matt levine goat. loved this bit from his newsletter:
Summary
There is another strange anecdote from Bankman-Fried’s even earlier days, as an intern at Jane Street Capital, the proprietary trading firm.2 Jane Street wants to teach its interns to think in bets, so they are encouraged to bet against each other all the time. To prevent disaster, there is a rule that no intern can lose more than $100 in a day.3 One morning, another intern, called “Asher” in the book, offers to bet Bankman-Fried on the maximum amount any intern will lose that day. “This cannot settle above one hundred or below zero, right?” confirms Bankman-Fried. And then he buys at 65: If any intern loses more than $65 that day, Asher will pay Bankman-Fried that intern’s losses above $65; if none do, Bankman-Fried will pay Asher the difference between $65 and the maximum loss. If an intern loses $100, the maximum, then Bankman-Fried gets $35. If the biggest loser loses only $50, he pays Asher $15.
Of course Bankman-Fried can easily win this bet by losing $100 himself. That is not optimal, for him, but he can use that fact to manufacture a good trade. He immediately turns to the other interns in the room and offers them $1 to take an even-money coin flip for $98. Somebody (Bankman-Fried or his counterparty) will lose $98 on this bet, so Asher will have to pay him $33 ($98 minus $65). If Bankman-Fried wins, he gets $98 (from winning the coin flip), plus $33 (from Asher), minus $1 (he paid the other intern a premium to do the coin flip), for a net gain of $130.4 If he loses, he loses $98 (coin flip) plus $1 (payment) but gets back $33 (Asher), for a net loss of $66.5 That’s a very positive-expected-value bet for him: Bankman-Fried has a 50/50 chance of winning $130 or losing only $66. But it’s also positive-expected-value for his counterparty on the coin flip. Lewis writes:
To the Jane Street way of thinking, Sam was offering free money. A Jane Street intern had what amounted to a professional obligation to take any bet with a positive expected value. The coin toss itself was a 50-50 proposition, and so the expected value to the person who accepted Sam’s bet was a dollar: (0.5 x $98) - (0.5 x $98) + $1 = $1.
Bankman-Fried easily saw how to manufacture the bad outcome for Asher. This is a key skill in trading, but especially in crypto trading. “Asher was now clearly deeply embarrassed.”
Bankman-Fried finds a taker, wins the coin toss and collects $98 from the other intern. Then he goes again:
To maximize Asher’s pain, some intern needed to lose one hundred dollars.
I’ll pay a dollar to anyone who will flip me for ninety-nine dollars, Sam shouted.
Now he had a machine for creating wagers in which both parties enjoyed positive expected value. That machine was named Asher. Interns were lined up to take the bet. “People get so obsessed with free dollars when you frame it correctly,” said Sam. … “If I’d have spent the rest of the internship flipping that coin, I’d have been satisfied.” And for a while it appeared that he might, as he won the second coin flip too.
I’ll pay a dollar to anyone who will flip me for ninety-nine fifty, shouted Sam.
The other interns clearly felt obligated to take the bets, but the mood in the room was shifting in response to Asher’s feelings. … But Sam won the third coin flip too, so to his way of thinking the gambling wasn’t yet over.
I’ll pay a dollar to anyone who’ll flip me for ninety-nine seventy-five, he shouted.
It wasn’t until the fourth flip that Sam lost — and by then everyone except Sam was unsettled by Asher’s humiliation.
The point of this story in the book is that Bankman-Fried gets in trouble with his bosses for being mean to Asher, which he thinks is unfair: “What he’d done to Asher was no more than what Jane Street was doing to competitors in financial markets every day.”
But there are two much weirder things in this anecdote.
First: “A Jane Street intern had what amounted to a professional obligation to take any bet with a positive expected value”? Really? I feel like, if you are a trading intern, you are really there to learn two things. One is, sure, take bets with positive expected value and avoid bets with negative expected value.
But the other is about bet sizing. As a Jane Street intern, you have $100 to bet each day, and your quasi-job is to turn that into as much money as possible. Is betting all of it (or even $98) on a single bet with a 1% edge really optimal?6
People have thought about this question! Like, this is very much a central thing that traders and trading firms worry about. The standard starting point is the Kelly criterion, which computes a maximum bet size based on your edge and the size of your bankroll. Given the intern’s bankroll of $100, I think Kelly would tell you to put at most $10 on this bet, depending on what exactly you mean by “this bet.”7 Betting $98 is too much.
