Month: December 2011

Onsdagslotto – when to play and win the superpulje

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The so-called “superpulje” in “Onsdagslotto” (Viking Lotto) has reached a record breaking amount on 125 millions and with extra so-called jackpots reaches 157 millions. This is around 30 million US Dollars or 22 million Greek Euros (equivalent with 22 million German Euros).

It is dangerous to talk about the statistics of Onsdagslotto as twice our local statistics watchdog Mikkel N. Schmidt has caught researchers giving the wrong odds: The first time blogging Mikkel caught Jørgen Hoffmann-Jørgensen from University of Aarhus giving the wrong odds. The second time Master Schmidt found that University of Copenhagen Professor Mogens Steffensen‘s odds or the Politiken newspaper reporting his odds were wrong.

Fearless of Mikkel I will now attempt my computations (which are probably wrong).

In Onsdagslotto you pick six numbers from 48. The number of different combinations/rows are (48*47*46*45*44*43)/(6*5*4*3*2*1) = nchoosek(48,6) = 12’271’512 = around 12 millions. The so-called superpulje is released if an extra independently picked number (a 7th number) hits one of the six numbers. The probability that the superpulje is released is thus 6/48 = 1/8. It means that on average you need to play nchoosek(48,6)*8 = 98’172’096 = around 100 millions rows before you win the superpulje.

Hoffman gave (48*47*46*45*44*43*42)/(7*6*5*4*3*2*1) = 73’629’072 for the superpulje. This number is correct if you were to hit 7 numbers from the 48. But this is not how the rules are (as far as I understand).

In the report from Professor Mogens Steffensen the newspaper made it sounds as if the value of 98’172’096 was the number of combinations from one coupon. But there are 10 games on each coupon, so the average number of coupons you need to play are nchoosek(48,6)*8/10 = 9’817’209 = around 10 millions, – as Mikkel notes.

Apparently, it costs 4 Danish Kroner (DKK) to play one row/combination/game. To play all combinations will cost you 12271512*4DKK = 49’086’048 DKK = around 50 million DKK. Peter Brodersen noted that as the superpulje was hit this week you could have gain a considerable number of money if you had played all combinations. The bad news for the strategy of playing all rows is, however, as Brodersen also mentions, that you do not know if the seventh number hits the 6 others and you do not know whether you need to share the amount with other players.

On average you need to spend nchoosek(48,6)*8*4DKK = around 400 million
DKK playing all combinations before you hit the superpulje. It seems to be more difficult to compute the probability that you have to share the amount from the superpulje. During these times with a large superpulje Danes are playing for around 65 to 82 millions DDK each round, meaning around 20 million combinations are played in Denmark and that on average each combination is played around one or two times (82000000/4/nchoosek(48,6)). However, the superpulje is shared with other countries in the Nordic region. One blogger notes that we are 33.4 millions in the region. If the people in the other countries play at the same rate as Danes, does that means that a superpulje winner has to share it with 9 other people on average? (33.4/5.5*82000000/4/nchoosek(48,6)=10.145). I am not sure I understand the rules correctly… Because last week when the superpulje could have been released no player hit the six correct numbers among the 48. If Danes are alone to play the probability of no-one not hitting the six correct is around 25% (1-1/nchoosek(48,6))^(65000000/4). Whereas if we use the Danish playing rate on the entire Nordic region population we get around 0.0003 (1-1/nchoosek(48,6))^(33.4/5.5*65000000/4). So either I am computing this wrong or I misunderstand the rules or the playing rate is quite lower in the other countries, – or it was a very unusual drawing. Yet another explanation is that some people play systematically. It has been reported that one particular combination was played 1’600 times. If you win the superpulje alone you will apparently also receive the secondary prizes, – if I understand correctly. That amount I read on one news site ( to be around 10 million DKK.

The rate of which other people play, their rate of systematic playing and the secondary prizes make the computation of when it is an advantage to play difficult. If you disregard the secondary prizes it seems that the superpulje needs to grow to at least 400 million DKK before it is an advantage to play “against” it. It needs to grow further if you count in the other players that might hit your six numbers.

One popup page on the Danish lottery website states that the average payback percentage is 45%. It is unclear for me how the payback is distributed between the different prizes. If we assume that 40% is used for the secondary prizes it means that if we play for 300 million DKK we will on average get 120 million DKK back from the secondary prizes, the rest, 180 million DKK is at stake for winning the carried-over superpuljen (if my understanding is correct). Given that the amount accumulated in the superpulje is now going towards the 180 million it seems that it is almost an advantage for me to play, – provided that the rest of you do not play so I have to share the prize.


(Correction: Typo 17:39)

Telenor driftstatus unavailable

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My Internet usually works ok, but two days ago I was hit by periodic dropouts on my Telenor broadband Internet. The “Internet” LED on the ZyXEL P-660R-D1 DSL modem at my place was unlit for several minutes many times during the evening and during these periods I was unable to get further than However, as the error was periodic I could occasionally get on the Internet and search for what was wrong. In this process I found the information on the status of Telenor’s Internet insufficient for me.

Telenor customer service is not available during evenings through telephone. You can report an error via a web form, but I didn’t manage to discover that page. I rebooted the modem several times by switching off the device. One page states that you should wait 20 seconds, – which I might not have done: It is possible that the device in the other end of the cable needs not just a reboot but several seconds to detect and correct the problem. I have entered my email so Telenor can send me emails about interruptions in the operational status of the Internet, but I have never seen an email from them. I could not get a clue from the Telenor status page. My search on Twitter on “telenor” got noone reporting problems except myself.

