Jon Stewart is insightful as always:

• The rise of VaR
• Felix takes on Tyler Durden
• A casualty of chance
• What is data science?

The Special Inspector General’s report on TARP has been released from embargo. It concludes that TARP was unsuccessful, and even its (debatable) short-term corrections are overshadowed by the extent to which it has returned the economy to its previous bubble state — “we are still driving on the same winding mountain road, but this time in a faster car.”

From the executive summary:

The substantial costs of TARP — in money, moral hazard effects on the market, and Government credibility — will have been for naught if we do nothing to correct the fundamental problems in our financial sys- tem and end up in a similar or even greater crisis in two, or five, or ten years’ time. It is hard to see how any of the fundamental problems in the system have been addressed to date.

• To the extent that huge, interconnected, “too big to fail” institutions contributed to the crisis, those institutions are now even larger, in part because of the sub- stantial subsidies provided by TARP and other bailout programs.
• To the extent that institutions were previously incentivized to take reckless risks through a “heads, I win; tails, the Government will bail me out” mentality, the market is more convinced than ever that the Government will step in as neces- sary to save systemically significant institutions. This perception was reinforced when TARP was extended until October 3, 2010, thus permitting Treasury to maintain a war chest of potential rescue funding at the same time that banks that have shown questionable ability to return to profitability (and in some cases are posting multi-billion-dollar losses) are exiting TARP programs.
• To the extent that large institutions’ risky behavior resulted from the desire to justify ever-greater bonuses — and indeed, the race appears to be on for TARP recipients to exit the program in order to avoid its pay restrictions — the current bonus season demonstrates that although there have been some improvements in the form that bonus compensation takes for some executives, there has been little fundamental change in the excessive compensation culture on Wall Street.
• To the extent that the crisis was fueled by a “bubble” in the housing market, the Federal Government’s concerted efforts to support home prices — as discussed more fully in Section 3 of this report — risk re-inflating that bubble in light of the Government’s effective takeover of the housing market through purchases and guarantees, either direct or implicit, of nearly all of the residential mortgage market.

• TIME: “It’s over!”
• Moral hazard and the NFL
• JPM, AXP ask taxpayers for money to pay back taxpayers
• The world according to Putin

Deep in southwestern Kansas, surrounded by miles and miles of absolutely nothing, is a giant stone-lined hole in the ground.

It’s not just any old hole, though — it’s the largest hand-dug well in the world. And according to the WSJ, it’s about to acquire a world-class museum:

The citizens of Greensburg are planning a $3 million Big Well museum and this month announced a contract with a high-profile design team, Ralph Appelbaum Associates Inc. of New York. The firm has designed exhibits at the American Museum of Natural History in New York, the U.S. Holocaust Memorial Museum in Washington, D.C., Bill Clinton’s presidential library in Little Rock, Ark., and the Country Music Hall of Fame in Nashville.

Greensburg has been hit by hard times recently. A 2007 tornado devastated the city’s downtown area and tourism has traditionally played a significant role in the local economy. Lately that support has been lacking:

In the 1970s and ’80s, as many as 75,000 visitors a year would stop by Greensburg to peer into the murky water. They’d drop a coin (or, oddly, a shoe) for good luck, maybe even buy a $2 ticket and descend 105 steps to the claustrophobic depths.

In recent years, however, drivers whizzing past on Highway 400 have been less prone to pull over, despite a series of promotional billboards stretched out over 50 miles to build excitement.

It’s easy to laugh at this seemingly ridiculous tourist attraction — it’s just a hole in the ground, after all. But I have to reserve judgement.

You see, I have been to the Big Well.

I’ve driven across Kansas. Twice. I’ve seen the billboards. And let me tell you, when you’re faced with nothing but bland prairie for hours, those ads look amazing: “Stop and see the giant well! Have a cold drink! Forget that you’re in Kansas, most boring state of all!” After all, your choices for stopping are the various McDonalds scattered along the highway median… or the GIANT WELL! And you probably stopped for a burger when you were only a third of the way across the state, which leaves only one option…

But here’s the kicker. Greensburg isn’t just the home of the world’s deepest human-dug hole; it’s also the home of the world’s largest pallasite meteorite! (No longer – now it’s just the world’s second largest pallasite meteorite.) One town, TWO record-setting objects which conjure immense vertical images, from the heights of space to the depths of the Earth. Moreover, under one roof (at least, until the tornado came through). And I ask you: after trekking endlessly toward Kansas’ uninterrupted horizon, how can you pass up this opportunity to transcend flatness?

