3 chance of the car being behind the revealed door. Therefore, a 2/3 chance remains that the car is behind the other unopened door (Wheeler 1991; Schwager 1994). Switching doors thus wins the car with a probability of 2/3, so the player should switch (Wheeler 1991; Mack 1992; Schwager 1994; vos Savant 1996:8; Martin 2002).
In order to convert this popular story into a mathematically rigorous solution, one has to argue why the probability that the car is behind door 1 does not change on opening door 2 or 3. This can be answered by an appeal to symmetry: under the complete assumptions made above, nothing is changed in the problem if we renumber the doors arbitrarily, and in particular, if we switch numbers 2 and 3. Therefore, the conditional probability that the car is behind door 1, given the player chose 1 and Monty opened 2, is the same as the conditional probability that the car is behind door 1, given the player chose 1 and Monty opened 3. The average of these two (equal) probabilities is 1/3, hence each of them separately is 1/3, too.
The analysis can be illustrated in terms of the equally likely events that the player has initially chosen the car, goat A, or goat B (Economist 1999):
The above diagram shows that a player who switches always gets the opposite of their original choice, and since the probability of that choice being a goat is twice that of being a car, it is always advantageous to switch. In other words, the probability of originally choosing a goat is 2/3 and the probability of originally choosing the car is 1/3. Once Monty Hall has removed a "goat door," the contestant who initially chose the door with a goat behind it will necessarily win the car, and the contestant who originally chose the door in front of the car will necessarily "win" the goat. Because the chances are 2/3 of being a contestant who originally chose a goat, probability will always favor switching choices.
Another way to understand the solution is to consider the two original unchosen doors together. Instead of one door being opened and shown to be a losing door, an equivalent action is to combine the two unchosen doors into one since the player cannot choose the opened door (Adams 1990; Devlin 2003; Williams 2004; Stibel et al., 2008).
As Cecil Adams puts it (Adams 1990), "Monty is saying in effect: you can keep your one door or you can have the other two doors." The player therefore has the choice of either sticking with the original choice of door, or choosing the sum of the contents of the two other doors, as the 2/3 chance of hiding the car hasn't been changed by the opening of one of these doors.
As Keith Devlin says (Devlin 2003), "By opening his door, Monty is saying to the contestant 'There are two doors you did not choose, and the probability that the prize is behind one of them is 2/3. I'll help you by using my knowledge of where the prize is to open one of those two doors to show you that it does not hide the prize. You can now take advantage of this additional information. Your choice of door A has a chance of 1 in 3 of being the winner. I have not changed that. But by eliminating door C, I have shown you that the probability that door B hides the prize is 2 in 3.'"
Morgan et al. (1991) state that many popular solutions are incomplete, because they do not explicitly address their interpretation of Whitaker's original question (Seymann), which is the specific case of a player who has picked Door 1 and has then seen the host open Door 3. These solutions correctly show that the probability of winning for all players who switch is 2/3, but without certain assumptions this does not necessarily mean the probability of winning by switching is 2/3 given which door the player has chosen and which door the host opens. This probability is a conditional probability (Morgan et al. 1991; Gillman 1992; Grinstead and Snell 2006:137; Gill 2009b). The difference is whether the analysis is of the average probability over all possible combinations of initial player choice and door the host opens, or of only one specific case—for example the case where the player picks Door 1 and the host opens Door 3. Another way to express the difference is whether the player must decide to switch before the host opens a door or is allowed to decide after seeing which door the host opens (Gillman 1992). Although these two probabilities are both 2/3 for the unambiguous problem statement presented above, the conditional probability may differ from the overall probability and either or both may not be able to be determined depending on the exact formulation of the problem (Gill 2009b).
