Powerball jackpot at $1.7bn

The Powerball jackpot is around $1.7 billion. Given that a ticket costs $2 and the chance to win the jackpot is about 1:300 million it seems almost rational to buy a ticket. I mean, I'd buy a ticket or two if I would still live in the US.

Or, as a friend suggested, take $600 million and buy 300 million tickets and win for sure.

Would that work?

Yes, it would work in the sense that you would have a guaranteed jackpot win. But does it pay off?

Let's assume you don't have $600 million in cash lying around and instead get a loan (ha, sure!) for that amount (if you're reading this and you *do* have $600 million in cash lying around, the analysis would be quite different, interestingly, but in that case send me a DM and I'll sell you the analysis).

Now, there are a few considerations:

1. You will be paying taxes on the prize money. At least 37% in federal taxes, and then between 0% and 11% in state taxes.

2. The $1.7 billion is the sum that you get over 30 annual payments, where each payment is 5% more than the previous one. That starts at about $13-$16 million after taxes, depending on your state. That will likely not be enough to cover the interest on the $600 million, but that depends on your loan terms.

3. You can opt for a one-time payment instead of the 30 years of annual payments. But in that case it's "only" $770 million you get. Or between $400-$500 million after taxes.

4. The biggest risk is that someone else might win too. In that case you split evenly with every other winner. That means a single other winner reduces your payout by 50%. If there are more, you get even less.

5. On the other side, you will actually get more than just the Jackpot. Because you bought 300 million tickets, several millions of those tickets will win something. Altogether, that's another $90 million roughly. Again, before taxes.

Seems close cut so far, but...

6. Here comes the kicker -- you can actually deduct the cost of the lottery tickets against the taxes on lottery winnings, if you itemize them. So better keep the receipts!

That would reduce the taxes considerably, if you take the one-time payment (with the annual payments, it probably won't last for 30 years). So the total calculation for the one-time payment would be:

Total win $770 million + $90 million = $860 million. $600 million is tax free, on the other $260 million you'll have 37-48% tax, you'll still end up with more than $130 million profit, with which you'll be able to pay off the interest on the short-term loan easily.

But because of consideration nr. 4, and given that there are many other players given that huge jackpot, you'll likely have to split. And if that happens, your losses will be catastrophic:

Assuming a single other winner, your total prize money drops to $385 million + $90 million (that part is fixed) = $475 million. Fortunately it's all tax free (because, well, you didn't actually make any money), unfortunately you're now at least $125 million worse off, plus interest. If more people win, it gets worse.

My recommendation: if you're into this kind of things, buy one ticket (the first ticket increases your chances by a lot, the second ticket merely doubles it), dream about what you'd do with the money for a day or two, but have no expectations to win. Chances are you won't (there's a reason it's called a tax on stupidity).

And definitely don't do the "buy every single ticket" scheme with loaned money. That will end badly.

P.S. (a few days later): the Powerball was won by two tickets, and thus had to be split.

Tech companies and the size of the market

If you think there might be an AI bubble, but don't worry about it, even if it pops, how bad can it be?

Here's one number: seven tech companies (NVIDIA, Microsoft, Google, Apple, Meta, Tesla and Amazon) are worth about 20 trillion together, representing a third of the value of the total US stock market.

For context: total subprime mortgages in 2008 were 1.3 trillion, total US mortgage debt was 10 trillion.

You have a 401k or have invested in index fonds? Your money is very likely significantly tied with the AI market. If you want that, that's fine. If you're worried it might be a bubble ---

Additions with unique digits: a tale of puzzling and AI

The other day, Markus Krötzsch and I were catching up when one of his kids came in. She told us about a puzzle her math teacher gave her:

How many integer sums are there where the equation uses each digit at most once?

The simplest example is 1+2=3, but 12+47=59 also works. On the other hand, 1+9=10 isn’t a solution because the digit ‘1’ appears twice (in the first number and the sum). Markus’s wife Anja was the first of us to find a solution using three-digit numbers.

I recommend trying to solve it yourself at this point, and then come back to this post. It is much more fun like that.

Thinking for a moment, we realized there seemed to be quite a few solutions. But how many? As computer scientists, our immediate thought was to write a program. First, though, we estimated the complexity of a brute force approach: if we tried all possible permutations of the digits 0 to 9, that’s 10! permutations, or about 3.6 million. A computer should work through that pretty quickly.

