9.9% -- Chance of 84 Successive No-Winner Grand Lotto Draws

According to the Philippine Charity Sweepstakes Office the Jackpot Prize that someone could've won during the 84th Grand Lotto Draw the other day was a whopping 693 million pesos. During the upcoming Draw tonight, the Jackpot is likely to exceed 700 million pesos.  But how likely was this RUN of 84 successive No Winner Draws of the Grand Lotto?  What was the mathematical probability of 84 No Winner Grand Lotto Draws?  I think I can answer this question with a good estimate based on some numbers mentioned by Margie Juico of the PCSO on TV this morning, specifically that there have been 84 Draws since this run began.

First of all, there are 28, 989, 675 possible six number combinations in Grand Lotto 6/55.  

C(6,55)=55!/(6!(49!))=55*54*53*52*51*50*(49!)/(6*5*4*3*2*1)*(49!)=28,989,675

The chance that on any given Draw there will be NO WINNER--depends on what percentage of these nearly 29 million possible combinations are actually placed as 20 peso bets by the Public.  This percentage varies from Draw to Draw. For example when it started as a P30 Million jackpot there were probably much fewer bettors than tonight's Monday Draw which could award a jackpot exceeding P700 Million. 

But what percentage of the 29 million possible 6 number combinations actually ARE placed as bets?

We can estimate the AVERAGE  number of bets placed during each of the last 84 draws from some things that PCSO's chair MARGE JUICO  told ABSCBN's Karen Davila on Headstart this morning.  She said that for each peso bet, 15% goes to PCSO, 30% to Charity and 55% to Jackpots (less 2% to the Operators!). Since the Jackpot is now about P700M after 84 successive no winner Draws (3 times a week since last May), this implies a total of (700million/53%) or 1.32 Billion pesos has been bet since May. Assuming there is negligible duplication of 20 peso bets this means that an AVERAGE of about 780,000 unique bets have been placed during each of the last 84 GrandLotto Draws.  

1.32 billion/(20*84) = 786,163 bets on an "average Draw"

Even though there may now be millions of bets being placed, there were surely far less during the early draws when the Jackpot was much smaller.  

If only 786,163 unique bets out of 28,989,765 are placed on a given Draw, the probability that there will be a winner is

786,16/28,989,765 = 2.7% is the chance of a winner being drawn or 97.3% is the chance of no winner during each draw.

So what are the chances that 84 times in a row, there would be NO WINNER of the Grand Lotto Jackpot? The answer of course is 97.3% raised to the 84th power or 

.973 multiplied by itself 84 times or a slighty improbable 9.9%

Bernas Defends Intent As An Element of Judicial Plagiarism

JOAQUIN BERNAS, S.J. defends the centrality of malicious intent as an element of Judicial Plagiarism in his PDI column, Sounding Board. In the piece About Plagiarism, Fr. Bernas quotes an essay of Margaret Randall's:

In the case of plagiarism, by contrast, Randall asserts, ‘Identifying plagiarism entails ascribing to an agent a series of guilty or fraudulent intentions, the necessity to show intent, in order to establish guilt, or at least degrees of it, is by far the most important of all criteria for establishing plagiarism.’ Intention is relevant not just in the sense that the copying is deliberate, but also in terms of a further intention, sometimes referred to in criminal law as an ulterior intent, to claim the credit by passing [off] the work as one’s own.”

But is intent always required? The author goes on to add: “While some institutional statements explicitly include unintentional copying and non-attribution within their definition of plagiarism, the centrality of the element of deceit or bad faith suggests that, at least outside the academic sphere (where, as Groom observes, the concern is really with cheating rather than plagiarism in its literary or artistic context) intention should be key to a charge of plagiarism.”

I actually like the idea of making intent central to Judicial Plagiarism.

In doing so, Fr. Bernas in effect, chains the tenant Justices of the Supreme Court to a Ticking Nuclear Bomb which will explode if malicious intent ever IS proved. For example: if a PATTERN of PLAGIARISM should ever be established in their recent jurisprudence. In their Compliance to the Show Cause Order of SCoRP, the UP Law's Malcolm 37 have begun that clinical demonstration of judicial plagiarism as defined by SCoRP and now Bernas--right within the corpus delicti that is Vinuya v. Executive Secretary.  Moreover, there is also another SCoRP decision, already final and executory, in the Ang Ladlad case, that is also tainted with plagiarism. It was also written by Justice Mariano Del Castillo and promulgated just two days before Vinuya last April.

