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Comment by Baader-Meinhof | Hacker News Reader

There was an illuminating interview he had before being arrested:

COWEN: ...let’s say there’s a game: 51 percent, you double the Earth out somewhere else; 49 percent, it all disappears. Would you play that game? And would you keep on playing that, double or nothing? So, what’s the chance we’re left with anything? Don’t I just St. Petersburg paradox you into nonexistence?

BANKMAN-FRIED: Well, not necessarily. Maybe you St. Petersburg paradox into an enormously valuable existence. That’s the other option.

https://conversationswithtyler.com/episodes/sam-bankman-frie...

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For anyone wondering about the verb to St. Petersburg paradox:

The game is a simple 50/50 for a win or loss. You begin with one unit (say: $1). Every round you don't lose the stake doubles. The game terminates if you lose. How much should you pay (expected value) to enter such game? Given the bank - offering you the gamble - has infinite resources the expected value is infinite.

Well of course one way [0] (another more nuanced way is to question the simple axiom of maximizing the expected value [1]) to resolve the paradox is to limit the resources realistically, analogous to Martingale [2].

Given the world's GDP at ~ $100 trillion (or about N ~ 46 rounds) the expected value (beginning with $1) would be only about $(N+1)/2 so in this case $23,5.

[0]https://en.wikipedia.org/wiki/St._Petersburg_paradox#Finite_... [Note: the numerical examples begin with $2]

[1]https://plato.stanford.edu/entries/paradox-stpetersburg/

[2]https://en.m.wikipedia.org/wiki/Martingale_(betting_system)

Why is the expected value infinite? It seems fairly obvious that you will not make much money on such a game as we all know you can't flip a coin many times without tails showing up. To make infinite money in such a game you would need effectively "infinite luck" no?

> as we all know you can't flip a coin many times without tails showing up.

We don't all know that. There's an ever-decreasing but nonzero probability that you will keep getting heads.

The probability that the next N flips will all be heads is small and gets smaller the larger N is.

But the probability that the next flip is heads is .5 no matter how many of the previous flips were heads :)

> There's an ever-decreasing but nonzero probability that you will keep getting heads.

But with enough flips, the odds getting heads on all of them comes close enough to zero that they are effectively zero.

"Effectively zero" times infinity is infinity. Infinity is like... really big.

Oh, I wish I could find it, but there's an excellent video by a mathematician explaining why an infinity doesn't work in your favor here. IIRC, it's because as the number of throws approach infinity, the odds also approach being infinitesimal, and you'll still lose.

This paradox is famously a case where the expected value of the game is infinite.

If you get 2 dollars on the first head, 4 dollars on the second, etc., then the probability of receiving each dollar amount multiplied by the dollar amount is 1 dollar.

1/2 * 2 + 1/4 * 4 + 1/8 * 8 ... = 1 + 1 + 1 ... = ∞

Of course, the proof only works if dollars continue to have linearly increasing value to you as you keep accruing them. If their value to you logarithmically increases, the expected value is not infinite.

Consider the chance of winning at least 100 times. It's 1 over 2^100, and you win at least 2^100. So the small chance and the big reward "balance out", kind of.

But the reward is not limited there. Once you reach each and every "balance point", the next step is 50% chance for doubling the reward. If you currently have X, the value of continuing to play is 1.5X. This is independent of how big X is, or how unlikely you have made it this far (sorta a reverse Gambler's Fallacy). And it's why the expected value is infinite.

it's an example of how expected value doesn't tell the full story

https://en.wikipedia.org/wiki/Risk_of_ruin

It seems that the scenario Cowen put forth and the St. Petersburg paradox are not quite the same? In St. Petersburg (at least as Wikipedia describes it) you walk away with the accumulated winnings, whereas in the example put forth if you lose you walk away with nothing.

I was wondering because it would seem with Cowen's example the expected value is just $1 (ignoring the 51% edge). The 51% edge ends up making the expected value infinite, so the intuition lines up even though the exact details don't.

I see it as a clever and extreme variation of the same underlying fallacy: a) the favored outcome is slightly more probable (51%) b) the expected value of losing could be expressed as negative infinity

That SBF answered this (rhetorical) question that confidently and quick with not necessarily but what followed was simply something like look on the bright side is effectively imho parroting but at least he handled the verb eloquently. It would certainly take me like 20-30 seconds to process it.

