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.
And some people seem absolutely unable to understand the probabilities involved. It seems to almost be a requirement for startup leaders.
Not over the long run. The house always wins.
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.
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.
> 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!
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.
Which could totally have been the case, naturally everyone on the floor had watched the movie and some knew the people involved.
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. 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 about $23.
[0]https://en.wikipedia.org/wiki/St._Petersburg_paradox#Finite_... [Note: the examples begin with $2]
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.
We don't all know that. There's an ever-decreasing but nonzero probability that you will keep getting heads.
But the probability that the next flip is heads is .5 no matter how many of the previous flips were heads :)
But with enough flips, the odds getting heads on all of them comes close enough to zero that they are effectively zero.
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.
I was wondering because it would seem with Cowen's example the expected value is just $1 (ignoring the 51% edge). I suppose the 51% edge ends up making the expected value infinite, so the intuition lines up even though the exact details don't.
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.
Anyway, kudos to Cowen for having SBF on there and letting SBF talk and expose himself.
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...