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>> Actually, what I’m saying is even stronger. I am saying that even if you have the edge, in the presence of the probability of ruin, you will be ruined. Even if you had the edge … If you play long enough.

> He wouldn't pass 1st year college math course with that one.

Seems pretty straightforward to me. Let's say you play a game with an edge where you win 2x your money 99% of the time. But if you lose once, you lose all your money (1% risk of ruin). If you play this game 70 times, you are very likely to end up ruined.

It’s a lot like smoking. One cigarette won’t kill you, but add up the probability cigarette after cigarette, pack after pack, year after year and the probability starts to skyrocket.

Exactly. I've often felt that a lot of the "wow humans are so irrationally risk-averse when it comes to money" conclusions that some researchers make are suffering from limitations of extremely limited models.

For example, imagine a stranger comes up to you on the street and offers you a coin game, where if you win you gain $1 billion, but if you lose you owe him $1 million. The simplified model would claim that you should play the game because the expected value is positive. A more nuanced model would understand that being that much in debt would be a lot more suffering for me than the offset from whatever I'd do with a billion dollars. Even if the coin was weighted more in my favor, and the penalty was less, an even more nuanced model would recognize that I'm probably doing OK enough in my life with the money I have and that anything to chip away at that is an unnecessary risk.

And then a model that even more completely captures the interplay of reasoning that humans do would acknowledge "wait a second, who the hell is this random stranger offering me a devil's bargain?" The researcher with a simple model would say "oh, just ignore that, just take the situation at face value," but that's never how any decision is made. Our priors for "suspicious people offering bargains too good to be true are actually trying to cheat you somehow even if you don't know how" is very high. This is embedded in cultural/religious parables that teach "you do not make deals with clever demons," and because the culture that taught that has survived and persisted over time, it's probably a good prior to hold onto.

All that complexity is lost if you only think in simple terms of expected value and single-iteration games.

I think you're giving researchers too little credit in your first example. They do at least know that rational agents maximise expected utility, not just expected money.

And then whenever they do a study they are very careful to fully convince subjects that there is no trickery going on. And then when interviewed the subjects don't say "I suspected trickery". So I think that such studies are justified in concluding that the subjects are acting irrationally.

>Our priors for "suspicious people offering bargains too good to be true are actually trying to cheat you somehow even if you don't know how" is very high. This is embedded in cultural/religious parables that teach "you do not make deals with clever demons," and because the culture that taught that has survived and persisted over time, it's probably a good prior to hold onto.

Right, right. But the question of "why do people make irrational decisions?" is exactly what the researchers are studying. They agree with you! The answer is that decisions which are irrational in one domain would be rational in the domain we were designed for.

>>The simplified model would claim that you should play the game because the expected value is positive.

No, it wouldn't. Humans are not maximizing EV of money won but utility of that money. This is fundamental to economic models which Taleb is criticizing.

>>All that complexity is lost if you only think in simple terms of expected value and single-iteration games.

It isn't lost unless you are for some strange reason maximizing expected amount of money which no one sane does (even people who don't understand what expected value is in the first place). If the game is single iteration or multi-iteration doesn't matter either, you just make the best play at every point and it doesn't change no matter if you will get a chanc to make another bet or not.

>>Seems pretty straightforward to me. Let's say you play a game with an edge where you win 2x your money 99% of the time. But if you lose once, you lose all your money (1% risk of ruin). If you play this game 70 times, you are very likely to end up ruined

No one sane plays a game like that with all their money on the line. This is not because there are future bets available but simply expected utility of such a bet is negative. If you play for example with constant sizing your risk of ruin is higher than 0 but lower than 1. It's very often very close to 0.

>>It’s a lot like smoking. One cigarette won’t kill you, but add up the probability cigarette after cigarette, pack after pack, year after year and the probability starts to skyrocket.

But it's not like that. Risk of ruin doesn't skyrocket even if your plan is to make infinitely many bets. That is unless you do something very silly like double the bet amount every time you win.