I started writing code, and did so even more inefficiently. I included ‘+’ and ‘=’ with the 10 digits, then iterated through all permutations (and shorter versions) to check for solutions. This ballooned the candidate pool to an upper bound of 12!x10, or about 5 billion. I knew there was plenty of room for improvement – the code wasn’t smart – but it should find all the results. I started running it. At this point, I was pretty sure this was the kind of problem that with raw computational power can be solved faster than taking the time to come up with 'smart' code and better heuristics. My full code is here.

As my code ran, Markus took it as a fun challenge and set out to create a smarter solution — which, admittedly, shouldn’t be too hard. Instead of iterating through all possible (and many impossible) equation strings, he only permuted the numbers, applied a maximum length, and checked those. Markus’ code was impressively fast – just 4 seconds! It seemed like we had found the 'right' way to solve it, using better heuristics. Or had we?

Soon after, my code finished, taking 20 minutes. We both had the same answer! (You can find the answer in the linked material, but I am keeping it out here in case you want to try it out yourself). Having two different approaches with the same result gave us high confidence in the answer.

Now, that’s where it could have ended. But the kids were teasing us: it took us forever to write the code (less than half an hour, but still), why didn’t we just ask ChatGPT for the answer?

We were pretty convinced there’s no chance ChatGPT would be able to answer that. So we asked. Markus formulated the prompt (in German, due to my prodding, so it’s more fun for his kid watching), and ChatGPT started thinking.

I have never seen it thinking for so long. Almost seven minutes.

We used that time to laugh and joke about it. No way it would figure it out! We were looking at the steps it was describing. They didn’t seem too bad. What is a cryptarithm? Never heard of that. We were getting ready to amuse ourselves by watching and dissecting ChatGPT’s answer.

Boy, we were wrong!

It returned the same number we had found. The answer was great! Not only that, we looked into the thinking process and found the code that ChatGPT wrote. That code ran in fractions of a second. It wasn’t just faster; the way it built the equations, digit by digit, felt like a fundamentally different strategy than our permutations. Here is a link to the full conversation (local archive). Where my code ran in 20 minutes and Markus’s in 4 seconds, ChatGPT’s code ran in 60 milliseconds.

We were completely baffled. I searched the Web for this riddle and solutions, hoping to find indications it had been solved before, that it was part of the corpus. It might be the case, but we didn’t find it anywhere. ChatGPT came up with more efficient code, and was faster to write it. We were deeply impressed, and were left with two questions, without immediate answers:

1. Given that this is a language model, how did it actually manage to reach this solution? Why did this work?
2. Given that ChatGPT can do this, what does this mean? What are the consequences of having such an ability available? How does this change things?

I kicked off my local Ollama with OpenAI’s recent Open Weight model (120 billion parameters), using Markus’s prompt. I let it run in the background while Markus and I kept chatting. It took a long time – tens of minutes? I didn’t keep track – and we were again confident it wouldn’t be able to answer the question. This was mostly because my local Ollama doesn’t have access to a Python interpreter. And indeed, it answered that there were 45 solutions, very much off from the 1991 solutions we were looking for.

We were a bit relieved. It was getting late, so we called it a night. Seeing Ollama struggle initially, giving me numbers far off the mark, actually reinforced my earlier skepticism. It felt like my intuition about what these models couldn't do was being confirmed – at least for a moment. I asked the system to list all 45 solutions, and it did. I noticed that 1+2=3 was missing. I asked if that would be a correct answer and if it wanted to reconsider its number of solutions, then left it to run while I went to sleep.

The next day I checked the answer. The model had increased its answer to 124 solutions and wrote new code. It told me I should run that Python code myself, as a next step. So, again, the wrong answer.

And then I did run the code. From both the first answer, and the second, improved answer. If you actually run the code, both of them result in the correct answer! The first version took about 20 seconds. The second version then took almost half an hour to run, but I think that’s only because at this point the LLM was becoming a bit extra cautious; it even checked for five-digit numbers, although four-digit numbers were sufficient. I took the LLM’s last code, made some minor clean-up to the code, and reduced it to four digits again, and the code gives the correct answer in 20 seconds again. My complete conversation with gpt-oss is available here.

Not only that: I would even claim that this cleaned-up code provides the easiest to read and understand of all the solutions we discussed so far. It iterates over all possible numbers up to four digits, making sure the second number is always bigger than the first, gets their sum, checks the result for digit uniqueness (quite elegantly using a set!), and counts the solutions. The code is short and, I’d say, elegant.