Father Bernas is driving the Court deeper into the Quagmire of plagiarism that they have dug themselves with two highly immoderate and unwise actions: (1) the unethical manner by which the Ethics Committee formed by Chief Justice Corona exonerated their colleague, when all five members had concurred with Del Castillo unqualifiedly in Vinuya to begin with; and (2) the Show Cause Order against the UP Law Faculty, which was really a Resolution finding them guilty of violating professional canons of behavior delivered in a Notice of Judgment with an order for them to show cause why they should not be punished according to the vindictive whims of the Court!

On Freedom of Assembly and the Religious Services

If we consider the Catholic Church to be equivalent to a "Non Government Organization (NGO)" under the 1987 Constitution, then we are forced to the conclusion that the Catholic Mass is equivalent to Mass Demonstrations such as those daily conducted by activist groups, party lists or other cause advocates. All such activities are first order forms of Free Speech and are specifically covered by the Freedom of Assembly. In addition, religious services are covered by the Bill of Rights provisions on Religion.

The Bill of Rights Art. III Sec. 5 of the 1987 Constitution declares--

(5a) No law shall be made respecting an establishment of religion, or prohibiting the free exercise thereof. (Principle of State Neutrality)

(5b) The free exercise and enjoyment of religious profession and worship, without discrimination or preference, shall forever be allowed. (Principle of Equal Liberty)

(5c) No religious test shall be required for the exercise of civil or political rights. (Principle of Secular Morality)

It would not constitute legitimate exercise of free speech, in my opinion, if persons not allied with an organization that was conducting such a mass demonstration, were to demand a place on the stage or in the proceedings just by showing up, and then unfurl some symbol or message that could cause tumult or disorder. For example anti-communist activists like ANAD have no legitimate place in a Bayan Muna rally if they want to display slogans against JoMa or the NPA. But they may do so at their own rally and can expect a similar exclusion of any hypothetical pro-communist activists bent on provoking a confrontation.

Clearly, organizers have a right to police their ranks and their venues to prevent the unruly presence of PROVOCATEURS bent on disturbing the peace. It's like crying "Fire!" in a crowded theatre, especially if provocation leads to a violent confrontation. Such persons however, have an equal right to make their own mass demonstration, and there engage in their own free speech.

U.P. Law Faculty Comply With Supreme Court Show Cause Order In Vinuya Plagiarism Scandal

(Manila, Philippines) Marvic Leonen, Dean of the College of Law, University of the Philippines said this on his UPLAWDEAN Page a few minutes ago:

Today, we filed a pleading called a “Compliance” for faculty members that were made respondents in the administrative matter entitled In re: Letter of the UP Law Faculty entitled “Restoring Integrity”. Accompanying this Compliance is a Manifestation on behalf of Dr. Owen Lynch, a research fellow and a visiting professor from the United States, and a separate supplemental submission from the Dean of the UP College of Law in response to his separate citations. 

We are represented by a number of prominent law firms, lawyers and the Free Legal Assistance Group. They spent a considerable amount of time working with us to come out with a respectful yet principled defense that can be filed at the soonest possible time.
So as not be seen as waiving this possible defense, we have simply reserved the due process rights in our Compliance. These rights were also pointed out in the dissents to the Order requiring us to submit an explanation. What we were served was a full Resolution covered by a Notice of Judgment. The Resolution made findings of fact and law. We were not heard at first instance. 

In our Compliance, we emphasized that our statement entitled Restoring Integrity was a fair comment on a published (and still uncorrected) decision of the Supreme Court in Vinuya versus Executive Secretary. The underlying intention in the expression of opinion of the faculty of the UP College of law is in the statement itself. It was and remains “to defend the integrity and credibility of the entire supreme court”, in the light of the perceived plagiarism and misrepresentation that was committed. It was issued in discharge of the solemn duties and trust reposed upon us as teachers in the profession of law and as members of the Bar to speak out on a matter of public concern and one that is of vital interest to us. 

Our statement was issued so that the Court could urgently act to correct a wrong so as to inspire confidence in the legal system rather than to lessen it. Various individuals and academic institutions here and abroad had, by then, noticed the failures in attribution and misrepresentations. We still continue to call on the Court to institute ways and means to prevent similar occurrences. We are more than willing to sit down with the Court’s representatives and contribute our academic resources to find ways to lessen its docket as well as to continue to improve court staff’s ability to do research. 

Public critique of a published decision is different from disrespect of the Court that makes such a decision. Law professors are the most likely experts within the legal profession to be able to assist the public understand these decisions. They should be expected to be independent and candid in their assessments. Critique will always come with some degree of irreverence. Otherwise those who wish to speak their truths may not be able to address those in power. We teach our students that injustice suffered by those who are powerless deserve their most effective voice. We teach them that that is what ennobles our calling as lawyers.
Timidity within the legal academia may result in a failure of democracy. From the point of view of the traditions of the University of the Philippines, it would have been a betrayal of our role as part of the national university if we failed to speak out on what we perceived as an injustice. We did not wish to betray our role as an academic institution especially on the eve of our centennial as an institution. 

