Magic card tricks

Interesting article in the New York Times today about how people to this day still do not know how magician David Berglass did his “Any Card At Any Number” trick. In this trick, a magician asks a person or two to name a card (e.g. Queen of Hearts) and a number (e.g. 37) and then in a variety of ways produce a deck where that card appears at that order in the deck. The supposed standard way to do the trick is for the magician to manipulate the cards in some way but Berglass does his trick by never touching the cards. He can even do the trick impromptu when you visit him by leading you to a deck of cards somewhere in the room or from his pocket that has the card in the correct place. Now, I have no idea how he or anyone does this trick but one way to do the trick is to use “full enumeration”, i.e. hide decks where every possibility is accounted for and then the trick is to remember which deck has that choice. So then the question is how many decks would you need? Well the minimal number of decks is 52 because a particular card could be in one of 52 positions. But how many more decks would you need? The answer is zero. 52 is all you need because for any particular arrangement of cards, each card is in one position. Then all you do is rotate all the cards by one, so the card in the first position is now in the second position for deck 2 and 52 moves to 1 and so on. What the magician can do is to then hide 52 decks and remember the order of each deck. In the article he picked the reporter’s card to within 1 but claimed he may only be able to do it to within 2. That means he’s hiding the decks in groups of 3 and 4 say and then points you to that location and lets you choose which deck.

The myth of the heroic entrepreneur

I sometimes listen to the podcast “How I built this“, where host Guy Raz interviews successful entrepreneurs like Herb Kelleher, who founded Southwest Airlines, Reid Hoffman of Linkedin, Stacy Madison of Stacy’s Pita Chips, and so on. The story arc of each interview is similar – some scrappy undervalued person comes up with a novel idea and then against all odds succeeds by hard work, unrelenting drive, and taking risks. The podcast fully embraces the American myth of the hero entrepreneur although Guy tries to do his best to extend it beyond the stereotypical Silicon Valley one typified by Steve Jobs or Elon Musk. At the end of each interview Guy will ask the subject how much of their success was due to luck and how much due to their ingenuity and diligence. Most are humble or savvy enough to say that some large fraction of the success was luck. While I have no doubt that each successful entrepreneur is bright, hard working, and possesses unique skills, there are countless others who are equally talented and yet did not succeed. Each success story is an example of survivor bias. We sometimes hear about spectacular failures, like the Edsel , but rarely do we hear about the story of “How I almost built this”.

There is a stock market scam where you email blocks of 1024 prospective marks a prediction of what a stock will do that week. For one half, you say the stock will go up and for the other half you say it will go down. Then for the half for which you were correct, you do the same thing and half of them (one quarter of the original) will receive a correct prediction. Finally after ten weeks, one of the original 1024 will have received 10 correct predictions in a row and think that you are either a genius or have inside information and will be primed to sign up for whatever scam you are selling. The lucky (or unlucky) person is fooled because they lack the information that 1023 others did not receive perfect predictions. Obviously, this also works for sports predictions.

While, I think most success is luck there do seem to be outliers. Elon Musk seems to be one. He manages to invent new industries and succeed with regularity. Warren Buffet does seem to be able to beat the market. However, it is for us as a society to decide how winners should be rewarded. In many industries there is a winner-take-all dynamic, where the larger you get the easier it is to crush the competition. Mark Zuckerberg is clearly skilled but Facebook is dominant right now because it is a monopolist; it simply buys up as many competitors as it can. The same goes for Google, Amazon, and AT&T until the government broke it up. Finance works that way too. The bigger a bank or hedge fund gets, the easier it is to succeed. A small fluctuation that propels one firm a little ahead of the rest at the right time will be exponentially amplified. While, I do think it is a positive thing to reward success I don’t think the reward needs to be so disparate. Right now, a very small difference in ability (or none at all) and a lot of luck can be the difference between flying to your house in the Hamptons in a helicopter or selling hotdogs from a cart on Fifth Avenue.