The conditional probability of winning by switching given which door the host opens can be determined referring to the expanded figure below, or to an equivalent decision tree as shown to the right (Chun 1991; Grinstead and Snell 2006:137-138), or formally derived as in the mathematical formulation section below. For example, if the host opens Door 3 and the player switches, the player wins with overall probability 1/3 if the car is behind Door 2 and loses with overall probability 1/6 if the car is behind Door 1—the possibilities involving the host opening Door 2 do not apply. To convert these to conditional probabilities they are divided by their sum, so the conditional probability of winning by switching given the player picks Door 1 and the host opens Door 3 is (1/3)/(1/3 + 1/6), which is 2/3. This analysis depends on the constraint in the explicit problem statement that the host chooses randomly which door to open after the player has initially selected the car.
The above solution may be formally proven using Bayes' theorem, similar to Gill, 2002, Henze, 1997 and many others. Different authors use different formal notations, but the one below may be regarded as typical. Consider the discrete random variables:
As the host's placement of the car is random, all values of C are equally likely. The initial (unconditional) probability of C is then
The host's behavior is reflected by the values of the conditional probability of H given C and S:
The player can then use Bayes' rule to compute the probability of finding the car behind any door, after the initial selection and the host's opening of one. This is the conditional probability of C given H and S:
where the denominator is computed as the marginal probability
Thus, if the player initially selects Door 1, and the host opens Door 3, the probability of winning by switching is
Sources of confusion
When first presented with the Monty Hall problem an overwhelming majority of people assume that each door has an equal probability and conclude that switching does not matter (Mueser and Granberg, 1999). Out of 228 subjects in one study, only 13% chose to switch (Granberg and Brown, 1995:713). In her book The Power of Logical Thinking, vos Savant (1996:15) quotes cognitive psychologist Massimo Piattelli-Palmarini as saying "… no other statistical puzzle comes so close to fooling all the people all the time" and "that even Nobel physicists systematically give the wrong answer, and that they insist on it, and they are ready to berate in print those who propose the right answer."
Most statements of the problem, notably the one in Parade Magazine, do not match the rules of the actual game show (Krauss and Wang, 2003:9), and do not fully specify the host's behavior or that the car's location is randomly selected (Granberg and Brown, 1995:712). Krauss and Wang (2003:10) conjecture that people make the standard assumptions even if they are not explicitly stated. Although these issues are mathematically significant, even when controlling for these factors nearly all people still think each of the two unopened doors has an equal probability and conclude switching does not matter (Mueser and Granberg, 1999). This "equal probability" assumption is a deeply rooted intuition (Falk 1992:202). People strongly tend to think probability is evenly distributed across as many unknowns as are present, whether it is or not (Fox and Levav, 2004:637).
A competing deeply rooted intuition at work in the Monty Hall problem is the belief that exposing information that is already known does not affect probabilities (Falk 1992:207). This intuition is the basis of solutions to the problem that assert the host's action of opening a door does not change the player's initial 1/3 chance of selecting the car. For the fully explicit problem this intuition leads to the correct numerical answer, 2/3 chance of winning the car by switching, but leads to the same solution for slightly modified problems where this answer is not correct (Falk 1992:207).
According to Morgan et al. (1991) "The distinction between the conditional and unconditional situations here seems to confound many." That is, they, and some others, interpret the usual wording of the problem statement as asking about the conditional probability of winning given which door is opened by the host, as opposed to the overall or unconditional probability. These are mathematically different questions and can have different answers depending on how the host chooses which door to open when the player's initial choice is the car (Morgan et al., 1991; Gillman 1992). For example, if the host opens Door 3 whenever possible then the probability of winning by switching for players initially choosing Door 1 is 2/3 overall, but only 1/2 if the host opens Door 3. In its usual form the problem statement does not specify this detail of the host's behavior, nor make clear whether a conditional or an unconditional answer is required, making the answer that switching wins the car with probability 2/3 equally vague. Many commonly presented solutions address the unconditional probability, ignoring which door was chosen by the player and which door opened by the host; Morgan et al. call these "false solutions" (1991). Others, such as Behrends (2008), conclude that "One must consider the matter with care to see that both analyses are correct."
