## Handshake puzzles and Birthday bets

Warning: use these tools wisely, they can keep nieces and nephews busy for hours

What is the sum of all the numbers from 10 to 1? That’s difficult.

One repeated theme – because it works! – is reframing. The same information but a new presentation changes our understanding.

What is the sum of these numbers: 10, 9, 1, 8, 2, 7, 3, 6, 4, 5? That’s easier. Reframe again, this time visually.

Each what is the sum question can be framed as a triangle. But reframe again, first to staircases, then as pairs.

Doesn’t this feel like magic? The universe presents this little nugget (What is the sum of all the numbers from 10 to 1?) and rather than slog through we skip over. Reframing numbers into shapes changes our tool from addition to multiplication. Magical. We went from brute force to clever pairing to formulaic: (n*(n+1))/2.

Another question: In a group, how many handshakes must occur for everyone to shake everyone else’s hand?

Two people have one handshake. Five have ten connections.

Like triangle numbers, it’s almost the same math! Rather than counting the dots, we want the connections. Rather than (n*(n+1))/2, the formula is (n*(n-1))/2.

It’s not only handshakes to count but games in a round robin, cables to connect computers, and shared birthdays.

In a group of 31 people, what are the chances any two people share a birthday? Thirty-one is a good number because it frames our thinking. “That’s like one month, so one-in-twelve”.

Ha!

The chances are closer to three-in-four thanks to our connections.

There’s a 99.7% (364/365) chance two people have different birthdays, (.997)1 (connection). The chance of five people having different birthdays, (.997)10, is 97%. Even the chance ten people have different birthdays, (.997)45, is 87%.

But keep going. Thirty-one people have 465 connections and a 25% chance of differing birthdays.

Every day on Twitter, the joke goes, someone is the main character – and you don’t want it to be you. Something is always happening because of this birthday/games/handshake structure. It’s easier not to get wrapped up in “this headline” knowing there will always be headlines.

## Michael Covel

Michael Covel (@Covel) joined Barry Ritholtz (@Ritholtz) to talk about trading, trending, and Thailand. Okay, not just Thailand,but it starts with ‘T’ and I’m a simple writer.

Covel – and Ritholtz – fall into the category of “good talkers” and I listen to at least part of all of their podcasts. Get them together and you get two solid hours of conversation.

This podcast wasn’t as into the weeds I know about but provided lots of superficial anecdotes about things I don’t know like the experiences of working in Japan, what it was like to see economic ideas change, and how capital is like Gap t-shirts.

One final personal note, Covel challenges my ideas on his podcast. Whether it’s something I don’t understand or something I’m not interested in – but I try to listen anyway. One of the ways to use Twitter for good is to bust your biases. That’s something true for podcasts as well.

Covel was influenenced by Richard Dennis(wiki) and the Turtle traders. The story goes, and Covel says he has no reason to doubt this, that Dennis and fellow trader William Eckhardt saw Trading Spaces (Eddie Murphy). Eckhardt said that could never happen. Dennis said it could, and he’d prove it. A bet was made.

Dennis recruited a group of – mostly average – applicants how to trade on a trend-following strategy that he created. This group of ‘Turtles’ turned out to be widely successful.

The application is true with regards to the podcast itself. Covel made himself into a great trader, writer, and podcaster. Ritholtz admits this too, that radio didn’t come naturally to him and that there was a learning curve. He’s gotten pretty good at it.

This is true for so many people, especially comedians.

Comedians are – sometimes sadly – not very good at anything. A lot of the art from people like Phil Rosenthal or Judd Apatow comes from places of pain or darkness.

Even people like Amy Schumer or  B.J. Novak weren’t born as comedians.

In his interview with Rithotz, Ken Fisher noted that even though his dad was a great writer, he wasn’t.

Ritholtz compliments Fisher’s work and says, “you’ve obviously inherited your dad’s writing skills.”

“Not true,” replies Fisher, “because if I had inherited them they would have come to me very naturally, but I worked hard to learn how to write.”

Except in rare, physical domains like sports, you can be good (or great) with some work.

Jack Canfield cautioned Tim Ferriss about pegging “being great” on only one thing. He tells the story of a family friend who wanted to be in the NBA. Of course, the guy wasn’t good enough to play professional basketball, so he took another route. He worked to get in the front office. He’s in the NBA, just in a different form than he first imagined.

It’s trend-following, not trend predicting.

As a simpleton (n00b), I didn’t really know what “trend-following” was. Covel set me straight when he said:

“If you’re a trend following trader you don’t have a mindset or prediction where any particular market is going to go. So when it starts to move, you’re just following the crowd.”

Later in the interview he adds, “nothing can be predicted.”

I was thankful to hear this because predication is hard. Like, really, really, really hard. It seems to me that Covel (trend-following) champions non-prediction. This is paramount for complex systems (trading, ecosystems, a college classroom). There will be some outcome, but not any particular one. Mathematicians explain it regarding birthdays, so I will too.

Imagine you’re in a room with 25 other people. Mostly strangers, none who you know well. One of them is me, and I approach you with a bet.

“Would you wager \$100 that two people in this room share a birthday?” I ask. Note, this is much easier on the internet because my poker face is terrible (and so is this bet).