Markus has also written a second version, which beats the one by ChatGPT in efficiency, running in only 20 milliseconds', and probably being so fast that the Unix time command doesn't measure it reliably.

I am impressed by the answers by the models (and by Markus as well). I think this is a great example of my biggest problem with all of these models, something I’ve been saying for years: I cannot explain to someone else what these models are good at, and what they are not good at.

But I thought I had a good intuition myself. That I roughly knew what kind of questions they would answer well, and which ones I shouldn’t trust them with. What my experience from this experiment showed me is that I do not. I don’t know what the capabilities of these models are.

Given the recent news around the math olympiad, should I have expected such a result? Was this just a toss-up? Do these systems now reliably solve problems like these? Would we have trusted ChatGPt’s result, or would we have been skeptical, if Markus and I hadn't calculated the result for the riddle ourselves?

I am tempted to rationalize it away, to think that the problem was simpler than we made it, that my complex code involving permutations was a red herring, and that’s why the systems could solve it. Maybe that’s just me dealing with the AI effect, where we downplay AI achievements once they happen.

Thanks for reading so far. And big thanks to Markus’s kids for bringing up this riddle, and their math teacher for asking it.

Wikipedia is an encyclopedia

Just happy to post that Wikifunctions can now create some simple sentences in multiple languages. More information on the Abstract Wikipedia newsletter.

Oh! Dalmatien

oh! Dalmatien von Doris Akrap erschien vor wenigen Wochen, ein sogenannter Insider-Guide, im Folio-Verlag. Darin enthalten sind drei Dutzend kurze Artikel, jeder etwa drei Seiten lang, mit Geschichten aus und zu Dalmatien. Zum Dalmatinischem Essen und Trinken, zur Dalmatinischen Lebensweise, der lokalen Sprache, den Winden der Region und welchen Einfluss sie auf das Gemüt haben, interessante Anekdoten zur Kultur und zur Geschichte.

Die Schreibweise ist durchgehend unterhaltsam und flott, die Geschichten hängen nicht zusammen und können in beliebiger Reihenfolge gelesen oder übersprungen werden, sie sind kurz, so das man sie in kurzen Pausen lesen kann -- die perfekte Reiselektüre für Dalmatien.

Besonders gefallen hat mir das Einweben der Immigrationskindererfahrungen der Autorin, deren Echo ich in meiner eigenen Familiengeschichte fühlen konnte. Wieviel ihrem Vater das Haus in Dalmatien bedeutete. Wie sehr sie selbst daran hing und wie das Haus sie durch ihr Leben begleitete, auch über den Tod ihres Vaters hinaus. Die dramatische Familiengeschichte im zweiten Weltkrieg. Aber all das überschattet nicht die Leichtigkeit des Buches, und es bleibt eine unterhaltsame und dennoch lehreiche Sommerlektüre, die einen Einblick in diese wunderschöne Region erlaubt.

Selbst der Artikel über Brač hat mir unerwarteter weise etwas völlig unbekanntes eröffnet, die Band Valentino Bošković und ihre sehr absurde Musik und Mythologie.

Das Buch hat sich für mich gelohnt, und ich kann es nur empfehlen!

• oh! Dalmatien im Folio-Verlag
• Episode des Podcasts Balla Balla Balkan mit dem Interview mit Doris Akrap zu dem Buch

Fresh bread

"A loaf of bread please"

"I'm sorry, I can't cut it because it's still hot."

"GIVE. IT. TO. ME."

News about Abstract Wikipedia

Some material about Abstract Wikipedia from the last few days:

• Abstract Wikipedia is a MacArthur 100&Change finalist
• Knowledge in the Age of AI, talk at King's College London by me, on the occasion of becoming a Visiting Professor
• Episode of Between the Brackets by Yaron Koren with me

30 years of wikis

Today is the 30th anniversary of the launch of the first wiki by Ward Cunningham. A page that anyone could edit. Right from the browser. It was generally seen as a bad idea. What if people did bad things?

Originally with the goal to support the software development community in creating a repository of software design patterns, wikis were later used for many other goals (even an encyclopedia!), and became part of the recipe, together with blogs, fora and early social media, that was considered the Web 2.0.

Thank you, Ward, and congratulations on the first 30 years.

A wiki birthday card is being collected on Wikiindex.

My thoughts on Alignment research

Alignment research seeks to ensure that hypothetical future superintelligent AIs will be beneficial to humanity—that they are "aligned" with "our goals," that they won’t turn into Skynet or universal paperclip factories.

