Moontower #82


This week I’m going to share some things I found to just be a joy to read.

When You Browse Instagram and Find Former Australian Prime Minister Tony Abbott’s Passport Number (Link)
The hacker known as “Alex”

I discovered this post via Trevor McKendrick’s outstanding (and concise) letter. His description is perfect:

“This is amazing writing because the story itself isn’t all that funny…But the writer has a very specific voice and tone, and uses it to turn a few moments into pure hilarity.”

You will learn stuff. Like the fact that your boarding pass number is a key to your phone number and passport details. And what can someone do with your passport?

  • Book an international flight as you.
  • Apply for anything that requires proof of identity documentation with the government, e.g. Working with children check
  • Activate a SIM card (and so get an internet connection that’s traceable to you, not them, hiding them from the government)
  • Create a fake physical passport from a template, with the correct passport number (which they then use to cross a border, open a bank account, or anything)

And if you are interested in some low level hacking using little more than browsers’ built-in “Inspect” function this post can help you.

But overall, the best part of this post is the writing. Don’t take big gulps of soda while reading it.

(Also, don’t forget to toggle “Hard Mode” on the upper right of Hacker Alex’s website)

David Foster Wallace humor

I haven’t read Infinite Jest. My only real exposure to DFW has been that outstanding “This is Water” speech which reinforced many ideas but mostly a reminder that we are so obliviously self-involved that empathy requires deliberate effort.

DFW did some journalism assignments. Here are 2 longer articles that I found hilarious. His writing style is right up my alley, I could fill pages of a swipe file with examples of inspiration. But by far his most impressive ability is his X-Men-level powers of observation. He sets a high standard for “attention to detail”.


  • Shipping Out: On the (nearly lethal) comforts of a luxury cruise (Link)
  • Consider The Lobster (Link)

The Money Angle

The permalink version of this week’s Money Angle if you prefer to save this for later

Path: How Compounding Alters Return Distributions (Link)

Full text:

Compounded returns experience “variance drain”. This idea captures the fact that typical result of compounded returns is lower than if you compute arithmetic returns even though the expected value is the same. We mostly care about compounded returns. This describes the situation in which your bet size or allocation is a fixed percent of your wealth, savings, or bankroll.

This is in contrast to keeping your bet size fixed (ie if you invested $10,000 in the stock market every year regardless of your wealth).

The distinction is critical because as humans we experience the path of our investments so we care about the distribution of returns in addition to the expected value.

Let’s back up for moment.

Recapping Intuition

  • What land are we in?
    • Compounding Land

      If you bet 1% of your wealth on a coin flip and win then lose, you are net down money. This is symmetrical. If you lose, then win, still down money.

      1.01 * .99 = .99 * 1.01

    • Additive Land

      In additive or non-compounding land we bet a fixed dollar amount regardless of wealth.

      So if I start with $100 and win a flip, then bet $1 again and lose the flip I’m back to $100. The obvious reason is the $1 I bet when my bankroll increased to $101 is less than 1% of my bankroll.

  • The order of win then lose, or lose then win leaves you in the same place in both worlds.

    The order does not matter if we are consistent about how we size the bet (so long as we are consistent to the style whether it’s fixed dollar or fixed percentage).

So is fixed percentage somehow “bad” in that it opens you up to volatility or variance “drag”? 

Well in the last example we used an alternating paths. Win then lose or vice versa. Let’s look at the case where instead of alternating wins and losses, we trend. Win-win or lose-lose.

  • In the additive case, we are either up 2% or down 2%
  • In the compounded case we are up 2.01% or down 1.99%

Wait a minute. In the compounded case, we are better off both ways! So the compounded case is not always worse.

The compounded case is better when we trend and worse when we “chop”.

If bet a fixed percent of our bankroll fair coin toss game we are in compound return land.

Compounding is not “bad”, it just alters the distribution of our terminal wealth

Your net compounded return in the coin-flipping game is negative more often than it’s positive, even though the game has zero expectancy.

So why is the median outcome negative?

It goes back to the trend vs the chop. Compounding likes trending and hates chopping as we saw earlier.

  •  Chopping happens more 𝐨𝐟𝐭𝐞𝐧 so you get a negative median
  • …but this is balanced by a larger trending bonus due to compounding.

Let’s illustrate.

