They look a lot better than the 99th percentile outcomes in almost-all-in (the strategy Sam prefers)!
And law of averages kicks in over time; it doesn’t for almost-all-in.
Conversation
1) I think that and I were talking about what _we_ think, and we do believe in utility, so I don't think it's appropriate for you to respond the way you did.
2) can you please address twitter.com/SBF_Alameda/st? Percentile outcomes as a metric fails.
1
I wasn’t saying you were being inconsistent with yourself
On percentiles: yes, directly optimizing median or any given percentile would probably not be coherent. But Kelly doesn’t try to do that. It just ends up doing that for all percentiles (other than 100%) eventually
1
Dan: "yes, directly optimizing median or any given percentile would probably not be coherent"
Also Dan: twitter.com/danrobinson/st
Could you please, in a single tweet thread here, define what exactly it is you _are_ aiming for?
Quote Tweet
Replying to @SBF_FTX @SBF_Alameda and @elliot_olds
No! I am not trying to maximize EV of anything!
I want to pick the strategy that beats yours 99.99% of the time. That’s my terminal goal
Kelly takes that input and spits out that I should maximize EV(log(wealth)), but that preference is the consequence, not the cause
1
1
This Tweet was deleted by the Tweet author. Learn more
Also Kelly isn't defined by "almost surely" either, that's an emergent property of it in some very specific infinite scenarios.
Kelly is defined by optimizing for log(wealth)
en.wikipedia.org/wiki/Kelly_cri
1
This part really is a language debate, but saying that it is defined by optimizing for log(wealth) IMO makes it sound like it’s driven by preferences about marginal utility of wealth, which it isn’t.
Would prefer “maximizing log return” or “maximizing annualized rate of return.”
1
"maximizing log return" is obviously equivalent to maximizing log wealth, it's just subtracting log(start_wealth) from all outcomes. Really not sure why you think that's an important thing to add!
3
Perhaps the more important is the latter (annualized return), or equivalently “average log return over time.”
All equivalent. But with these latter terms it is much more obvious why you might want to optimize for them if you care about compound interest
1
twitter.com/SBF_Alameda/st
to be clear I think you're not understanding correctly what Kelly is here.
You're saying we should define Kelly as a thing which is *not* Kelly but is instead the other different thing that you believe.
Quote Tweet
Replying to @SBF_FTX @danrobinson and 4 others
But "maximizing annualized rate of return" is *not* kelly in general! It's only Kelly in some very specific situations.
e.g. if you only have a single coin flip ever and it's in 1 year then max annualized rate of return = max return = max linear EV != kelly
The formula for annualized rate of return is (W_t/W_0)^(1/t), right?
After not too many gambles the expectation of this converges pretty quickly.
But you’re right, the formal definition for that does require t->infinity, so withdrawn
1
3
How about “maximizing expected geometric growth rate”?
Or “maximizing average log return over time.”
All equivalent, but this gets at the WHY. I like Kelly because I want to maximize compounding growth, not because I have preferences about the log of my wealth.
1
3
Show replies
Kelly's Criterion requires an accurate estimate of probability. How can you accurately assess the probability on gambling market? What is the probability of an asset growth ~1000%+ in 1 second?