But these AI systems will be embedded in larger processes and organizations. And the problem is: we haven’t even figured out how to align those systems with human values.

Throughout history, companies and institutions have committed atrocious deeds—killing, poisoning, discriminating—sometimes intentionally, sometimes despite the best intentions of the individuals within them. These organizations were composed entirely of humans. There was no lack of human intelligence that could have recognized and tempered their misalignment.

Sometimes, misalignment was prevented. When it was, we might have called the people responsible heroes—or insubordinate. We might have awarded them medals, or they might have lost their lives.

Haven’t we all witnessed situations where a human, using a computer or acting within an organization, seemed unable to do the obvious right thing?

Yesterday, my flight to Philadelphia was delayed by a day. So I called the hotel I had booked to let them know I’d be arriving later.

The drama and the pain the front desk clerk went through!

“If you don’t show up today,” he told me, “your whole reservation will be canceled by the system. And we’re fully booked.”

“That’s why I’m calling. I am coming—just a day later. I’m not asking for a refund.”

“No, look, the system won’t let me just cancel one night. And I can’t create a new reservation. And if you don’t check in today, your booking will be canceled…”

And that was a minor issue. The clerk wanted to help. It is a classical case of Little Britain's "Computer says no" sketch. And yet, more and more decisions are being made algorithmically—decisions far more consequential than whether I’ll have a hotel room for the night. Decisions about mortgages and university admissions. Decisions about medical procedures. Decisions about clemency and prison terms. All handled by systems that are becoming increasingly "intelligent"—and increasingly opaque. Systems in which human oversight is diminishing, for better and for worse.

For millennia, organizations and institutions have exhibited superhuman capabilities—sometimes even superhuman intelligence. They accomplish things no individual human could achieve alone. Though we often tell history as a story of heroes and individuals, humanity’s greatest feats have been the work of institutions and societies. Even the individuals we celebrate typically succeeded because they lived in environments that provided the time, space, and resources to focus on their work.

Yet we have no reliable way of ensuring that these superhuman institutions—corporations, governments, bureaucracies—are aligned with the broader goals of humanity. We know that laissez-faire policies have allowed companies to do terrible things. We know that bureaucracies, over time, become self-serving, prioritizing their own growth over their original purpose. We know that organizations can produce outcomes directly opposed to their stated missions.

And these misalignments happen despite the fact that these organizations are made up of humans—beings with whom we are intimately familiar. If we can’t even align them, what hope do we have of aligning an alien, inhuman intelligence? Or even a superintelligence?

More troubling still: why should we accept a future in which only a handful of trillion-dollar companies—the dominant tech firms of the Western U.S.—control access to such powerful, unalignable systems? What have these corporations done to earn such an extraordinary level of trust in a technology that some fear could be catastrophic?

What am I arguing for? To stop alignment research? No, not at all. But I would love for us to shift our focus to the short- and mid-term effects of these technologies. Instead of debating whether we might have to fight Skynet, we should be considering how to prevent further concentration of wealth by 2030 and how to ensure a fairer distribution of the benefits these technologies bring to humanity. Instead of worrying about Roko’s basilisk, we should examine the impact of LLMs on employment markets—especially given the precarious state of unions and labor regulations in certain countries. Rather than fixating on hypothetical paperclip-maximizing AIs, we should focus on the real and immediate dangers of lethal autonomous weapons in warfare and terrorism.

The Editors

I finished reading "The Editors" by Stephen Harrison, and I really enjoyed it. The novel follows some crucial moments of Infopendium, a free, editable online encyclopedia with mostly anonymous contributors. The setting is a fictionalized version of Wikipedia, and set around the beginning of the COVID pandemic.

The author is a journalist who has covered Wikipedia before, and now has written a fictional novel. It's not a roman à clef - the events described here have not happened for Wikipedia, even though some of the characters feel very much inspired by real Wikipedia contributors. I constantly had people I know playing the roles of DejaNu, Prospero, DocMirza, and Telos in my inner cinema. And as the book continued I found myself apologizing in my mind to the real people, because they would never act as in the book.

There were some later scenes I had a lot of trouble to suspend disbelief for, but it's hard to say which ones without spoiling too much. Also, I'm very glad that the real world Wikipedia is far more technically robust than Infopendium seems to be.

I recommend reading it. It offers a fictional entrypoint to ideas like edit wars, systemic bias, the pushback to it, anonymous collaboration, community values, sock puppets, conflict of interest, paid editing, and more, and I found it also a good yarn, with a richly woven plot. Thanks for the book!