For years, my brother and I have laughed privately at the odd-couple billboards we once saw (and obeyed): “See the world’s largest hand dug well… and meteorite!” Maybe now we can share that amusement with other cross-country drivers.

Oh, and just in case you still harbor some concern that the Big Well (or Kansas more generally) can’t compete in this plugged in, Disneyfied world, let them go:

In 2008, a popular vote online tabbed Greensburg’s Big Well as one of the Eight Wonders of Kansas, on par with the Underground Salt Museum in Hutchinson (and a cut above the town of West Mineral’s star attraction—”Big Brutus,” an enormous electric coal shovel).

• Dude, that’s a toad
• Math is hard!
• One way, the wrong way
• The Yom Kippur effect

It was announced at the official opening of the tallest building in the world that it will no longer be called the Burj Dubai, but rather the Burj Khalifa, a nod to the President of Abu Dhabi, Sheik Khalifa.

One will of course recall that just a few weeks ago, Abu Dhabi rescued Dubai from the brink of bankruptcy in the form of a desperately needed $10B infusion. The name change is unquestionably a “thank you!” to the neighboring emirate. It might even represent collateral – if Dubai defaults again, hey, at least we got a landmark! Let’s hope current bondholders don’t have to find out.

Perhaps they could be consoled by knowing the money was put to good use in the most amazing fireworks show ever :

Click here to view the embedded video.

(The Burjwas last seen in TGR’s most popular post to date)

• Yurtle the Turtle had nothing on this!
• Big Apple Burj Dubai (again!)
• Cancel all orders!
• Top Gear season 13 is coming!!

From a WSJ opinion lamenting the state of Manhattan Chinese food (of all things):

Walk through New York’s Chinatowns—there are two—and you’d think that the Chinese don’t know about fine dining. Here it’s all about shared tables at food stalls and loud, crowded dining halls that feel trapped in an era when Mao was still alive. Well, let me tell you: There are plenty of Chinese people with money, and they like to spend it on things besides U.S. Treasurys.

Is “Treasurys” an accepted spelling of “Treasuries”? I find the typo – if such it is – somewhat amusing, but I’m more than willing to confess my own ignorance if that’s the case. A quick Google suggests that “ies” is the way to go, does anyone else have an opinion?

Update: an answer!

• Thursday trends are one day late
• A casualty of chance
• Thursday trends are so hot right now
• “We hate you guys.”

This article ran in the print version of the Wall Street Journal with the headline “Airbus Fixes Mandated.” After reading it, I wondered “Airbus fixes mandated what?“

But I was wrong. I read “Fixes” as a verb and “Mandated” as an adjective. The headline writer had intended for “Fixes” to be a noun and “Mandated” to be a verb.

English is hard.

• On revisions, episode IV (A New Hope?)
• Things that keep me up at night: signing into Amazon
• Easily the biggest news story of 2010 (so far)
• I have the hammer

Senator Dodd’s proposed financial reform bill is long on words (1136 pages, but there’s an 11-page summary) and short on solutions. Institutions, posts and policies will be created; reports, hearings and testimonies will be given; escape plans, living wills and registrations will be submitted; and in the end very little will actually be done.

This is what I call a “watched pot” plan – it seems to operate on the principle that with enough people staring at the economy, it won’t boil over. And we better hope not, because there’s not much in this plan that tells the watchers what to do differently when it does.

So, let’s meet our watchers:

First up, the Consumer Financial Protection Agency: a sort of FDA or CPSA for retail financial products. I have to wonder how exactly this is going to work; what will be the determination of a “fair” financial product? There won’t be a smoking gun, like contaminated food or dangerous toys. But financial products are legal contracts, meaning the specification of every product is explicitly detailed in its prospectus. The prospectus goes far beyond the nutritional facts on the side of a box of cereal, specifying the product’s details down to the manner in which the number of days between interest payments should be calculated. Since that document must be provided prior to a sale, there is little for the CFPA to do in the way of information transparency outside requiring warning labels that say, “Caution: do not apply for this mortgage if you are pregnant or nursing.”

Instead, the CFPA will likely focus on the manner and clarity with which that information is presented. This will effectively result in banks outsourcing their marketing operations to the government. Now, it would be great for consumers to be better educated about financial products (indeed, the CFPA will embrace a new Office of Financial Literacy) but it’s hard to imagine what sort of investigative abilities the CFPA will actually bring to bear. Would they be able to declare a recall of option ARM mortgages? I can’t figure out how that would work. And would better knowledge of how an option ARM works really have prevented Americans from going after them like crazy? I am not convinced that the problem is that American’s didn’t know their rates would increase; I think a lot of it has to do with investors’ myopic views and their simply not caring.