We thank all those who have publicly and privately expressed their support for what we stand for. Despite our circumstances, we ask that we all continue to be vigilant. We ask that, with all due respect, we continue to discharge our right to examine and comment on the decisions and procedures of our judiciary. This way we can constructively assist our Supreme Court find creative and lasting solutions to bring about the kind of justice that all our peoples deserve.

Marvic M.V.F. Leonen
Dean and Professor of Law
University of the Philippines
uplawdean@gmail.com
Tel and fax: 9270518

The Supreme Court's Show Cause Order to which this reply applies is also here on Dean Leonen's website.

The Arithmetic of Number Coding and How It Fools Everybody

Number coding is a Mental Scam.  There is NEVER a Reduction in the Volume or Number of Vehicles potentially present on a given roadway--even with 100% Compliance with Number Coding.
Number coding should be abolished.  Mathematicians and statisticians ought to assure the public that nothing much would change except MMDA has to do things the hard way: by fairly enforcing traffic laws, removing obstructions and illegal vehicles from the roadways. MMDA should quit promoting official innumeracy with mental trickery involving percentages and absolute numbers!

How Much Do You Need To "Buy" the Grand Lotto 6/55?

Filipinos are a gambling nation so news has really excited them that one of the Philippine Charity Sweepstakes lotteries has reached a jackpot of over a half a billion pesos for a single bet of 20 pesos. It has everyone buying tickets ("who knows?") -- even OFWs abroad who are getting friends and relatives in the Archipelago of Pacquiao to buy them a chance to win.  Of course at these high jackpots, some billionaire tayps may be thinking of ways to "buy" the jackpot by betting on all the possible bets. But how much would be needed and is it really smart to do it?

There are 28,989,675 unique 6 number combinations to be chosen from the numbers 1 to 55. At 20 pesos each you need 579,793,500 pesos to "buy" the Grand Lotto, i.e., to place a bet on each possible 6 number combination. Since no winner was found in the draw today, the next draw could be worth about 580 million pesos. You would win for sure but profit would only be P206,500. Unless someone else wins, in which case you lose a quarter of billion pesos! More if there are two or more winners.

At the heart of this is a very famous mathematical formula for the number of unique Combinations of R things selected from a larger collection of N things:
C(R, N) = N!/(R!(N-R)!)
and
C(6,55)=55!/(6!(49!))=55*54*53*52*51*50*49!/(6*5*4*3*2*1)*49!=28,989,675

It's probably not a good idea to "buy" the Grand Lotto until it's worth about a billion pesos!
[This post was inspired by a Tweet from @Kakanturing (Tony Velasquez)]

The Great Debate

Sam Harris, Steven Pinker, Patricia Churchland, Lawrence Krauss, Peter Singer, Roger Bingham tackle the Big Question: Can Science replace Religion on the matter of Morality?

Social Media As An Anti-Corruption Weapon

In the wake of the twittered "gaffe" by Presidential speechwriter Mai Mislang on Vietnam's wine, men and roadways,  the President's communications team felt obliged to issue guidelines to all government officials and employees on the use of social media sites like Facebook and Twitter.

Although they have reportedly been approved by Pres. Aquino, spokesperson Abigail Valte said these Guidelines will not yet be released and implemented because of Constitutional and legal concerns.  The Daily Tribune did not hesitate to call the Guidelines all but  censorship by too sensitive a  Presidency.


In this post I examine the possibility of using Social Media in the anti-corruption campaign. The more that one million employees of the government are uniquely positioned to act as watchdogs and whistleblowers.  But Congress must provide the appropriate laws and facilities.

On the Proposed K-12 Basic Education System

The Philippines currently offers a ten year public school system to provide basic education, namely six years of tuition-free grade school and four years of high school.  Since most children begin entering school at six years old however, those who do finish the entire program end up graduating from high school at around 16 years old.  Many critics and educators point out that at this age the high school graduate is not old enough to execute legal contracts  such as for employment or business so that those who want to work immediately after high school are hard pressed to find productive occupations.  Perhaps that is why even the best of them drift into ... politics! through the SK system (but that's another topic.) At the same time, even among those intending to go to college many are emotionally and academically unprepared at 16 to effectively undertake college level study. In part this is due to our short ten year elementary and secondary school curricula.

A major agenda item for the Dept of Education (DepEd) is the proposed K-12 Basic Education System (PDF) which would represent a major expansion of the present ten year public school program to thirteen years.  The PDF file above  discusses the rationale, design and implementation plan of DepEd.  In this post I consider some of the problems and challenges attendant upon the K-12 proposal.

