In this issue:

• academic acceleration
• wrapping up Kelly
• option topics from the RH Summit
• game and food recs

Friends,

One of my close friends runs an advisory for HS students applying to college. He wrote this guest post years ago: Moneyballing College Admissions.

He lives in the Bay Area and told me he’s seeing more parents complaining about the lack of acceleration options in the public school. He said outside CA it’s becoming far more common for high schoolers to take AP Calculus BC before senior year. My 8th graders’ goal is to take it by junior year, giving himself a chance to take Multivariate Calculus by senior year at a local college. This is already offered in some high schools across the nation, including some on the peninsula. Just this week, I talked to someone whose 9th grader was in Calc BC. That only sounds crazy if you haven’t been paying attention to what I’ve been sharing about Math Academy students (my 8th grader says his 5th grade little bro is already doing the same stuff his “advanced” math class is doing.)

In our local school district, we are finally seeing the pendulum swing the other way on math instruction. A few years ago, they got rid of “tracking” in 6th grade, forcing all kids, regardless of their interest/aptitude, into the same class. Well, the seeds of change are obvious in this survey I just filled out, as I don’t think we could have even had this conversation 5 years ago:

That #7 offers choices besides “supportive” and “very supportive” tells me these 2 articles are as important as I think they are.

Smarter Than Yesterday (6 min read)

Pamela Hobart argues “the academic acceleration community needs a viable brand”. Co-sign. Terrific post. I’ve had many of the same thoughts, especially as my kid’s schoolwork will leave me wondering, as Pamela has, “what are we even doing here?”

Everyone Wants a Child Like Eileen Gu (10 min read)

”almost nobody today wants the childhood that produced her.”

Violet Gordeljevic spitting truth in this one. I’ll share a few excerpts that resonated with me. You should read it to see what lands or doesn’t for you.

On Discipline and Exceptionalism

• “So when people say she sounds and talks so disciplined, and that she knows her own mind—well, yes. That is what a decade of being asked to do your best looks like from the outside.”
• “Nobody arrives at exceptional by accident. It doesn’t turn up later as a nice surprise because the child was left alone and bored for long enough.”

On Passion and Competence

• “Passion doesn’t usually come first and then get supported. Usually exposure comes first, then competence (from actually having gone through practice), and passion tends to arrive somewhere after that, because human beings mostly love the things they are good at.”
• “What is important to understand is that she could not have fallen in love with skiing, or Mandarin, or Olympiad maths, if nobody had ever put her in front of these things…A child who is never introduced to numbers will not reveal unusual mathematical ability. A child who never sits at an instrument will not discover she has an ear.”

On Modern Parenting and “Full Schedules”

• “We didn’t lighten the load at all. We drive our children to more things than any generation in history. We just stopped asking them to become good at any of it.”
• “If we are honest, the schedule is full but the demand is zero. It’s honestly like we have swapped skill for entertainment.”
• “Underneath every version of this conversation sits the same line: I don’t need my child to be exceptional, I just want them to be happy. … But being the parent who stretches a child—who asks for one more go, who expects them to learn to write something properly or figure out that math equation, who holds the line at six when she wants to quit ballet—doing this is harder and considerably less pleasant than being her friend.”

On Warmth, Adversity, and Long-Term Value

• “Protecting a child from effort is not the same as protecting a child.”
• “What separates people with more demanding childhoods from those with easy, low demand ones, isn’t how much or even what was asked. It’s rather whether the asking sat inside enough warmth to be survivable.”
• “The choice was never between pressure and love. It was always meant to be both.”

And then my 2 favorite:

• “I have met a great many people who regret being allowed to quit”
• “The thing is, children are not good judges of what they will be glad to be good at at thirty.”

Money Angle

Wrapping up Kelly

I know I’ve published a few articles on the Kelly Criterion recently, but if you prefer other mediums:

🤳🏼 This is the IG story version

If you prefer a more in-depth lesson, the lecture version with Matt Zeigler dropped this week:

📊Accompanying Kelly Slides

Robinhood Summit 2026

I was in Houston this week for the Robinhood Summit to help with 2 sessions.