Aids to understanding
Why the probability is not 1/2
The contestant has a 1 in 3 chance of selecting the car door in the first round. Then, from the set of two unselected doors, Monty Hall non-randomly removes a door that he knows is a goat door. If the contestant originally chose the car door (1/3 of the time) then the remaining door will contain a goat. If the contestant chose a goat door (the other 2/3 of the time) then the remaining door will contain the car.
The critical fact is that Monty does not randomly choose a door – he always chooses a door that he knows contains a goat after the contestant has made their choice. This means that Monty's choice does not affect the original probability that the car is behind the contestant's door. When the contestant is asked if the contestant wants to switch, there is still a 1 in 3 chance that the original choice contains a car and a 2 in 3 chance that the original choice contains a goat. But now, Monty has removed one of the other doors and the door he removed cannot have the car, so the 2 in 3 chance of the contestant's door containing a goat is the same as a 2 in 3 chance of the remaining door having the car.
This is different from a scenario where Monty is choosing his door at random and there is a possibility he will reveal the car. In this instance the revelation of a goat would mean that the chance of the contestant's original choice being the car would go up to 1 in 2. This difference can be demonstrated by contrasting the original problem with a variation that appeared in vos Savant's column in November 2006. In this version, Monty Hall forgets which door hides the car. He opens one of the doors at random and is relieved when a goat is revealed. Asked whether the contestant should switch, vos Savant correctly replied, "If the host is clueless, it makes no difference whether you stay or switch. If he knows, switch" (vos Savant, 2006).
Another way of looking at the situation is to consider that if the contestant chooses to switch then they are effectively getting to see what is behind 2 of the 3 doors, and will win if either one of them has the car. In this situation one of the unchosen doors will have the car 2/3 of the time and the other will have a goat 100% of the time. The fact that Monty Hall shows one of the doors has a goat before the contestant makes the switch is irrelevant, because one of the doors will always have a goat and Monty has chosen it deliberately. The contestant still gets to look behind 2 doors and win if either has the car, it is just confirmed that one of doors will have a goat first.
Increasing the number of doors
It may be easier to appreciate the solution by considering the same problem with 1,000,000 doors instead of just three (vos Savant 1990). In this case there are 999,999 doors with goats behind them and one door with a prize. The player picks a door. The game host then opens 999,998 of the other doors revealing 999,998 goats—imagine the host starting with the first door and going down a line of 1,000,000 doors, opening each one, skipping over only the player's door and one other door. The host then offers the player the chance to switch to the only other unopened door. On average, in 999,999 out of 1,000,000 times the other door will contain the prize, as 999,999 out of 1,000,000 times the player first picked a door with a goat. A rational player should switch. Intuitively speaking, the player should ask how likely is it, that given a million doors, he or she managed to pick the right one. The example can be used to show how the likelihood of success by switching is equal to (1 minus the likelihood of picking correctly the first time) for any given number of doors. It is important to remember, however, that this is based on the assumption that the host knows where the prize is and must not open a door that contains that prize, randomly selecting which other door to leave closed if the contestant manages to select the prize door initially.
This example can also be used to illustrate the opposite situation in which the host does not know where the prize is and opens doors randomly. There is a 999,999/1,000,000 probability that the contestant selects wrong initially, and the prize is behind one of the other doors. If the host goes about randomly opening doors not knowing where the prize is, the probability is likely that the host will reveal the prize before two doors are left (the contestant's choice and one other) to switch between. This is analogous to the game play on another game show, Deal or No Deal; In that game, the contestant chooses a numbered briefcase and then randomly opens the other cases one at a time.
Stibel et al. (2008) propose working memory demand is taxed during the Monty Hall problem and that this forces people to "collapse" their choices into two equally probable options. They report that when increasing the number of options to over 7 choices (7 doors) people tend to switch more often; however most still incorrectly judge the probability of success at 50/50.