So: it’s nice to have clarity in financial marketing, but this certainly won’t be “A Watchdog with Real Teeth.”

Next, the Agency for Financial Stability. This group will identify systemic risks and implement barriers to growth if a firm gets too big. It’s a bit like a preemptive trust buster. It also relies on the ability to predict failure, something the government has been abjectly horrible at doing. This sounds a little like a rebranding of the Fed, except it will have no natural relationships with any the firms it is charged with regulating. Perhaps a better comparison is the Basel II accords, which were set up for exactly the same reason.

Finally, the Financial Institutions Regulatory Administration will combine existing financial regulators under one umbrella in the interest of efficiency. I am always a fan of efficiency.

Below that triad, the SEC will gain oversight of investment advisors with more than $100 million in assets, including hedge funds. One must wonder, given the teams of auditors that pour over these teams every year (with mixed results), how the SEC will possibly manage to pay attention to all the firms under its jurisdiction. A possible upside would be the implementation of standardized portfolio reporting systems – but I doubt it. The Madoff scandal shows that large firms can slip under the SEC’s radar. Now small firms will have that opportunity as well. I’m kidding – fraud is, of course, an important area for government regulation. Let’s be sure we’re not creating a backstop for imprudent investors with one hand while the other one claims it’s removing moral hazard in large institutions.

Moreover, the draft is quite clear in specifying that “investors in securities will be better protected by improving the competence of the SEC.” It’s actually quite a relief to see that admitted in writing, especially given that the agency is going to have even more firms under its jurisdiction. May I suggest improving the competence of investors as a secondary measure?

The Office of National Insurance is a new department at the Treasury tasked with overseeing – yup – insurance companies.

The new Office of Credit Rating Agencies at the SEC suffers the same problem as its parent – how can it possibly penetrate the depths of the firms it is charged with overseeing? Here’s a paraphrasing of this office’s abilities:

1. Require ratings organizations to disclose methodologies, use of third parties for due diligence, and ratings track record.
2. Require agencies to consider information from sources other than the organization being rated if they find it credible (huge “if” there!)
3. Compliance officers can not work on ratings, methodologies or sales
4. Investors can sue ratings agencies for knowingly providing flawed services
5. Require ratings analysts to pass qualifying exams and have continuing education.

On the one hand, none of this inspires any confidence in the rating agencies even after implementation. We already have their methodologies right here. On the other hand, it completely fails the “McDonald’s all-white meat” test: if all of these would be new regulations, what were the rating agencies made of before??

Finally, the Municipal Securities Rulemaking Board is going to protect municipalities so that they aren’t fleeced a la Jefferson County. It’s unclear to me why that would be handled by a separate body than anything else – the interest rate products that were sold in Alabama weren’t municipal; they were merely sold to a municipality. Misleading the client by any other name…

So, we’ve got all these people watching the system. The hope is obviously that they prevent anything bad from happening, and the major tool they have for ensuring that outcome is their ability to enhance financial transparency. While no one would deny that transparency can be helpful, is it really going to prevent a systemic failure? Hardly; but it might yield an early warning. (“Might” is a very strong word. How about “it might yield an early warning if the various regulators tune in to the right firm at the right time and accurately predict how future events will affect that firm’s ability to do business as well as its relationships with other firms and their respective operative conditions.”)

So what will our watchers do as the pot starts to bubble? Not much. Most of the options outlined in the draft would either have little impact or be impossible to carry out in practice.

One of the big bullet points is breaking up large companies. I don’t see how this makes a dramatic difference – GM had to go into bankruptcy before it was broken up, and by then it was too late to stave off a failure (by definition). Breaking up a hurt company would be a gesture at best – imagine telling Citigroup today they had to split in two. For that matter, imagine telling them that in 2007, on the basis that “we think you’re going to be dangerous in two years.”

The regulators will have much more success with their second bullet: increasingly strict rules as financial firms grow larger. At least, they will have more success if progress is measured by “fewest number of large companies.” There are not – and have not been – any monopolies in financial markets. Goldman Sachs has demonstrated that there is absolutely nothing universally systemic about this failure; they have succeeded despite the crash. So why are we afraid of large companies? Because of our fear that their failure could trigger Armageddon? Is there anyone who believes that if Lehman Brothers had not gone bankrupt, the economy would be healthy? Bank failure is a symptom of a dying economy, not a cause. There is no such thing as “too big to fail”; there is only “we’re too scared to let you fail”.