• A “trading lab” class where Mat Cashman and I gave a lesson on buying options.
• I was also invited to play the role of “trader” on a panel featuring a few of the data providers on RH’s new agentic trading platform. You can think of it like an app store, where users can subscribe to have vetted providers’ data accessible within RH’s trading agent.

Since this panel was on the “main stage” the recording is available here:

Money Angle For Masochists

2 examples from the Summit.

Mat Cashman and I did a teach-in session to a large audience of conference-goers who use options. Here’s one idea from that session.

What does optionality actually buy you?

The simplest way to understand the value of buying an option for directional reasons is to benchmark it to the counterfactual: how do I perform relative to “if I just bought the stock?”

If you buy a call, you do better in the large up move OR the large down move vs just buying the stock. You have more upside leverage, and if the stock craters, you only lose your premium. The tradeoff is that the option strategy underperforms owning the shares on intermediate-sized moves. That’s why we say owning an option is “long volatility” even if someone resists thinking in such admittedly abstract terms.

The chart subtracts the P/L of 100 shares from the P/L of ~2.2 calls on the 1-year 110 strike, at expiry. The calls cost $2,194 and carry the same delta as shares that cost $10,000 (100 shares of a $100 stock).

The shares win between roughly $78 and $137. The gap is widest at $110, where the calls expire worthless and the shares are up $1,000, a $3,200 difference. Below $78, the calls lose $2,194 at most while the shares keep falling. Above $110 the calls behave like 217 shares instead of 100.

If you buy a call and lose your premium, you can’t evaluate if this is a good or bad outcome without considering the counterfactual.

The INTC calls and a possible Micron sympathy trade

This was one of the examples I discussed in the live stream session where we talked about combining sources of data to reason through trade ideas.

1. The print. On Sep 28th, there was notable size buying in INTC October 16 130 calls.
2. An odd expiry. It was a lot of premium spent on high gamma & theta calls which expire a week ahead of Intel’s October 23 earnings call. Why spend that much premium on a short-dated bet that rolls off before the stock’s own catalyst?
3. The sympathy hypothesis. Micron was reporting on the day I was talking after the close, Sep 30th. Maybe the buyer was using INTC as a semis proxy, owning short-dated calls to catch a sympathy move off Micron’s print. It’s one possible story, not something I can confirm.
4. Did the seller make a mistake? A seller may think “these don’t capture earnings, so they don’t deserve a premium,” or INTC shouldn’t move much in the quiet blackout period before an earnings report, ignoring possible spillover effects from MU’s bellwether report and guidance.
5. The next question. Is Micron earnings even a big deal? Look at Micron’s earnings straddle. If the implied move is small, the market isn’t expecting Micron to move much. Then the sympathy thesis loses most of its appeal, since there’s less distance for INTC to get dragged along. Turn out MU earnings were priced cheaply compared to the last few years.
6. Then look at what INTC vol already costs. Implied vol was middle-of-the-road but high cross-sectionally (ie relative to other stocks in the current market regime). Call skew was rich, though not extreme.
7. Put it together. Rich vol plus a firm call skew, the primary market for MU volatility saying earnings are going to be a non-event, and a possible story for putting the INTC buyer “on a hand” adds up to making me more inclined to want to fade the INTC call buyer. Possible trades are selling INTC straddles or, if you already own the stock, writing calls against it.
8. You don’t have to sell the 130s to fade the 130 buyer. Heavy buying in one strike lifts vol across that whole expiry. Strikes near each other move together, so the bid in the 130 calls shows up in the 125s, the 135s, and the at-the-money options too. Selling the straddle, or whatever structure fits your book, still takes the other side of this buyer. Don’t anchor on the exact strike that printed. Put-call parity ensures the entire surface gets richer.

Finally, an analogy I didn’t make at the conference, but notice how much like poker the chain of thought is. The cards you can see (ie the flop) are the measurables like IV rank or call skew. The quantity of options purchased is the bet size. The expiry is like thinking about the position they bet from (ie “under the gun” or right after the button to last position or “dealer”). One of the market-makers’ advantages is that they keep tabs on notable flow, like a poker bot which examines online players’ hand histories and tendencies.