“Hmm,” you think to yourself, “this seems like a good bet.” There are only 25 people in the room, and there are 365 days in a year. Chances are definitely against it. Right? “Sure,” you say, “I’ll take the bet.”

So you and I go around the room (with a paper plate) and write down birthdays until we get a match, and chances are that we will.

This birthdays bet (explained very well by John Allen Paulos in Innumeracy, and Clay Shirky in Here Comes Everybody) demonstrates the something will happen ethos that trend-following subscribes to. We can’t predict what birthday will match, only that one probably will. The math, very briefly, looks like this.

Trend-following lives in this same cul-de-sac of knowledge. There will be something that happens, and you can profit by acting when it does. (And now you have a bet for the next in-law family reunion)

Would you rather have a chance of 80% of yes or 20% of no?

Covel and Ritholtz touch a bit on Kahneman’s work on framing and loss aversion.

Look at the question above, it seems like they would be the same but Kahneman found that the responses people give are quite different.

If people are given a 40% chance on winning \$100 or just to take \$20, they’ll often favor the latter. The saying could go, \$20 in hand is better than any psychology mumbo jumbo and rewards in the bush.

That’s well and good and unremarkable, except that people switch their choices around when the outcome is reversed. If people are given the chance to  a 40% chance on losing \$100 or just to lose \$20, they’ll often favor the former. People are risk seeking to avoid losses. This matters in trading because if you’re trying to get back to zero, psychology suggests you’ll take more risks.

Related to this is loss aversion, which Richard Thaler explains beatutifully with a pyramid analogy. Also in that post is how Josh Brown creates win-win situations from down markets.

The prostate test test.

Covel says that he and Ritholtz are at the age for getting a prostate test, but should think twice about it. The side effects may be higher than advertised and the payoffs lower. (Note above we just mentioned our tendency to seek risks – have the test and side effects – to avoid a loss).

Covel says that reading Gerd Gigerenzer has changed his view on this. Gigerenzer has been on this blog before. When Scott Galloway spoke with Rithotz he outlined his five aspects of great companies. His model is simple and we noted that that’s good because we don’t want models that fit too well. In Gut Feelings Gigerenzer writes, “In an uncertain world, a complex strategy can fail exactly because it explains too much in hindsight.” That could be part of Cove’s apprehension of prostate exams. The other part is bad math, which Covel also got from Gigerenzer.

Let’s explain.

Pretend that 14% of a population has a disease, and a screening tool exists that is 98% effective. If we have 1,000 people, how many will be correctly diagnosed? Much like our birthday bet, things are not as they first appear.

Let’s do the easy math first. If 14% of 1,000 people are sick, then we have a chart that looks like this:

 Has disease Does not have disease Total people: 1,000 140 860

Not so hard, and if we had a test with perfect prediction, then that would be the end of it. But our test is only 98% accurate.

Of our 140 sick people, we will correctly identify 98% of them, 137. Our chart gets updated.

 Has disease (140) Does not have disease (860) Tested positive 137 (98% of 140) Tested negative 3

Then we do the same to the ‘does not have disease’ group.

Of our 860 not sick people, we will correctly identify 98% of them, 843.

 Has disease (140) Does not have disease (860) Tested positive 137 (98% of 140) 17 Tested negative 3 843 (98% of 860)

We see then that 20 (3+17) of our original 1,000 people will get the wrong diagnosis – 5% of the general population.

Now if you thought this was a bit murky math, you aren’t alone. Doctors miss this too.

Successful people have systems, and follow the rules.

“This is not a day to day guessing game,” Covel says. There’s not single point in the interview where I noted the emphasis on systems, but by the end it was clear. Covel is a systems advocate. When Dennis taught people, he taught them a system.

When Covel speaks about trend-following he explains it as a system with rules:

1- What’s the portfolio?

2- What will force you in?

3- How much will you be in for?

4- When will you exit for a loss?

5- When will you exit for a win?

Those questions are easy in hindsight, but hard in application. In part because it takes time and temperament.

Systems don’t have to be complicated either. Ritholtz says “never ask a room full of people what they want for dinner.” That’s a system too. Like a basic computer code or logic statement; if more than 8 people, then do not ask what people want for dinner.

Warren Buffett aims to avoid the “institutional imperative” at Berkshire. Scott Adams compares people to moist robots and has rules for that system.

Systems are good, but systems won’t be perfect.

Covel’s rule #4 (When will you exit for a loss?) is easy to state, but hard to act on. Ritholtz says that when he was a trader it was “okay to be wrong, but not okay to stay wrong.” You can’t reach and try to get back to even because you’ll take more risks getting there.

Some problems are too hard for any system. In his book The Hard Thing About Hard Things, Ben Horowitz notes that for hard problems there’s no prescription.

“The problem with these books (about business) is that they attempt to provide a recipe for challenges that have no recipes. There’s no recipe for really complicated, dynamic situations.”

The best systems are ones where the big mistakes are eliminated (as best they can be, but never absolutely) and wiggle room is given for the small choices.

Books

Beside Kahneman’s Thinking Fast and Slow, Covel suggests Blue Ocean Strategy, The Fountainhead, Linchpin, The Wisdom of Insecurity, and The Success Equation.

Thanks for reading, I’m @mikedariano on Twitter. Want to catch up on the posts, The Waiter’s Pad: Volume 6 is available here. You can also donate a few bucks here. If you want to work together, please get in touch.