But don’t worry – there won’t be any government intervention. Companies will be required to provide their own capital injections by issuing hybrid securities. Will it work? Sure, as long as anyone’s willing to provide them with capital. This worked extremely well for banks when the FDIC backed their debt. It didn’t work so well without a guarantee.

And should the grim reaper come to take your firm to the giant trading floor in the sky, the company will have been required to provide a plan for its “rapid and orderly shutdown”  - a living will. The regulators will basically say, “Hey, Large Firm – we want to be able to close out your operations quickly and smoothly. Provide us a plan for doing so. Keep in mind that in such an event, you’ve likely lost most of your employees, have no excess cash or liquidity, and are inundated by screaming customers trying to extract what little value they can before you inevitably disappear. Don’t forget that the market won’t give you a good price on anything. Oh, and if you can provide a simple map of your subsidiaries, that would be great.”

Meanwhile, derivatives will be traded on an exchange with a central clearinghouse. Nevermind that neither of those can provide any utility unless the derivative in question is widely adopted and traded. And banks that securitize products will be required to keep 10% of the credit risk. What does that mean? They must keep 10% of the exact product, by notional? Can they keep a different tranche, if the credit exposure is the same? What risk is it, exactly? None of these questions are answered, because they would require a definition of “risk”.

So, we have a lot of new eyeballs on the scene and a few new ways to keep firms from getting big. I remain unconvinced that size is the qualifier here – firms don’t have to be very big to do a lot of damage. Long Term Capital Management had fewer than $5 billion in assets when it required a government bailout. I don’t really see how all of this will prevent another economic disaster. A lot of it is fine – the efficency, the education – but let’s not delude ourselves into thinking everything is ok because we’ve designed a way out of the mess. Anyone who bought portfolio insurance in 1987 will agree.

Remember how a decade ago everyone was putting money into firms that produced nothing and had no assets, but sounded really good? More recently, banks started handing money to anyone who said they wanted to buy a house – just because they could. Now we have the government pursuing actions because they would have helped if they’d been in place before (according to the people implementing them). It looks like a regulation bubble from here, complete with shaky reasoning and all.

And the next time that the pot boils over, we’ll be able to go back and see who wasn’t watching whom the way they were supposed to. And maybe we’ll assign someone to watch them in the future. Because the future, you see, always happens like the past.

• More reverse convertibles: cutting the nose to spite the face?
• JPM, AXP ask taxpayers for money to pay back taxpayers
• Driver’s ed for finance
• TIME: “It’s over!”

In a cab last night, I heard a radio station broadcast a medly of “Barack Obama will be the next President of the United States” calls, followed by a heavily caffeinated announcing repeatedly that it has been one year since Obama was elected and soliciting comments from his audience.

Yesterday was November 3. Obama was elected on November 4.

I don’t think that Election Day qualifies as a floating holiday in the same way that Thanksgiving or Columbus Day do. T-shirts from last year rarely displayed “Election Day 2008″ – instead, they grounded their message with a real date: November 4, 2008. Somehow the claim that the election was “one year ago” doesn’t sit right with me. I guess the real question is when do the Obamas toast the anniversary of their victory – did they do it last night or will they wait for tonight? I know it’s the latter, but my radio station would obviously fall behind the rest with stale reports on things nobody cares about anymore because another media outlet had an excuse to broadcast it earlier.

• Coming this November
• Oh! Bama!
• Fact-checking the singularity
• The First Nerd

As much as I agree with Maureen Dowd’s latest opinion (shocking, yes), this drives me crazy:

If W. had gone to Dover in the middle of the night to salute the war dead, Limbaugh and Liz Cheney would have been gushing about his patriotism.

But since it’s Obama who at last showed up there to see the brutal cost of war, they simply have to dismiss the moving moment as a publicity stunt.

This sort of statement seems the lynchpin of modern political debate, and it’s a travesty. It’s a conditional conjecture disguised as fact, and highlighted by comparison to an opposite set of circumstances. Bush did not go to Dover, and even if he had we do not know what Limbaugh and Liz would have said. It is ludicrous to use this as evidence for an argument.

It would be different if Dowd compared Obama’s Dover trip to an actual trip that Bush made under similar circumstances, and illustrated the difference in Limbaugh’s response then and now; that would be a real comparison, and she does come closer to that ideal in a later paragraph. This excerpt, however, is purely speculative (or at least, unsupported in her opinion).