From My Actual Life

Once the RH Summit ended, I was rewarded with some nice personal moments. I took Mat Cashman to Camaraderie in the Heights area of Houston for an exceptional meal by super chef Shawn Gawle.

Shawn is a friend of mine. He lived with Yinh and I for a couple of months when he first moved to SF to be the pastry chef at Saison. If you are in Houston, do not miss Camaraderie.

Then on Friday, Yinh and I celebrated our 17th wedding anniversary. (We’ve been together for 23 years in total).

We both played hooky and went hiking up in Fairfax (Marin County) before an exceptional dinner at Vin in San Rafael. It’s both casual (we were still in hiking clothes) and worth going out of your way for. Unbelievable eating week. Might as well. I have a colonoscopy later this week, so I need to follow some dietary restrictions for the next few days.

We also did a bit of shopping in downtown San Rafael. Picked up some used vinyl at Red Devil and also went to one of the best game shops I’ve ever been in:

This Gamescape has a shared lineage with the classic one on Divisadero in SF but the San Rafael one is much larger. Their game wall is immense and ordered from least to most complex.

I picked up these 2:

Acquire is one of my favorite games and while I have it already, this newer edition has irresistible plastic buildings. I must support this.

Brass Birmingham has been at or near the top of the BGG rankings for nearly a decade, which is Nigel Richards’ level of domination. My favorite boardgame is the first edition of Brass released in 2007, but supposedly the 2018 Brass Birmingham is much better. Time to find out.

Stay groovy

☮️

In this issue:

• soulcraft
• grab a coffee and derive this with me

Friends,

My second favorite thing after a piece of art, writing, music, movie, and sport that I love is watching someone else gush over things they love. It’s why the Lost in Vegas guys are so endearing, especially when the channel first started. You were watching hip-hop heads not only discover but unpeel the layers in Tool’s music.

One of my dad friends recently bought a 1979 Jeep to restore with his son and asked if my son Zak (13) would like to help. Zak’s “hell yea” beat the sound of my last syllable when I asked him. He started watching YouTube, and we landed on a channel where these obsessed details comb the U.S. looking for “barn finds” to clean for the owners. For free! It’s free because the channel has almost 2 million subscribers clamoring to watch an impossible cleaning.

I watched a few videos. I get it. Renewal of beauty, just like the objects of renewal never goes out of style. The process is as timelessly rewarding as the result.

Caitlin’s tweet is an appeal to our spirit of obsession and craft.

Which brings me to a luxurious reading experience:

I like ‘em thick (Adam Mastroianni)

This essay not only feels good but is an important lens on the fast-approaching experiment of whether infinite electric monkeys will pound out Shakespeare.

Normally I might apologize for extensive excerpting but they are the point. I can do no better than this.

It opens:

I owe an apology to every English teacher I ever had. I always assumed that so-called “great” literature was a hoax, a punishment inflicted upon adolescents for the crime of being young. These books did not have anything special about them, and covering up that fact was simply a make-work exercise for former English majors, a sort of “jobs for snobs” program.

I was wrong about this. There is such thing as greatness. More specifically, there is such thing as thickness. Great works of fiction—for that matter, great works of any art—unfurl in response to your attention. The more time you spend with them, the more you get out of them. That kind of responsiveness is so addicting that it can lead people to do crazy things, like try to teach literature to high schoolers.

But thickness is tricky, because rewarding the careful reader often means repelling the casual one. And this is where I would like an apology in return from my English teachers, because while this might have been obvious to them, they never made it obvious to me.

I was presented with art and literature as if it was self-explanatory, and that everything wonderful about it was plainly visible from the outside. But those works were much more like dark, winding caves with treasure stashed inside of them. My teachers were like, “Right, well, into the cave you go!” and I was like “But there’s nothing in there” and they were like “Entering the cave is 30% of your grade” and so I took a few steps into the darkness and I was like “Just as I suspected: an empty cave” and then I came trudging back out and pretended that I saw something.