This is the epitome of "understands how things work but makes bad decisions".

You do have to be smart to see that there might be a more positive outcome. But you have to be unwise to gamble.

My first boss (trading) told me, "Our job is to be in business tomorrow". Which is relevant because in that business you actually can blow up in a day.

Almost by definition the only “huge winners” at the roulette table are the people who keep putting it all on black and let it ride. Because the people who take their winnings off can’t ever get the huge payouts.

And some people seem absolutely unable to understand the probabilities involved. It seems to almost be a requirement for startup leaders.

> Almost by definition the only “huge winners” at the roulette table are the people who keep putting it all on black and let it ride.

Not over the long run. The house always wins.

He's a gambler and gambler be gambling. At the beginning of that interview with Tyler Cowen, he's asked what makes him better. He doesn't sound like he knows, but he doesn't want to acknowledge luck. Instead he speaks like someone who can see patterns in entropy. I think at one point SBF started believing in his own legend and thought that he's actually doing something special that sets him apart. He can read the language of chance. The way that an addict tries to repeat the exact routine of the day that led to a past big win, before his next gambling spree, thinking that "surely, spilling a bit of maple syrup in my coffee that morning had something to do with it".

If I were a gambler I’d be furious when compared to such a cereal box criminal.

Why is it we have to insult the loser to make a point?

“Cereal box” is not an insult, and criminal is a fact as far as I can tell.

> This is the epitome of "understands how things work but makes bad decisions".

I'm not sure I'd even call this 'understands how things work' - everyone who's heard of marginal utility knows that large scale double-or-nothing 51/49 gambles very rarely make sense to take.

To me this sounds more like someone hopped up on a nootropic that causes compulsive gambling, like Emsam.

If only there was a nootropic that made people stop behaving like an idiot.

Agree. The St Petersburg paradox isn't about a single 50/50 wager. Both SBF and Cowen seem to not understand that. Instead they simply start jacking off to infinity because lizard brain says Petersburg is related to infinity somehow.

The "logic" that are using here would justify everyone to go to a casino and put their life savings down on black.

It's gambler brain logic just couched in pseudo-intellectual terminology to make them sound smart. The equivalent of techno babble for gambling.

From just that snippet, Cowen sounds like he's challenging SBF on it. I don't see Cowen "jacking off to infinity", but rather seemingly expressing that such a wager is a horrible idea. He says:

> And would you keep on playing that, double or nothing?

The point being that if you'd push that button now, in this world, then what would be different in the new world to stop you from pushing the button again? There's no stopping point, hence the St. Petersburg paradox. Maybe the button has already been pushed, maybe multiple times. If anything, Cowen seems to be presciently pointing out that SBF's attitude will inevitably lead to disaster.

SBF does seem to be misunderstanding: push the button forever, and maybe magic will happen!

I took it to mean "I understand the St Petersburg Paradox, but I think I have a way out".

Which is actually why it's both intelligent and dumb at once. You have to have done some reading in your life to understand this thing. As someone who did well at math and worked in trading, he would have come across it. But it's also unwise because actually lots of other people have also studied it for a long time, and they are not declaring victory.

Your boss wasn't the one to employ Nick Leeson, and you weren't working for Barings.

Is it a famous quote or something? I doubt he was the first guy to think of it, and neither was anyone at Barings. Anyone in trading could feasibly have thought of it independently.

Leeson certainly wasn't the first guy to think of it but he did in fact bring down the house by using exactly that strategy and Barings ended up not being there tomorrow one day on account of that. Lots of oversight failures.

Ah, I thought you meant that the quote was from someone related to Barings, and my boss had nicked (lol) it.

Which could totally have been the case, naturally everyone on the floor had watched the movie and some knew the people involved.

I think the mistake is mine, I should have asked if your boss said this before or after Baring's went under.

That's reminiscent of a Martingale but the roles are reversed. That was a great question to put to him and gives some insight into how these things happen.

That was a good interview as it exposed SBF. His answers were painfully stupid for a billionaire. I lost a lot of respect for the VC community after listening to that interview, I don't know how they got this so wrong. Perhaps it was just the sham nature of crypto that put blinders on everyone?

Anyway, kudos to Cowen for having SBF on there and letting SBF talk and expose himself.

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