I hoped we were past the point where a colloquial call to induction like “you know if the situation were reversed he would have said so and so…” would not be considered appropriate evidence for a formal argument. (Even though I think she’s right.)

• Oh! Bama!
• Republicans are/are not resurgent
• Let’s focus on what really matters
• Maybe they don’t get it

It’s an extraordinarily sad state of affairs when you can come to this country at the age of 12 as a refugee, train as a gifted runner in San Diego junior high and high schools, attend UCLA as an incredible four-time All-American award winner, become a naturalized US citizen as you graduate college, compete in the Olympics and win a silver medal for the United States and finally become the first American to win the NYC Marathon since 1982… and still have people insist you’re not an American?!

• It’s American as sweet potatoes (but not sweet potato pie)
• More homes!
• “A revolution in the American fantasy”
• Enlightenment

A few days ago, the NYT published a bizarre article which suggested – or rather, which discussed a paper that itself suggested – that the Large Hadron Collider was actually being sabotaged. By itself. From the future. (I promise you won’t regret clicking that link. I’ve watched the video four times just writing this.)

Confused, I emailed a friend who works on the LHC, basically asking, “Is this for real?” I’m sure I wasn’t the only person asking him for insight, and to help out those of us who won’t be getting doctorates in physics anytime soon, he’s posted a full response to the article on his blog – worth a read for anyone curious:

Okay, “out there” physics, but not necessarily wrong. Where the author loses me is his argument about pulling cards from a deck….

That part is pretty nutty. How is nature to believe us? Are we supposed to really, really promise that we won’t run the LHC if we draw the card? What if we cross our fingers? Does nature count that?

And yes, I shamelessly stole his title.

• How Shazam works
• Don’t know much about calculus
• Damn the physicists, full speed ahead!
• In space, no one can hear your gyroscopes

It was buried deep, deep in the Arts section of Tuesday’s NYT, but nonetheless, sitting in an airport food court, I found it:

‘Hitchhiker’s Guide’ Sequel Lands in Britain

Apparently it is not standard practice for British men and women to gather dressed in bathrobes and toting towels. When hundreds of fans thus clad assembled in London on Sunday, it was to celebrate the 30th anniversary of “The Hitchhiker’s Guide to the Galaxy,” the comedic science-fiction franchise created by Douglas Adams, and the publication of a new book in the series, The Guardian reported. At Hitchcon 09, held at the Royal Festival Hall in London, fans assembled (many of them dressed in the shabby costume of the series’s hapless hero, Arthur Dent) to pay tribute to Mr. Adams, who died in 2001. He was the author of the original “Hitchhiker’s Guide” radio plays and the five-book sequence they spawned.

And most importantly:

The convention also served as a kickoff for “And Another Thing…,” a new novel by the “Artemis Fowl” author Eoin Colfer that is cheekily being billed as the sixth entry in the “Hitchhiker’s Guide” trilogy. The American edition of “And Another Thing…” was released by Hyperion on Monday.

• How did I miss this?
• 42
• Perspective
• The burger’s good, too

When the world has just learned that its suspicions about your secret nuclear ambitions are frighteningly accurate, you should probably go ahead and flaunt ten days of missile testing.

• If it looks like a missile, sounds like a missile, fires like a missile…
• Why the administration may be missing its chance
• Iran has a secret nuclear plant
• It is not only possible – it is essential!

I am hardly surprised, and fervently hope this erodes any remaining legitimacy that the present Iranian government has managed to cling to.

(Via everyone)

• Lessons in diplomacy
• Thoughts on Obama’s first primetime press conference
• Progressive taxation
• It is not only possible – it is essential!

A funny thing happened in the Bulgarian national lottery this week: the same numbers were drawn as last week.

The BBC and the AP both report the odds at 1 in 4 million; ABC Australia calls it 1 in 14 million. People are demanding that the Bulgarian lottery perform an investigation because no one can believe the result. Now, it’s not every day this sort of probability question comes up in the news, let’s take a second to walk through the problem.

The Bulgarian lottery format consists of 6 numbers drawn from a collection of 42, without replacement.  Let’s start by considering the probability of observing any single combination of balls. You might begin like this: The first ball could be any of 42. Once it is chosen, the next ball could be any of the remaining 41. After that, the third ball has 40 possibilities, etc. The number of possible outcomes is therefore

However, this would consider 1 – 2 – 3 – 4 – 5 – 6 to be different from 6 – 5 – 4 – 3 – 2 – 1, which is wrong because order does not matter in the Bulgarian lottery. To figure out the correct number of combinations, we instead need to use the choose function, or the binomial coefficient.