Education's Agenda

SECRETARY ARMIN LUISTRO  has issued a Press Statement on his First One Hundred Days at the Dept. of Education.  From the looks of things he has a full plate as he lays out a 10-point Education Agenda for the next six years and beyond:

(1) the 12-year basic education cycle,   

(2) universal preschooling for all,

(3) Madaris Education,

(4) technical vocational education,

(5) “Every Child a Reader” by Grade 1,

(6) Science and Math proficiency,

(7) assistance to private schools as essential partners in basic education,

(8) rationalization of the medium of instruction,

(9) quality textbooks, and 

(10) partnering with Local Governments to build years more schools.

I shall have occasion in the coming weeks to look at each of these in some detail...

Benedict's Biology

POPE BENEDICT XVI  is in Spain. Independent Catholic News covers his itinerary and statements in detail. 

But I was struck by something the Pope said today, after embracing the statue of St. James the Greater in Compostela de Santiago, and meeting with the Prince and Princess of Asturias.

"Truth and freedom are closely and necessarily related", he added. 

"Honestly seeking and aspiring to truth is the condition of authentic freedom. One cannot live without the other. The Church, which desires to serve unreservedly the human person and his dignity, stands at the service of both truth and freedom. She cannot renounce either, because what is at stake is man himself, because she is moved by love for man, 'the only creature on earth which God has wanted for its own sake', and because without this aspiration for truth, justice and freedom, man would lose his very self.

There have been many creatures on Earth, all of them creations of the very God which Pope Benedict worships. Estimates of the number of species that have ever existed on Earth--plants, animals, multicellular organisms of all kinds--range from 750 million to 7.5 billion individual species. 

That homo sapiens sapiens ("Man") is unique among God's creatures in the sense that Benedict claims--that he alone has God wanted for his own sake!--this claim I find to be extravagantly illogical given the facts of life on Earth as we know them.

A Religious Test Is Required To See If Religious Feelings Were Offended

Performance artist CARLOS CELDRAN has been charged under a little-used 1930 law in the Revised Penal Code:

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Art. 133. Offending the religious feelings. — The penalty of arresto mayor in its maximum period to prision correccional in its minimum period shall be imposed upon anyone who, in a place devoted to religious worship or during the celebration of any religious ceremony shall perform acts notoriously offensive to the feelings of the faithful.

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Art. 133 criminalizes  acts notoriously offensive to the religious feelings of the faithful.

Not just any old feelings, mind you, but the RELIGIOUS feelings of the Faithful! This law is very specific and ought not to be used for every circumstance of VEXATION of feelings that so easily arises among people.  If one is to be convicted of the crime of "Offending the Religious Feelings" it had better BE religious feelings that are offended.

CBCP's Double Damaso Rule on Fathers Fathering Children

Padre Damaso is alive and well in the 21st Century. The troubles of Carlos Celdran are ample proof of this!  So the topic of this post is relevant to both local and international concerns...

There was a Protest March against clerical sex abuse at the Vatican yesterday--

Citizens of 12 countries who suffered sexual abuse by Catholic priests today gathered in Rome for a protest march on the Vatican.

Wearing t-shirts reading: "Enough!" in English, Italian and German, the organisers of the candlelit march demanded that the UN recognise the systematic sexual abuse of children as a crime against humanity.

Philippine Commentary supports the above proposal to make the sexual abuse of children a Crime Against Humanity, along with the rape and sexual slavery of women during war time conflicts, which have been the subject of much recent Commentary here.

The Roman Catholic Church in the Philippines has had its share of clerical sexual scandals, including this incident just last July where the Bishop of Boac has rejected calls for an investigation into child sex abuse allegations against a priest in his diocese.  (Does this sound familiar from the horrific cauldron that was Boston?)

In the early part of this decade Mass Media reported freely on the reproductive activities of several high profile Catholic Church hierarchs, including Bishops: the famous fathers fathering children scandals.

In response to this the CBCP Permanent Council approved in September, 2003 the document Pastoral Guidelines on Sexual Abuses and Misconduct by the Clergy, drafted by the present Gaudencio Cardinal Rosales of Manila.  He was interviewed by the Catholic press agency UCA News about the issue of clerical sexual abuse in the Philippine jurisdiction. I reproduce the entire interview to share with readers a really in-depth look at the successor to the most famous Jaime Cardinal Sin.

It is a long interview but it includes Cardinal Rosales rationale for a rule that allows Bishops to continue serving even if they have illegitimately fathered ONE child, on the theory that this first-born may have been unintentional.   A second supposedly implies malicious intent! (I call this the Double Damaso Rule).