A simple way to demonstrate that a switching strategy really does win two out of three times on the average is to simulate the game with playing cards (Gardner 1959b; vos Savant 1996:8). Three cards from an ordinary deck are used to represent the three doors; one 'special' card such as the Ace of Spades should represent the door with the car, and ordinary cards, such as the two red twos, represent the goat doors.
The simulation, using the following procedure, can be repeated several times to simulate multiple rounds of the game. One card is dealt face-down at random to the 'player', to represent the door the player picks initially. Then, looking at the remaining two cards, at least one of which must be a red two, the 'host' discards a red two. If the card remaining in the host's hand is the Ace of Spades, this is recorded as a round where the player would have won by switching; if the host is holding a red two, the round is recorded as one where staying would have won.
By the law of large numbers, this experiment is likely to approximate the probability of winning, and running the experiment over enough rounds should not only verify that the player does win by switching two times out of three, but show why. After one card has been dealt to the player, it is already determined whether switching will win the round for the player; and two times out of three the Ace of Spades is in the host's hand.
If this is not convincing, the simulation can be done with the entire deck, dealing one card to the player and keeping the other 51 (Gardner 1959b; Adams 1990). In this variant the Ace of Spades goes to the host 51 times out of 52, and stays with the host no matter how many non-Ace cards are discarded.
Another simulation, suggested by vos Savant, employs the "host" hiding a penny, representing the car, under one of three cups, representing the doors; or hiding a pea under one of three shells.
Variants – slightly modified problems
Other host behaviors
The version of the Monty Hall problem published in Parade in 1990 did not specifically state that the host would always open another door, or always offer a choice to switch, or even never open the door revealing the car. However, vos Savant made it clear in her second followup column that the intended host's behavior could only be what led to the 2/3 probability she gave as her original answer. "Anything else is a different question" (vos Savant, 1991). "Virtually all of my critics understood the intended scenario. I personally read nearly three thousand letters (out of the many additional thousands that arrived) and found nearly every one insisting simply that because two options remained (or an equivalent error), the chances were even. Very few raised questions about ambiguity, and the letters actually published in the column were not among those few." (vos Savant, 1996) The answer follows if the car is placed randomly behind any door, the host must open a door revealing a goat regardless of the player's initial choice and, if two doors are available, chooses which one to open randomly (Mueser and Granberg, 1999). The table below shows a variety of OTHER possible host behaviors and the impact on the success of switching.
Determining the player's best strategy within a given set of other rules the host must follow is the type of problem studied in game theory. For example, if the host is not required to make the offer to switch the player may suspect the host is malicious and makes the offers more often if the player has initially selected the car. In general, the answer to this sort of question depends on the specific assumptions made about the host's behaviour, and might range from "ignore the host completely" to 'toss a coin and switch if it comes up heads', see the last row of the table below.
Morgan et al. (1991) and Gillman (1992) both show a more general solution where the car is randomly placed but the host is not constrained to pick randomly if the player has initially selected the car, which is how they both interpret the well known statement of the problem in Parade despite the author's disclaimers. Both changed the wording of the Parade version to emphasize that point when they restated the problem. They consider a scenario where the host chooses between revealing two goats with a preference expressed as a probability q, having a value between 0 and 1. If the host picks randomly q would be 1/2 and switching wins with probability 2/3 regardless of which door the host opens. If the player picks Door 1 and the host's preference for Door 3 is q, then in the case where the host opens Door 3 switching wins with probability 1/3 if the car is behind Door 2 and loses with probability (1/3)q if the car is behind Door 1. The conditional probability of winning by switching given the host opens Door 3 is therefore (1/3)/(1/3 + (1/3)q) which simplifies to 1/(1+q). Since q can vary between 0 and 1 this conditional probability can vary between 1/2 and 1. This means even without constraining the host to pick randomly if the player initially selects the car, the player is never worse off switching. However, it is important to note that neither source suggests the player knows what the value of q is, so the player cannot attribute a probability other than the 2/3 that vos Savant assumed was implicit.