It goes on to describe spectacular examples of “thickness”. You won’t want to miss the The Garden of Earthly Delights painting and its unintended invitation to hear “butt music”.

Adam presents 4 qualities that make something thick with examples from a children’s book, the “ears” in Hamlet, and Penn (of Penn and Teller fame) eating fire.

There’s an amazing takedown of what passes for popular non-fiction.:

Reading a book like this feels like wandering through a Potemkin village. Touch any of the ideas, and they tip over.

He contrasts gilded examples of non-fiction with solid gold:

Thickness comes from surfacing a few facts well, and in such a way that you realize the existence of entire universes of additional facts that could be known….[Jane Jacobs book] is pointing out a fact that millions of people observe every day, but almost none of them notice.

He addresses an easily anticipated objection, which you’ll be familiar with if you have read any of deBoer on “poptimism”:

If you allow for the existence of secret treasures that can only be accessed with effort and analysis, then you empower the elitists and the snobs. “Buddy, don’t even talk to me until you’ve been in the cave!”

But look around. The snobs are in full retreat. We have swung the pendulum so far toward poptimism, toward the blinkered idea that all art is equal because all humans are equal, toward the ethos that guilty pleasures are simply pleasures, that I’m not sure if we can ever swing it back.

And finally, Adam addresses the elephant:

Erasing the line between the thick and the thin has left us defenseless against slop at the exact moment of its onslaught. Everyone can sense there’s something amiss with the prose that comes out of the machines, but we lack the language to talk about it, and so we’ve converged on the idea that slop simply means using too many em dashes, bullet points, and line breaks.

What separates substance from slop is thickness. Slop holds no secrets; it signifies nothing. Under scrutiny, it evaporates. All it can offer is bottomlessness—sure, there’s nothing on, but at least there are infinite channels!

That’s why I’m neither surprised nor dismayed when studies find that people prefer AI art to human art. Of course they do! In the short term, thinness prevails. When people are making snap judgments, they want pretty flowers, poems that rhyme, pleasing pablum, the simulacrum of thought. But none of these last…

About once a week, I get a pitch from some AI startup that wants to automate some part of my writing. The most recent one says it’s “built for credible thinkers who have a book’s worth of ideas but not the time it typically takes to write one”.

I’m sorry, but if you’re building or using a tool like this, then you’ve got slop for brains. There is no such thing as having a “book’s worth of ideas” that are all ready to go except for the small matter of choosing the right words and putting them in the right order.

I know exactly the feeling that these slop-trepeneurs are preying on, because I feel it all the time: I’ve got these thoughts in my head, and boy oh boy they’re good ones, all-timers, really, and it’s so annoying that I have to spend all this time making the words sound good, when the ideas behind the words are already so good!

But this is an illusion. The ideas are not already good. They need to be thickened. I understand why it’s tempting to force a machine do the hard part for you, but it can’t, and the hard part is the only part worth doing anyway.

Money Angle

People seemed to like the post I wrote 2 weeks ago teaching readers how to compute Kelly optimal bet sizes in their heads. A lot of people reached out saying that despite learning Kelly in the past, this treatment not only made it clearer but also helped them appreciate how its approach informs risk-taking in wider contexts.

Panoptica graciously asked me to republish it under their own banner:

After this post you will be sizing bets in your head (Panoptica)

Just to put a bow on it, I’ll restate what I think are the most crucial lessons without dwelling on the formula:

1. Even educated people are terrible at sizing bets. It’s not because it’s so complex, but I guess it’s like squatting. It seems like you should just know how to do it, but it’s actually something you need to learn the mechanics of.
2. Overbetting is incinerating money. This is something that’s hard to appreciate until you see the math. The reason you size smaller is because of the asymmetry of being wrong on your edge. If you underbet, you slow your growth rate but slow risk even faster. At least you’re exchanging lower returns for a better risk/reward. But if you overbet, you lower your growth rate AND increase your risk even faster than you reduce your reward. Both the numerator and denominator of your risk/reward move in the wrong directions!