2 Coin Flips

There’s 4 actual scenarios:

2u (trend)
1u, 1d (chop)
1d, 1u (chop)
2d (trend)

Zoom in on “compounding bonus/drag”:


  • Chop and trend happen equally.
  • The magnitude of the boost/drag is also equal.

3 Coin Flips

There’s 8 total outcomes, but again order doesn’t matter. So there’s really just 4 outcomes.

The “chops” are bolded. They represent compounding “drag”


  • You drag 75% of the time!
  • The larger positive boost magnitudes make up for the frequency.

Now that you have the gist, let’s do 10 flips.

10 Coin Flips

  • 65% of the results are chop giving you compounding drag.
  • The times you trend though crush your performance if you only bet fixed dollar!

Visualizing “The Chop”

Let’s take a look visually at paths where N=10  to see the “chop”.

Pascal’s Triangle is a quick way to to get the coefficients of a binomial tree. The coefficients represent combinations which are weighted by the probabilities in the binomial expansion.

I enclosed the “chop” or drag paths

100 Coin Flips

  • The negative median now becomes very apparent in the “cumulative probability” column.
  • The chop occurs in 68% of paths. The median return is -.50% after 100 flips though the expectancy is still zero.
  • In additive world if you win 50 $1 bets and lose 50 $1 bets your p/l is zero.
  • In compounding world, where you bet 1% each time you are down 50 bps in that scenario.
  • The negative median associated with compounding is balanced by better outcomes in the extremes.

Both the maximum and minimum returns in simulations are better than the fixed bet case. This simulation by Justin Czyszczewski (thread) shows just how substantial the improvement is in those less probably trending cases:

Lessons From Compounding Coin Flips

  • Your overall expectancy is zero because the common chop balances the rare but heavily compounding trends.
  • Paths affect distribution of p/l even if they don’t affect expectancy.

Since we actually experience “path” and all its attendant emotions, it pays to think about the composition of expectancy and returns.

Last Call

Song Exploder (Netflix series)
Various Artists

This series goes behind the scenes on the making of iconic songs. The series started as a podcast and now has nearly 200 episodes but the Netflix series launched 2 weeks ago. We got lured in by the Lin-Manuel Miranda episode but stayed for REM and Ty Dolla Sign. If you are into music docs this is catnip.

Yinh Interviewed Jessa Jones (Link)
Growth From Failure Podcast
This was one of my favorite interviews Yinh has done. Jessa, who founded iPad Rehab, is irreverant and lives life in a very first principles way. Yinh’s teaser:

Jessa’s story is one of my favorites – she has a PhD in molecular genetics from The Johns Hopkins University and today is a a masterful Microsolderer. This episode highlights her journey from slicing up fruit fly eyeballs to fixing logic boards of phones and laptops. We discuss her journey of how that transition happened from smashing up a toilet to recover her phone!

I loved hearing about the emotional connection she has in device recoveries and we talk about everything from porn stars and newborn babies to homicide victims. Jessa’s profile and mindset makes me question conventional wisdom and might change my perspective of pajamas forever.

The Economics Of Vending Machines (Link)
The Hustle
This side gig is anything but passive income, but this market is extremely fragmented attracting many side-giggers. Now we just need a deep-dive into the Japanese vending machine market!

From my actual life 

I helped out with the learning pod this week, spending time with the 2 2nd graders. Here’s what I covered:


  • I had them try to decode the following code:

    4 15 7

    (with some prodding they eventually figured out it was a simple letter-number cipher spelling “dog”)

  • We played the game Mastermind.

    How to play:

    1. A codemaker constructs a hidden sequence of 4 different colored beads (out of a possible 6 colors).
    2. The codebreaker tries to guess the sequence by arranging 4 colors in order.
    3. The codemaker gives non-verbal feedback:

      a) Identifies how many of the colors used are correct
      b) Identifies how many beads are the right color AND in the right position

    4. Repeat until the code is cracked

      Enrichment questions:

      How can the game be made easier?
      How can the game be made harder?

      And if you have an older onlooker…how many possible codes can be created?

      And if you have an Excel fan in the vicinity, see how you can solve such problems using the hypergeometric distribution. (A Reddit thread targeting game designers)

A Money Lesson

You can find my script in the below post. It covers income and budgets and begins the conversation of business:

A Socratic Money Lesson For 2nd Graders (Link)

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