D. L. Ferguson (1975 in a letter to Selvin cited in Selvin 1975b) suggests an N door generalization of the original problem in which the host opens p losing doors and then offers the player the opportunity to switch; in this variant switching wins with probability (N−1)/[N(N−p−1)]. If the host opens even a single door the player is better off switching, but the advantage approaches zero as N grows large (Granberg 1996:188). At the other extreme, if the host opens all but one losing door the probability of winning by switching approaches 1.
Bapeswara Rao and Rao (1992) suggest a different N door version where the host opens a losing door different from the player's current pick and gives the player an opportunity to switch after each door is opened until only two doors remain. With four doors the optimal strategy is to pick once and switch only when two doors remain. With N doors this strategy wins with probability (N−1)/N and is asserted to be optimal.
A quantum version of the paradox illustrates some points about the relation between classical or non-quantum information and quantum information, as encoded in the states of quantum mechanical systems. The formulation is loosely based on Quantum game theory. The three doors are replaced by a quantum system allowing three alternatives; opening a door and looking behind it is translated as making a particular measurement. The rules can be stated in this language, and once again the choice for the player is to stick with the initial choice, or change to another "orthogonal" option. The latter strategy turns out to double the chances, just as in the classical case. However, if the show host has not randomized the position of the prize in a fully quantum mechanical way, the player can do even better, and can sometimes even win the prize with certainty (Flitney and Abbott 2002, D'Ariano et al. 2002).
History of the problem
The earliest of several probability puzzles related to the Monty Hall problem is Bertrand's box paradox, posed by Joseph Bertrand in 1889 in his Calcul des probabilités (Barbeau 1993). In this puzzle there are three boxes: a box containing two gold coins, a box with two silver coins, and a box with one of each. After choosing a box at random and withdrawing one coin at random that happens to be a gold coin, the question is what is the probability that the other coin is gold. As in the Monty Hall problem the intuitive answer is 1/2, but the probability is actually 2/3.
The Three Prisoners problem, published in Martin Gardner's Mathematical Games column in Scientific American in 1959 (1959a, 1959b), is isomorphic to the Monty Hall problem. This problem involves three condemned prisoners, a random one of whom has been secretly chosen to be pardoned. One of the prisoners begs the warden to tell him the name of one of the others who will be executed, arguing that this reveals no information about his own fate but increases his chances of being pardoned from 1/3 to 1/2. The warden obliges, (secretly) flipping a coin to decide which name to provide if the prisoner who is asking is the one being pardoned. The question is whether knowing the warden's answer changes the prisoner's chances of being pardoned. This problem is equivalent to the Monty Hall problem; the prisoner asking the question still has a 1/3 chance of being pardoned but his unnamed cohort has a 2/3 chance.
Steve Selvin posed the Monty Hall problem in a pair of letters to the American Statistician in 1975 (1975a, 1975b). The first letter presented the problem in a version close to its presentation in Parade 15 years later. The second appears to be the first use of the term "Monty Hall problem". The problem is actually an extrapolation from the game show. Monty Hall did open a wrong door to build excitement, but offered a known lesser prize—such as $100 cash—rather than a choice to switch doors. As Monty Hall wrote to Selvin:
A version of the problem very similar to the one that appeared three years later in Parade was published in 1987 in the Puzzles section of The Journal of Economic Perspectives (Nalebuff 1987).
Phillip Martin's article in a 1989 issue of Bridge Today magazine titled "The Monty Hall Trap" (Martin 1989) presented Selvin's problem as an example of what Martin calls the probability trap of treating non-random information as if it were random, and relates this to concepts in the game of bridge.