If interested, Matt does this neat meta series “Notes on Notes”. It’s a short chat about how and why a particular article comes together in the first place. You can watch it here:

via Matt Zeigler@CultishCreative

A short yet broad-ranging talk with @KrisAbdelmessih on @Panoptica_ai for his @EpsilonTheory: Unplugged essay, “After this post you will be sizing bets in your head” Kelly bets, using AI to learn math, creativity… NEW Notes on Notes!

To round out this Kelly sprint, I have 2 more bits that are again overtures to curious learners who may find math intimidating.

1) Slides

The first is a condensed slide version, which I hope makes this accessible. It was born out of teaching Kelly to my 8th grader at breakfast this past Tuesday. “Zak, I wanna see if I can teach you something neat in 5 minutes.” He rolled his eyes, but at least he humored me while scarfing down his cereal.

📊Moontower Kelly Slides

2) An empowering derivation

The derivation of the Kelly formula is so fun because as it rolls downhill, a number of concepts we talk about in this letter stick to it, so when we get to the end it feels like something grand, but it’s so damn compact.

Another teaching experiment. Let’s see if I can narrate the derivation in a way so that as you follow along it never feels “hard”. I want to prove that this is fun to do and while I don’t expect to convert everyone, I do think there’s a bunch of you who’d like to be able to learn this but feel blocked because you have gaps in your foundations or can’t remember HS math, or just lack some confidence.

Screw all that, I’ll lay my jacket over the puddles so you can see that it’s not so bad out here. Just come along.

Money Angle For Masochists

Deriving Kelly From Scratch

Stating the question

You have a bet. You win with probability p and lose with probability q = 1 − p. If you win, you get paid B times what you risked. If you lose, you lose what you risked. B is also just a return. So if you double your money on a bet, B=1=100% return.

You’re going to bet the same fraction f of your bankroll every time and let it ride.

What’s the f that yields the highest compounded return?

Step 1: What one bet does to your wealth

If your wealth is W and you bet the fraction f:

Win: W → W(1 + Bf) Lose: W → W(1 − f)

Example:

Your starting wealth is $100 and you bet 50% of it on a coin flip. Remember B =1 because when you win you make 100%. When you lose you always lose f which is your bet size.

Win: 100 → 100(1 + 1*.50) = $150 Lose: 100 → 100(1 − .50) = $50

You keep the part you didn’t bet no matter what. A win adds B times your stake. A loss takes your stake away.

Step 2: What many bets do to your wealth

Play n bets. You win h of them and lose the other n − h. Each bet multiplies whatever the last one left you, so the multipliers stack:

Wₙ = W₀(1 + Bf)ʰ(1 − f)ⁿ⁻ʰ

The order of wins and losses doesn’t matter. Only the count does.

Example:

I bet 50% of my wealth each turn on the coin. I play 4 times and I win 3 of them.

100(1+1*.5)3(1-.5)1= 168.75

Order doesn’t matter. If I lost 50% on the first flip, then won 3 in a row:

Start: 100 Lose (×0.5): 50 Win (×1.5): 75 Win (×1.5): 112.50 Win (×1.5): 168.75

Step 3: Turn total growth into a growth rate

Wₙ is where you end up. We want a per-bet growth rate.

You already know how to do this. If an investment grew by a factor of (1 + 8%)¹⁰ over 10 years, you take the 10th root to get the CAGR back. Same move here: take the nth root of this equation: Wₙ = W₀(1 + Bf)ʰ(1 − f)ⁿ⁻ʰ

Note that W₀ can be divided out, just as if your starting identity was 150 = 100(1+8%)¹⁰ and you turned that into 1.5 = 1.08¹⁰ before taking the 10th root to get to annual growth rate.

This equation took our simple total growth equation and turned it into a growth rate equation:

Step 4: Let probabilities take over

We can clean up our new growth equation with several handy notation substitutions.