First of all, some people do play games like that. But put that aside for a moment because it’s immaterial. Look at what Taleb is essentially saying: if there is a chance you will be ruined, and you play long enough, you will eventually be ruined. Even if that chance is 1%, probabilities add over time. 1.0170 = 2. If the chance of ruin is 1% then after 70 plays the chance of ruin is 100%.

What kind of math is that? In your contrived example it should be 1 - .99^70. It's hard not to question your background in probability when you're involving 1.01 and 2..

Nice ad hominem attempt, but even though I accidentally switched a minus for a plus, the point the math teaches is the same: risk of ruin accumulates with the number of bets.

For more information check "Risk of Ruin" https://en.wikipedia.org/wiki/Risk_of_ruin

You are assuming people are betting their whole bankroll on one bet. No one remotely sane does that. If you do something like betting constant amount then risk of ruin is often very close to 0 (and always less than 1 if you have an edge).

You are wrong twice there... sane people make that bet every day by smoking (limited upside gain, risk of ruin loss) and by taking many prescription medicines that have side effects including death.

Using a cell phone is taking that bet. You are betting that 50 years of cell phone exposure won't cause brain cancer. Nobody knows for sure yet, nobody has had cell phones for 50 years. I'm not saying it will or it won't cause cancer. I don't know. But it has the possibility of risk of ruin.

Second, constant amount betting does have risk of ruin even with an edge. Take a fair coin flip where you start with $500 and get $51 for heads and lose $50 for tails. A clear edge with a constant betting amount. In 100 flips, you have a 27.23% chance of ruin.

For more information consult the concept of "Gambler's ruin" https://en.wikipedia.org/wiki/Gambler%27s_ruin

How much should you bet to never be ruined but maximize the long term expected value of your bets?

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

>> No one sane plays a game like that with all their money on the line.

Already mentioned in another comment, see LTCM as a prime example:

https://en.wikipedia.org/wiki/Long-Term_Capital_Management

>> No one sane plays a game like that with all their money on the line.

It's essentially the game we played with the housing bubble.

> If you play this game 70 times, you are very likely to end up ruined.

If you play 70 times, you have a 1-0.99^70 = 50.5% probability of ruin.

I totally agree with your summary, but to be fair to Taleb "absorbent barrier" is a real term from the study of Markov Chains. (https://en.wikipedia.org/wiki/Markov_chain#Absorbing_states)

The term is absorbing barrier. Synonymous words, but nobody says absorbent barrier.

The original audio isn't actually good enough to tell which of these he's saying.

Even then, he did twist 'absorbing states' into the basically unused "absorbent barrier."

It's good you brought up Markov chains; I can't believe they haven't been mentioned in the article or the comments

"Kelly maximizes utility of money modeled as a logarithmic function."

Absolutely true, but consider what log utility also creates a decision rule that leads to growth-rate optimization under multiplicative bets.

You may find these notes from Ole Peters interesting https://ergodicityeconomics.files.wordpress.com/2017/03/ergo...

One interpretation of Kelly is maximizing the e.v. of the log return. Another (equivalent) interpretation is maximizing the expected IRR -- which is where the "in the long run" comment comes in, since "in the long run" you care more about the internal rate of return than the expected value of any individual bet.

E.g., imagine a bet that costs $1 to play and pays out $2 with probability 60% and $0 with probability 1%. How much would you bet? The expected value of the bet is $1.2 per dollar you bet, so for a single bet, you might wager 100% of your bankroll. But "in the long run" you'll loose all your money doing this. Instead, Kelly would recommend that you bet only 20% of your bankroll. "In the long run", you'll make infinite money doing this. (Not only that, but there's no other strategy that will make you money faster.)

>(Not only that, but there's no other strategy that will make you money faster.)

That's not true. If you bet 99% of your money each time then there's still no probability that you go bankrupt (it's literally impossible to go bankrupt unless you bet all your money), and you make money much faster.

Perhaps we could add in a lower bound, like you have to stop betting if you have less than $1. But then it's possible to go bankrupt even if you use the Kelly criterion. Furthermore we've introduced a fixed quantity into the problem, which means there's no longer any justification for saying that your bet should be the same proportion of your wealth every turn.