I am being imprecise, and for various reasons you might not expect the interns to stick to Kelly in this situation. But when I read about interns lining up to lose their entire bankroll on bets with 1% edge, I think, “huh, that’s aggressive, what are they teaching those interns?” (I suppose the $100 daily loss limit is the real lesson about position sizing: The interns who wipe out today get to come back and play again tomorrow.)
But I also think about a Twitter argument that Bankman-Fried had with Matt Hollerbach in 2020, in which Bankman-Fried scoffed at the Kelly criterion and said that “I, personally, would do more” than the Kelly amount. “Why? Because ultimately my utility function isn’t really logarithmic. It’s closer to linear.” As he tells Lewis, “he had use for ‘infinity dollars’” — he was going to become a trillionaire and use the money to cure disease and align AI and defeat Trump, sure — so he always wanted to maximize returns.
But as Hollerbach pointed out, this misunderstands why trading firms use the Kelly criterion.8 Jane Street does not go around taking any bet with a positive expected value. The point of Kelly is not about utility curves; it’s not “having $200 is less than twice as pleasant as having $100, so you should be less willing to take big risks for big rewards.” The point of Kelly is about maximizing your chances of surviving and obtaining long-run returns: It’s “if you bet 50% of your bankroll on 1%-edge bets, you’ll be more likely to win each bet than lose it, but if you keep doing that you will probably lose all your money eventually.” Kelly is about sizing your bets so you can keep playing the game and make the most money possible in the long run. Betting more can make you more money in the short run, but if you keep doing it you will end in ruin.
I don’t know what actually happened at Jane Street that day. I assume that the anecdote in Going Infinite comes from Bankman-Fried. “People get so obsessed with free dollars when you frame it correctly,” he says; he is the one framing this story. What I take from this story, and from other anecdotes here about his early trading career, is that Bankman-Fried is good and facile and clever at calculating expected value, and at finding ways to inflict pain on counterparties, but he is … not even bad at trade sizing; he just doesn’t think about it at all. It is not a part of his life. He goes all in on everything. In his model of the world, if you are offered a bet with a 1% edge, you should put all of your money on it, over and over again, until you lose everything. How will that play out in the second half of the book?
Here’s the other weird thing about the anecdote: These bets obviously have negative expected value?
Not for his counterparties, who get paid $1 to take a fair coin flip, but for Bankman-Fried. And not the first one; that one is fine; the math above is right. He pays $1 to play, he gets a fair coin flip, he makes $33 from Asher, fine, good trade. But then he keeps going to eke out a few marginal pennies from Asher.9 When he wins the first flip, Asher owes him $33, the difference between their $65 strike price and the $98 that the first intern lost. When he wins the second coin flip, Asher owes him an additional one dollar: Their bet is on the maximum loss, not the total loss, so finding another intern to lose $99 increases the payoff by only $1.10 The second flip is an even-money proposition for Bankman-Fried: He pays $1 to do it and gets an extra $1 from Asher. The third and fourth flips, where he pays $1 to get 50 and then 25 cents from Asher, have negative expected value. The last flip, which he loses, costs him $100.75 and brings in nothing.11
Again, I don’t really know what happened. Perhaps I have misunderstood how the bets worked, or perhaps Lewis did, or perhaps Bankman-Fried misremembered, or perhaps he really did get these bets wrong. But isn’t this version of the story revealing? In this story:
- Bankman-Fried found a perfect trade, for him: It was risky but it had a lot of edge, it made him look smart, and it made his counterparty look dumb.
- He did it, it paid off, he looked smart, his counterparty looked dumb, all was right with the world.
- It was so intoxicating to be right that he kept doing the trade.
- He never noticed that the trade stopped being good: The glow of being right persisted long after he became wrong.
- Eventually he lost the bet and everyone was mad at him.
Everything about Sam Bankman-Fried’s life was perfectly optimized for becoming a famous billionaire and an infamous criminal defendant, in that order.
