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Deriving the Kelly Criterion to Maximise Profits

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Re: Deriving the Kelly Criterion to Maximise Profits

#31

Post by CrazyStat »

nonameiguess wrote: post #21
CrazyStat wrote: post #18

I had never paid much attention to Effective Altruism or SBF before FTX blew up, but when that happened I spent some time reading old EA forum posts and SBF tweets and interviews. One of the things that absolutely shocked me was the dismissal of the Kelly criterion by SBF and other EAs. The argument was that the Kelly criterion was only rationalized by a logistic utility function, and if you were going to use your mo…

I don't want to denigrate the whole community or anything as quite a lot of thought-provoking and interesting reading has come out of it over the years, but I can't help but recall very serious defense of the notion of quantum immortality on LessWrong after Eliezer's fairly convincing rants that any serious scientist has to conclude multiple worlds is the only sensible interpretation of quantum mechanics. If you hone…

Hah!

I had forgotten about this line of argument, but I came across it in a post on the EA forums arguing that you should choose what to do with your life this way. Basically if you believe that in this branch you have far above average ability (compared to yourself in other branches) to do good in the world then you should devote your life to altruism; conversely, if in this branch you have below average ability (again compared to yourself in other branches) then it's ok to spend your time playing video games instead.

Re: Deriving the Kelly Criterion to Maximise Profits

#32

Post by kqr »

mudita wrote: post #30
nighthawk454 wrote: post #23

A few links through, this Ship Investor simulator is a great super-simple game to test some intuition: https://xkqr.org/ship-investor/ship-investor.html

The game is a bit weird. It often offers very bad deals, without an option not to invest. For example for the Gibraltar strait, the game gives the information that the probablity of success is between 90% and 100% and that it’s been traversed 31 times with a 90 % success rate. Then it offers me the choice between an investment of different sizes, where I cannot win back more than my investment, so I have to risk mone…

Author here. Huh, you're right. 13 turns into the first scenario I opened[1] I get offered very weird deals, such as investing my full 184 ducats in a shipment worth only 182 ducats. Or! Investing 1878 ducats when I only own 184...

I wrote this game a few years ago, and it didn't use to have this bug. I can't take the time to figure it out now, but clearly something went wrong along the way!

[1]: Fortunately it's easily reproducible: put down the minimum in all first 12 turns and then look at the weirdness that is turn 13! https://xkqr.org/ship-investor/ship-investor.html?seed=883

Re: Deriving the Kelly Criterion to Maximise Profits

#33

Post by kqr »

roenxi wrote: post #8

A word that is good to know here is ergodic [0]. Which I must admit to not really understanding although it is something like the average system behaviour being equivalent to a typical point's behaviour. If a process is non-ergodic then E[X] is usually not as helpful as it seems in formulating a strategy. [0] https://en.wikipedia.org/wiki/Ergodic_process

Ergodicity in the mean refers to the ensemble mean being the same as the temporal mean, i.e. measuring one process 1000 times will give the same average as a single measurement of 1000 different processes.

One way for a process to not be ergodic in the mean is when there's some sort of barrier, as sibling comments allude to.

Another is if the overall mean value is picked randomly each time the process starts, but is different each time the process runs. So for example personal monthly expenditures are not ergodic in the mean, because some people are born into circumstances that make them wealthy, and they will on average spend more each month than people not born into such good circumstances.

The ensemble average will tend towards people's average spending, while the temporal average will tend towards each individual's spending.

Re: Deriving the Kelly Criterion to Maximise Profits

#34

Post by kqr »

wenc wrote: post #2

The Kelly criterion is almost never used as-is because it is very sensitive to probability of success, which is hard to know accurately and in many cases, dynamically changing. This is easy to see in an Excel spreadsheet. Changing the probability by even 0.01 percent can vastly shift the results. The article calls this out in the last paragraph. The article mentions fractional Kelly is a hedge. But what fraction is o…

> Changing the probability by even 0.01 percent can vastly shift the results.

No, not generally. Since it's a quadratic function we're optimising, it's surprisingly flat at the top. Sure, there are some bets where the edge is tiny and 0.01 percent is a large proportion of that, but that doesn't invalidate the Kelly criterion – by what other criterion would you determine the appropriate bet size?

> is more a rule of thumb that says roughly if you have x $ and probability p, in a perfect world you should only bet y amount.

It applies far more broadly than to binary bets. It tells you how to allocate your spending optimally across any number of opportunities, based on joint probability of outcomes.

Both of your misconceptions are common, and they are addressed in the article linked in the submission: https://entropicthoughts.com/the-misunderstood-kelly-criteri...

Re: Deriving the Kelly Criterion to Maximise Profits

#35

Post by diab0lic »

diab0lic wrote: post #14
roenxi wrote: post #8

A word that is good to know here is ergodic [0]. Which I must admit to not really understanding although it is something like the average system behaviour being equivalent to a typical point's behaviour. If a process is non-ergodic then E[X] is usually not as helpful as it seems in formulating a strategy. [0] https://en.wikipedia.org/wiki/Ergodic_process

An example that may be useful to aid in understanding… Casinos are non ergodic. A million players each placing a single bet will have an expectation of losing the house edge. A single player placing a million bets has an expectation of $0. The fact that the aggregate and the single entity Experience different expectations despite both placing a million bets is what makes this ergodic.

Errr that last sentence should end with “is what makes this non-ergodic.”

Re: Deriving the Kelly Criterion to Maximise Profits

#36

Post by obrhubr »

avidiax wrote: post #7

Here's a link to a bigger graph for the Blackjack Scenario: https://github.com/obrhubr/kelly-criterion-blackjack/blob/ma... I think it shows that Blackjack is not even theoretically winnable over time if you have to pay for information on the count in the form on minimum bets. The ideal case it that you bet $0.49 for every $1,000 in your investment pool when the count is extraordinarily high. Even if you hack the cas…

Thanks for linking the image. You're right in my simulation there is almost no growth, even at a high count and if you're forced to bet every round you would certainly lose money. But it's a simplistic simulation and a real casino offers slightly better odds if the rules are right.

Re: Deriving the Kelly Criterion to Maximise Profits

#37

Post by monicaaa »

bdjsiqoocwk wrote: post #13
gwbrooks wrote: post #4

A million years ago, when you could still find video poker games with 100%+ theoretical return or poorly thought-out promotions offering enough cash-back to get you over 100%, we'd calculate the Kelly number for a given opportunity -- the bankroll necessary to ride out hills and valleys in favorable situations. Spoiler: It's almost always 3-4x the value of a royal flush. So you needed $12-16k if you were playing a $1…

I would like to understand in detail what you just wrote. "$1 per coin game" is this a game where you put in $1 to play and get paid either $2 or $0 with 50-50 probability (0 expected). And the what does it mean %1 edge? Does it mean the probabilities are such that the expected payout is 1c per coin flip?

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