The choose function is pronounced as “n choose k” and yields the number of ways that samples of size k can be chosen from a population of size n, if order does not matter. This is exactly what we are looking for – how many combinations of 6 balls can be formed from a group of 42, irrespective of order? The answer is

So the chance of seeing any specific outcome in the lottery (or, put another way, the chance of winning the lottery) is 1 in 5.2mm.

What’s the probability of seeing the same outcome in two consecutive weeks? One’s first impulse might be to say it’s 1 in 5.2 million squared, or nearly 1 in 28 trillion. But, unsurprisingly, our first instinct is wrong. The chance of seeing a specific combination of balls (such as 1 – 2 – 3 – 4 – 5 – 6) in two consecutive weeks is indeed 1 in 28 trillion. However, the chance of seeing any combination of consecutive draws is… 1 in 5.2 million.

How so? Start with what we know: for a given outcome, the chance is 1 in 28 trillion of seeing it twice in a row. But there are 5.2 million possible outcomes, any of which could have a double header. Thus, the math for any outcome repeating is the 1 in 28 trillion chance of a repeat times the 5.2 million different outcomes, for a final likelihood of 1 in 5.2 million.

This holds true for any population with n choices – and is always one factor smaller than what the human brain naively believes. Consider a coin flip. It has two outcomes, heads and tails (n = 2). After f flips, there are possible outcomes, and exactly n of those outcomes exhibit the same result in every flip. This is because the number of outcomes increases geometrically but the number of repeated items can never exceed the number of initial states. So, after two flips there are four outcomes (HH, TT, HT, TH) with two repeated results and after three flips there are eight outcomes (HHH, TTT, HHT, HTT, HTH, THT, THH, TTH) and still just two repeats. We may conclude that after any number of flips, the probability of seeing a repeated outcome is

After two coin flips, the probability is 2 in 4 or 50%; after three flips it is 2 in 8 or 25%. These simple cases extend nicely to the case where n = 5.2 million and f = 2, where it should be 5.2 million in 5.2 million squared. That simplifies back to 1 in 5.2 million.

I prefer to think of the problem like this: “Given a draw in the first week, what’s the probability of seeing that draw again?” In other words, conditional on the first week’s number, what’s the probability that the second week’s number is the same as the first? Since all combinations are equally likely, the first week’s numbers have only a 1 in 5.2 million chance of being drawn the second week as well. Some people may not like this logic because they feel it ignores the 5.2 million outcomes in the first week, but they actually are accounted for. By conditioning on the first week, we no longer need to consider all of its possibilities.

Let’s take it one step further. These calculations gives the probability of seeing consecutive draws in a two week span, but ignore the fact that this lottery is played every single week. In a year, that’s 51 chances at getting a consecutive draw – surely that improves the odds of observing this result! The probability of not drawing consecutive outcomes in any two weeks is

It is expressed as the number of non-consecutive outcomes divided by the total number of outcomes. Unsurprisingly, it is 5.2 million-less-one to 1 against. After 51 weeks, the probability of not seeing any consecutive outcomes is that number to the 51st power, or 0.9999903. Therefore, the probability of at least one repeat during the year is the complementary probability, or just more than 1 in 100 thousand. Take that out over a number of years and the odds of observing repeats continues to increase. Remember that even the most unlikely event has a fairly high chance of being observed if the outcome is run many times. If you asked the question, “What’s the probability of seeing consecutive draws at any point in the history of the Bulgarian lottery?” you might find the answer surprisingly high. It’s just the probability of this specific week in September 2009 being the repeat which is so low.

The most interesting thing to me is that no one won the lottery the first week but a record 18 people won the second week – it would appear that playing the previous week’s numbers is a strategy people follow. Since the numbers are independent, there’s nothing smart or foolish about this from a probabilistic standpoint, though if you employed a little psychology you would stay away from “popular” numbers in order to avoid sharing the pot if you won.

Anyway, I digress. I put the probability of this observed outcome at 1 in 5.2 million. I’m curious to know how the other news agencies calculated their odds; perhaps there’s some twist in the lottery I’m unaware of?

• Lottery math is not so easy
• So you’re telling me there’s a chance?
• Living in a Bayesian world
• All the news that’s fit to calculate (and brought to you by The Clash)