Next day the unstability was over, but I called Telenor to get a postmortem debriefing. After waiting perhaps 7 minutes to get to a human the person at the other end told me that there had been a problem. He got my email so he could write to me with more information, but I have received no email so far. The present information on the Telenor status page gives me no indication of the problem, – the closest message is from 14. december 2011 14:15:57 which gives information about work on their hosting platform. At one point this Telenor status page displayed rather funnily the message “Service unavailable” (remember Hamlet: Something is rotten in the state of the state of Denmark).

During the exponential growth of Wikipedia and Twitter you would often run into capacity problems with these services. For Twitter you would have the famous failwhale that gave a clear indication and understanding that there was a problem. You could use to check the availability of webservices. To me the dropouts that from time to time (sort of reasonably rarely) occure in my broadband Internet access are enigmas. One other Telenor customer has reported that the broadband problems might be due to a so-called lorte-central. Given no other information I have to accept that explanation.

Cavling prize 2011

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Tomorrow 14 December 2011 the nominated to the Cavling Prize is announced. The prize is the most pretigious journalistic prize in Denmark. 44 suggestions for nominations have been received by the prize committee. The prize is presented to the winner at a ceremony the 6. januar 2012. Here are my guesses for a winner:

  1. Anton Geist and Ulrik Dahlin. Every journalist dream seems to be to get the head of a minister on a silver plate. In the case of Geist and Dahlin their articles managed to remove the Minister for Integration (of immigrants), Birthe Rønn Hornbech. The case concerns the handling of young stateless people. According to a United Nation convention signed by Denmark stateless persons born and raised in Denmark may seek Danish citizenship. The authorities not keen on giving citizenship to for example criminals and suspected terrorist let the convention be open to their own kind of interpretation. The journalists were directed to the case by member of parlament Hanne Agersnap that made an alert note of a particular remark Hornbech made in parlament. From there Geist and Dahlin were running with the ball. The journalist are suggested for the prize by no less than six persons, including the two former prize winners Peter Øvig Knudsen (2007) and Jesper Tynell (2009). Geist and Dahlin will be unsurprising winners. The case is summed up on Danish Wikipedia in an article where I have written a major part.
  2. 2011 was also the year of the wonderful case of neuroscientist Milena Penkowa, see my earlier comment. Poul Pilgaard Johnsen was the primary journalist digging into the case. I guess he must have been provided with leaked information somehow. In a particular claim to fame he managed to investigate an investigation of an investigation and found that a Spanish firm called “RRRC Pharmaceuticals” was likely an ficticious invention of Penkowa, thus making a mock of a former investigation by the President of the University of Copenhagen. The case may also have caused that a minister was removed from office. Former Minister of Science Helge Sander knew Milena Penkowa personally and before the story broke big in the media he was replaced as part of a major government reshuffle. Most likely he was removed because he wasn’t particular popular among students and researchers. But one may wonder whether the Prime Minister knew that the friend of Sander was already at that time involved in a criminal case. Johnsen is suggested by 6 persons, including one of the scientists involved in the case. Four of the journalists suggesting Poul Pilgaard Johnsen for the Cavling Prize write: “According to our knowledge the case is the largest scientific scandal in the history of Denmark and the first time in the history of Danish press, that investigative journalism within science and research has resulted in so extensive exposé and consequences.” This case is also summed on the Danish Wikipedia in the lengthy article on Milena Penkowa of which I have also written a good part.

I am less family with the work fo the other suggestions for the Cavling Prize. One suggestion is Rasmus Tantholdt. His name appear frequently in the media these days as he himself is involved in a case of leakage of confidential information.

One outsider is Preben Juul Madsen that has been suggested by seven people. Madsen runs his own website and seems to have some devout followers. My guess is that he is not a likely winner.

Poul-Erik-Heilbuth, the man behind a Curveball documentary is suggested. One of the few with international reach.


(Update 15. december 2011: Ok, so Dahlin and Geist were nominated, but not Johnsen – )

Are you on Google Scholar?

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Google introduced (was it a few weeks ago) a new version of Google Scholar where you as a scientist can claim your name and your scientific papers that you have authored. Previously you could just search, e.g., to get your papers listed, see my previous blog post. However, if you got a common name, e.g., “J. Larsen” you would run into the problem that your publications would be entangled with the publications of other people called “J. Larsen” or “RJ Larsen” or “JC Larsen”, etc. With the new system it almost seems that Google does co-author mining so they are better to distinguish the different similar-named authors. Furthermore, – and most important – with a Google Scholar account you can claim your papers which solves the ambiguity problem, – and you can add and merge papers. Editing functionality was already present in CiteSeer long ago (if I remember correctly) and in Microsoft Academic Search you can also do editing of the publication list.

You can see my Google Scholar account here. By a strange coincidence I have found that my number of citations is presently exactly the same as one of my co-authors, Cyril Goutte: 1668.

The new Google Scholar functionality seems not to be that good in discovering new relevant papers, e.g., those papers that cite you. There the old fashion Google Scholar email alert seems better. What is does provide is a nice overview for h-index junkies. The number is automatically computed and makes Google Scholar a serious competitor the the pay-walled ISI Web of Science.