23
Jan
2017

God’s number

God’s number is the minimum number of moves it takes to complete the Rubik’s cube, from any position. And His number is 20. That is, someone might be able to do the cube with less moves. But wherever you start from, even the hardest starting positions, you will always be able to complete the cube in 20 moves or less.
Although a simple number, it took lots of computing power donated by google and was only discovered in 2010, so it took 30 years of people thinking about the problem to work this out.

An algorithm will solve the cube, with 100% certainty. But the guarantee of success is expensive. Often it is better to use heuristics to solve combinatorial problems, like the travelling salesman problem. A rule of thumb that gives the right answer most of the time (but not always) is a heuristic. Some of the most impressive things done with computers (eg chess playing computers that beat Grandmasters) are by using heuristics, rather than algorithms.

By coincidence, 20 is also a number that Buffett, talks about in a different context. He reckons (and he should know) that it takes just 20 decisions over a lifetime to make a fortune.
When Warren lectures at business schools, he says,

“I could improve your ultimate financial welfare by giving you a ticket with only 20 slots in it so that you had 20 punches—representing all the investments that you got to make in a lifetime. And once you’d punched through the card, you couldn’t make any more investments at all.” He says, “Under those rules, you’d really think carefully about what you did and you’d be forced to load up on what you’d really thought about. So you’d do so much better.”

I’m never quite sure why he chose 20, or what evidence he basis this on. It’s probably just a rule of thumb. But if you take £1 and double it 20x you get to be a millionaire. Or perhaps more realistically, if you start with £1000 of investment, and double it 20x you get to be a billionaire. But no one has ever become a billionaire like this.

Although I’ve owned 9 shares that have doubled or more (Adnams, Cineworld, Legal and General, Red24, Bank of Georgia, The Mission Marketing Group, Domino’s Pizza Poland, Burford Capital, Somero) this hasn’t turned my original £1000 into a quarter of a million. I’m not halfway (on this measure of doubling 20x) to becoming a billionaire.  Even if Capital Gains Tax and transaction costs didn’t exist, you need to be 100% certain that when you sell a company that has doubled, that you can invest the proceeds in a new company that will also double. And you need to do that 20 times. It’s like trying to do the cube, but where someone is messing with your cube after each move, always shifting in an uncertain ways. But you still have to be 100% certain that you are making the right move. No one is able to do this and it wasn’t what Buffett was suggesting. 
Instead, it is easier to find one company that has a chance of increasing in value 20x, than 20 companies that you can be 100% certain will double.  One company that turns your original £1000 into £20,000 is nice to have, but not a fortune. But 5 successive 20 baggers, gets you to £3.2bn.  It’s the concentration on successful strategies that compounds your wealth.

Taking concentrated positions in “baggers” and holding on seems to be how people get rich with as little effort as possible eg Claude Shannon.

Ironically with his free time and independence, Shannon built a device that could solve the Rubik’s Cube (along with a flame throwing trumpet.)  
What is clear is that algorithms don’t seem to be able to identify these companies. But maybe learning systems might. That’s why I’m messing around with this book about building neural networks. 
As the financial world becomes more dominated by trading algorithms and high frequency quant strategies, no one seems to be looking at technology that makes fewer, better decisions.  It seems to me that that heuristics which help with a few good decisions will become more valuable. And maybe technology can learn to do this. Maybe.
In the meantime, one heuristic for investing is “keep holding until the story changes”.

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