A restated version of Selvin's problem appeared in Marilyn vos Savant's Ask Marilyn question-and-answer column of Parade in September 1990 (vos Savant 1990). Though vos Savant gave the correct answer that switching would win two-thirds of the time, she estimates the magazine received 10,000 letters including close to 1,000 signed by PhDs, many on letterheads of mathematics and science departments, declaring that her solution was wrong (Tierney 1991). Due to the overwhelming response, Parade published an unprecedented four columns on the problem (vos Savant 1996:xv). As a result of the publicity the problem earned the alternative name Marilyn and the Goats.
In November 1990, an equally contentious discussion of vos Savant's article took place in Cecil Adams's column The Straight Dope (Adams 1990). Adams initially answered, incorrectly, that the chances for the two remaining doors must each be one in two. After a reader wrote in to correct the mathematics of Adams' analysis, Adams agreed that mathematically, he had been wrong, but said that the Parade version left critical constraints unstated, and without those constraints, the chances of winning by switching were not necessarily 2/3. Numerous readers, however, wrote in to claim that Adams had been "right the first time" and that the correct chances were one in two.
The Parade column and its response received considerable attention in the press, including a front page story in the New York Times (Tierney 1991) in which Monty Hall himself was interviewed. He appeared to understand the problem, giving the reporter a demonstration with car keys and explaining how actual game play on Let's Make a Deal differed from the rules of the puzzle.
Over 40 papers have been published about this problem in academic journals and the popular press (Mueser and Granberg 1999). Barbeau 2000 contains a survey of the academic literature pertaining to the Monty Hall problem and other closely related problems.
The problem continues to resurface outside of academia. The syndicated NPR program Car Talk featured it as one of their weekly "Puzzlers," and the answer they featured was quite clearly explained as the correct one (Magliozzi and Magliozzi, 1998). An account of the Hungarian mathematician Paul Erdős's first encounter of the problem can be found in The Man Who Loved Only Numbers—like many others, he initially got it wrong. The problem is discussed, from the perspective of a boy with Asperger syndrome, in The Curious Incident of the Dog in the Night-time, a 2003 novel by Mark Haddon. The problem is also addressed in a lecture by the character Charlie Eppes in an episode of the CBS drama NUMB3RS (Episode 1.13) and in Derren Brown's 2006 book Tricks Of The Mind. Penn Jillette explained the Monty Hall Problem on the "Luck" episode of Bob Dylan's Theme Time Radio Hour radio series. The Monty Hall problem appears in the film 21 (Bloch 2008). Economist M. Keith Chen identified a potential flaw in hundreds of experiments related to cognitive dissonance that use an analysis with issues similar to those involved in the Monty Hall problem (Tierney 2008).
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Posted: 19 Apr 2010 01:04 AM PDT
Ahli parlimen Batu Tian Chua mendakwa rakyat Hulu Selangor kecewa kerana calon Barisan Nasional (BN) Hulu Selangor P. Kamalanathan gagal menyediakan sebarang manifiesto dan juga visi kepada mereka.
Menurutnya, Kamalanathan hanya memberi fokus untuk mendekati diri pada rakyat tetapi tidak pula memikirkan perubahan dari segi menyediakan manifiesto baru pada rakyat Hulu Selangor yang sepatutnya lebih diutamakan.
"Kamalanathan tidak mampu menyediakan atau menyatakan apakah dasar yang dapat disumbangkan kepada rakyat hingga sekarang.
"Saya kecewa kerana sehingga sekarang beliau,calon BN Hulu Selangor tidak mempunyai visi ataupun rancangan terbaru yang sepatutnya disediakan pada rakyat," kata Pengarah Strategik PKR itu.
Tian berkata, setiap kali muncul pilihan raya terbaru, BN mula mencetuskan provokasi dengan menjanjikan pelbagai perubahan pada rakyat tetapi tidak pernah ditunaikan.
Tambahan beliau, perubahan yang dijanjikan calon-calon BN semasa pilihan raya adalah dari segi pembangunan baru seperti pembangunan persekolahan, universiti dan sebagainya tetapi ianya hanyalah untuk mengaburi rakyat memilih BN dalam pilihan raya diadakan.
