the jackpot age

[-]Nition4mo244

Another simple way to understand why the coin flip scenario makes you lose money: If you have $100, double it with heads to $200, then lose 60% on tails, you have $80 - less than you started with.

[-]Auspicious4mo72

Thanks for this. I was confused when I first read it, but I had been skimming and thought it meant "keep 60%" (or in other words, lose 40%).

[-]rcwhiteley4mo72

That's what I thought when reading this, the opposite of double (100% gain) is half (50%) loss, so if you've lost by more than 50% on the negative coin toss result you will tend to lose money over time.

If the negative was less than half (say, 40%), you would gain money over time.

[-]ankitmaloo4mo149

I was reading this and thought of the Kelly criterion. The choice is not binary, you already know the optimal bet sizing here. The kelly fraction at 0.25 gives you what a 3% growth rate? f=1 is obviously a flawed scenario that should not be happening. ( i dont know enough to know whether SBF made the same point. 3AC did bet the house though). Culprit is all in bet, not linear sizing.

Survivorship bias and worshipping is not a new phenomenon either existed since atleast last 40 years in tech where a median dev is not paid as much as one at Google or Microsoft.

If i were to grant the premise that every individual should use log sizing, how does that ensure that we are devoting enough resources to home run outcomes in biotech, space etc.? That is where the toy model breaks because these spaces demand a lot of money to get started and have any meaningful breakthrough. Beyond the individual level, there is clearly a civilizational utility to be swinging for the fences and maximizing the expected value. At an individual level, if people are making sub optimal choices, perhaps the solution is more financial education.

[-]gjm5mo90

I think readers using Firefox (or forks thereof) with its "enhanced tracking protection" turned on will not see images here; at any rate, they are blocked for me with the note "Socialtracking" in the network tab of the devtools, which I think means that ETP blocked them.

I don't know whether there's some other place to host images for LW articles that won't provoke such issues.

[-]thiccythot5mo80

thanks for letting me know. I've reposted the images.

[-]gjm4mo40

They show up properly for me now.

[-]Darklight4mo60

Apologies if this is a newbie math comment, as I'm not great at math, but is there a way to calculate a kind of geometric expected value? The geometric mean seems to require positive numbers, and expected values can have negative terms. Also, how would you apply probability weights?

[-]aphyer4mo*110

Not in general. As you say, GM requires positive numbers, but there's a reason for this: imagine GM as log-scaling everything and then performing AM on the results.

So to get the GM of 10 and 1000:

Realize that 10 = 10^1, 1000 = 10^3
Then average 1 and 3 to get 2.
So your result is 10^2=100.

But now notice that:

0.01 is 10^-2
0.00001 is 10^-5
0.0000000001 is 10^-10
0 is 10^[negative infinity]?
-1 is...uh...

and so the GM of 1 million and 0.00000000000000000000000001 is 0.00000000000001, and the GM of 1 billion and 0 is 0. This won't really lend itself to calculating a GM of a list including a negative number.

One thing you can do, though, which makes sense if you are e.g. calculating your utility as log(your net worth) in various situations, is calculate the GM of [your current net worth + this value].

For instance, if you are considering a gamble that has a 50% chance of gaining you $2000 and a 50% chance of losing you $1000:

If your net worth is $1000, this replaces $1000 with a 50% chance of $3000 and a 50% change of $0. Since GM(3000, 0) = 0, this is worse than just staying with the $1000 .
If your net worth is $2000, this replaces $2000 with a 50% chance of $4000 and a 50% chance of $1000. Since GM(4000, 1000) = 2000, you are indifferent.
If your net worth is $4000, this replaces $4000 with a 50% chance of $6000 and a 50% chance of $3000. Since GM(6000, 3000) ~= 4242, this is better than staying with the $4000.

[-]Archimedes4mo10

The geometric expected value for the +100% or -60% gamble in the post is straightforward.

If you gain 100% and then lose 60% (or lose 60% and then gain 100%), overall you'll end up down 20% from where you started since (1 + 100%) * (1 - 60%) = 2 * 0.4 = 80% = 1 - 20%. This loss is what's expected over two iterations, so the loss over one iteration is sqrt(80%) = 89.44% = 1 - 10.56%, so the expected loss is that 10.56% of your starting capital per flip.

[-]Kaarel4mo100

https://www.lesswrong.com/posts/DMxe4XKXnjyMEAAGw/the-geometric-expectation

[-]Linda Linsefors4mo50

The geometric (and also arithmetic) average is over remaining net worth (divided by initial net worth), which is always positive.

I was also confused about this, so I looked at the code. But you can also figure this out from looking at the graph that starts at 1.

[-]BryceStansfield4mo0-1

Edit: said something very silly about weighting.

Nothing says you can't take the geometric mean of a series that includes negative numbers, just that if you have an even number of elements, but an odd number of negative elements, you'll get a complex answer.

To weight the elements of your series, you should be able to take the geometric mean of p(X)*X, then divide by the geometric mean of your p(X).

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[-]Donald Hobson4mo4-2

The techno-optimist dream of an abundant post-AGI world where humans devote their days to art and leisure will look more like billions of people chasing negative sum capital and status jackpots with UBI stipends.

In a post AGI world, the world mostly looks like whatever the AGI wants. Capitalism has a strong incentive to create sports betting, and wave it in peoples faces. AGI doesn't.

[-]thiccythot4mo40

the path matters just as much as the destination

[-]Yeonwoo Kim1mo32

You’re right. Everyone’s “heads” and “tails” — their gains and losses — are different. Some people gain more when things go well, and others lose a bit more when things go badly. But if you repeat that process endlessly, the result still tends to converge toward zero. In a way, that’s what the rat race in a technocratic society looks like — it’s less like the Buddhist idea of universal enlightenment and more like the Christian idea of selective salvation, where only a few are “saved.” It’s a kind of winner-takes-all world.

My thought is this: maybe it’s time to reframe faith, not around the traditional relationship between God and humans, but around the relationship between humans and artificial intelligence. The core of Christianity is about the relationship between the Creator and the created, or in other words, between the infinite and the finite. In the past, the “infinite” was represented by God — Yahweh, or perhaps the Buddhist cycle of rebirth. But now, maybe that infinite aspect is found in humanity itself — in our self-referential capacity for thought — while AI becomes something that follows or reflects that.

In that sense, instead of “Be humble before God,” perhaps the guiding idea should become “Be humble before AI.” I think that might actually work, at least until biology fully uncovers how the human mind operates. If so, humanity might regain some of the pride and dignity that were lost.

After all, the very idea of “human dignity” only really emerged in the modern era, not because human rights were suddenly invented, but because the old God–human relationship had briefly collapsed. Superiority and inferiority are always relative. In the past, people believed all humans were equal because even the greatest person still stood beneath God. But perhaps now, all humans can be equal again, not because we are less than something divine, but because each of us, no matter how limited, can feel whole in front of AI.

Anyway, I hope that doesn’t sound too far-fetched.