Ps and Qs

h/n is the share of bets won

(n-h)/n is the share of bets lost

Over a long run, the fraction of bets you win settles down to your win probability:

h/n → p and (n − h)/n → q

G

Wₙ/W₀ is just a wealth multiple. If you made 200% on your investment portfolio over a decade, your wealth multiple is 3 because you started with $1 and ended up with $3.

We’ll call that wealth multiple G (for “gross multiple”)

So the per-bet growth factor becomes:

G = (1 + Bf)ᵖ(1 − f)ᑫ

G = 1.05 means your bankroll grows 5% per bet on a compounded basis. In traditional investing, we’d substitute the word “year” for “bet”. Each flip is like a year.

Our job is to find the f that makes G (the gross multiple of our wealth) as big as possible.

Step 5: Take the log to make the math easy

Maximizing G means taking its derivative with respect to f and setting it to zero.

It’s 2026, you don’t need to know how to actually differentiate an equation. You just have to awaken that part of your brain that knows:

a) a derivative is the slope of a function at a given point on a curve

b) when the slope of a curve is 0 this is a maximum or minimum

c) intuitively, we can reason that this is a growth curve is a hill with no bumps. Its slope starts positive and only ever gets smaller as you bet more, so it can hit zero exactly once, and when it does, you’re at the top. (the jargon version: this growth curve is concave: it bends downward everywhere from the max, with no inflection points)

We are still here:

G = (1 + Bf)ᵖ(1 − f)ᑫ

But G is a product of powers, which is nasty to differentiate.

But remember from simple pleasures, logs fix this. They are the inverse of exponentiation, allowing them to turn multiplication into addition!

Push the cobwebs away to recall that this works:

log(100) = log(10 × 10) = log(10) + log(10) = 1 + 1 = 2

That’s not all logs do.

They pull exponents down in front: log(xᵖ) = p · log(x).

We can prep that equation for differentiation by taking the log of both sides and using both of those sexy log features:

log(G) = p · log(1 + Bf) + q · log(1 − f)

Maximizing log(G) gives the same f as maximizing G, because log always rises when its input rises.

There’s another little bonus.

Log(G) is the log return per bet, the same quantity as ln(S₁/S₀).

It re-expresses a compounded, multiplicative growth factor as a continuously compounded rate, and rates add cleanly.

Step 6: Differentiate and set to zero

Once you know this is a derivative problem because you are trying to maximize then we can rely on crutches (Claude) for thing that’s hard to remember.

Namely that:

• the derivative of log(x) is 1/x.
• If there’s something inside the log, also multiply by the derivative of that inside piece (the chain rule)

So we have our equation:

log(G) = p · log(1 + Bf) + q · log(1 − f)

then we differentiate our terms to be added with respect to f:

• p · log(1 + Bf) → pB/(1 + Bf) (the inside, 1 + Bf, has derivative B)
• q · log(1 − f) → −q/(1 − f) (the inside, 1 − f, has derivative −1)

Set the sum equal to zero, which is where the growth curve is flat at its peak:

pB/(1 + Bf) − q/(1 − f) = 0

Step 7: Solve for f

Move the second term across and cross-multiply:

pB(1 − f) = q(1 + Bf)

pB − pBf = q + qBf

pB − q = pBf + qBf

pB − q = Bf(p + q)

But don’t turn your pattern recognition noggin off!

Since p + q = 1, this collapses to:

f = (pB − q) / B

f = p − q / B

Can you reproduce this right now on a blank sheet of paper?* Probably not. But go through it once the way you used to trace when you learned the motions for drawing comic book characters or flowers or in my case TMNT. After a single reproduction by hand, I assure you some neural pathways will re-open that have had construction signs in front of them for years.

And to tie this back to the beginning, that is the joy of thickness.

[Get your mind back over here, this is a family letter.]

*You will be able to reproduce it on your own after 2 or 3 attempts. I don’t know why the motion of the pencil is a 10x better instructor than reading it a bunch of times (generation effect maybe?). But this is one of those learning principles I take seriously and impress on my kids.

The world will seduce you with ease where you’d be better served by friction. It is a 21st-century skill to have a point of view on the difference.