"BN tidak pernah menunaikan apa yang dijanjikan kepada rakyat dan hanya bersandiwara meraih perhatian rakyat bagi memenangi pilihan raya yang diadakan.
"Saya rasa BN perlu rasa malu bersifat pembohong kepada rakyat dengan menaburkan janji-janji manis dan BN akan terus membelakangi rakyat setelah mendapat apa yang diinginkan," katanya lagi.
Beliau berkata, rakyat Hulu Selangor akan terus kecewa jika memilih calon yang tidak mampu memberi sebarang jaminan pada rakyat dan hanya mencari kemenangan untuk kepentingan diri sendiri. -FMT
Posted: 19 Apr 2010 06:35 AM PDT
Penang Chief Minister Lim Guan Eng said if Umno-led Barisan Nasional won the Hulu Selangor parliamentary seat based on the campaign strategy to attack Hulu Selangor PKR candidate Zaid Ibrahim over his past drinking habit, it would be a victory "without morals" and urged the people to respect Zaid's admission of his failings.
He also said Zaid was better than those in Umno who had not repented their shortcomings. Quoting from the Bible, Lim said, "Why punish those who have repented, but not those who have not? Those who wish to cast the first stone must make sure they have not sinned."
Also, why does Umno attack Zaid when it has accepted Chua Soi Lek, the first 'ex-porn star' of BN?! Aiyah, Zaid should have just stayed in Umno. Then, he would have been 'licensed' to drink all he wanted!
Posted: 18 Apr 2010 10:37 PM PDT
LIVE What's happening today in Hulu Selangor? Quotable quotes, planned events, and unplanned occurances as they occur in P. 94.
10.00am: MIC member B Purusothaman said the only way for the party to regain support of the Indian community in Hulu Selangor was for party president S Samy Vellu to step down immediately.
Samy Vellu had previously promised to step down only after 14-months. Purusothaman is a staunch supporter of former party deputy president S Subramaniam, who is Samy Vellu's arch rival.
11.20am: Dr Halili Rahmat (left in pix), a close associate of Anwar Ibrahim, quits PKR and to join Umno. He was the Hulu Selangor PKR division treasurer. Former PKR secretary-general Salehuddin Hashim was present at the press conference held at a hotel in Petaling Jaya.
BN deputy chief Muhyiddin Yassin hinted yesterday that a 'major defection' from PKR would happen.
11.30am: Independent candidate VS Chandran scheduled to call a press conference in Kuala Kubu Baru to announce his withdrawal from the by-election.
11.50am: PKR Youth chief Shamsul Iskandar Akin (centre in pix) lodge report with Election Commission over slanderous banners and billboards, among others, includes doctored picture portraying Zaid Ibrahim consuming alcohol.
12.05pm: In Kuala Kubu Baru, PKR information chief Latheefa Koya brushes off Halili's defection. She said Halili had no principles for defecting because he allegedly was upset after overlooked as the by-election candidate.
"They normally wait for by-elections to jump ship, when the price will be higher."
12.20pm: As promised on the front page of Umno-owned daily Utusan Malaysia, the Gerakan Anti-PKR (right) blog today published a picture of Zaid Ibrahim, portraying him clutching a bottle of whiskey.
No details behind the picture was provided in the blog posting. The picture is believed to be doctored. The blog post also insinuates that PKR vice-president Azmin Ali purposely challenged detractors to 'prove' that Zaid had a drinking problem in order for the picture to surface.
1.15pm: Independent candidate VS Chandran processing documents to withdraw from the Hulu Selangor race.
2.00pm: Domestic Trade, Cooperatives and Consumerism Deputy Minister Tan Lian Hoe to attend ceremony to give out aid to the Orang Asli community at Desa Anggerik, Serendah.
5.00pm: PKR president Dr Wan Azizah Wan Ismail and Zaid Ibrahim's wife will attend hi-tea with women leaders at the party's operation centre in Kuala Kubu Baru.
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