I've never yet seen a convincing argument for Kelly betting aside from the when utility is logarithmic.

>If you bet 99% of your money each time then there's still no probability that you go bankrupt (it's literally impossible to go bankrupt unless you bet all your money), and you make money much faster.

Go back and read through the Math for the Kelly Criterion - when you know your edge and odds, it's the optimal solution. It's basically the balance point between taking advantage of current betting opportunities and preserving capital to take advantage of future betting opportunities.

If you bet 99% of your money on a coin flip, you'll eventually lose a flip and have too little money to take advantage of future coin flips.

Let me try another explanation: your return from a series of coinflips comes from two sources. The first is the return from the next coin flip, which when you have an edge, makes you want to bet as much as possible on this flip. The second is the return from all future flips, which makes you want to bet less so that a poor result doesn't permanently diminish your ability to make bets. Mathematically, the Kelley Criterion is the point where adding or removing bet sizing moves these two values the same amount, resulting in a change in expected value per bet size of zero, which means it's a maximum.

>>If you bet 99% of your money on a coin flip, you'll eventually lose a flip and have too little money to take advantage of future coin flips.

You are comparing Kelly bets to being stupid so of course Kelly wins. Kelly maximizes just one thing - log of bankroll. If your utility is not logarithmic it's not optimal to use Kelly bet sizings and if your utility is logarithmic with some multiplier then you need to adjust Kelly as well (which btw gamblers using Kelly are doing as pure Kelly criterion is universally considered too risky).

>>The first is the return from the next coin flip, which when you have an edge, makes you want to bet as much as possible on this flip. The second is the return from all future flips, which makes you want to bet less so that a poor result doesn't permanently diminish your ability to make bets.

While pure result diminish (or kills) your ability to make money from further bet betting it all and winning increases it. If you want to maximize EV of total amount of money you bet all at every turn and this is the optimal solution to optimize that. If you want to optimize logarithm of total amount of money you bet Kelly. If you want to maximize more conservative utility then you bet something else. There is nothing magical about Kelly criterion other than that.

I guess one thing you can say about the Kelly criterion without mentioning utility is that if Alice uses the Kelly criterion and Bob uses some other strategy (which is still of the form "bet some fixed proportion of your money each turn") then the probability that Alice has more money than Bob tends to 1 as the number of turns increases.

Of course in the cases where Bob has more money he might have much more money, so this fact isn't very relevant to them unless they have appropriate utility functions.

Another thing that occurs to me is that your utility function is changed by the opportunities you expect to encounter. If your utility function for money would normally be U_0, and you are about to be allowed to make a bunch of bets, then your current utility function, U_-1, is equal to the expectation of U_0 under the probability distribution that results from you betting optimally starting with however much money you have.

Maybe there's a family of utility functions for which if U_0 is in that family then U_-1 is approximately logarithmic? Then that would be a good justification for using the Kelly criterion if you have a long string of bets ahead of you. On the other hand I just checked the HARA (https://en.wikipedia.org/wiki/Hyperbolic_absolute_risk_avers...) family of utility functions, and they're all stable under the process I described. So there are certainly a lot of functions that don't become logarithmic.

Thanks for the interesting comment and a link. I will be using your the first paragraph from your post in the future :)

> That's not true. If you bet 99% of your money each time then there's still no probability that you go bankrupt (it's literally impossible to go bankrupt unless you bet all your money), and you make money much faster.

The huge mistake you're making is in assuming that money is infinitely divisible. Let's say you start with $1 and you bet 99 cents and lose. Now try betting 99% of 1 cent and see if you don't go bankrupt.

It's very simple to verify Kelly's findings by building a naive simulator.

>The huge mistake you're making is in assuming that money is infinitely divisible. Let's say you start with $1 and you bet 99 cents and lose. Now try betting 99% of 1 cent and see if you don't go bankrupt.

But then it's possible to go bankrupt even if you use the Kelly criterion.

Kelly criterion never claimed to prevent bankruptcy. It only tells you how to bet to achieve the maximum theoretical return possible given a set of odds and payouts.

I say theoretical because unless you're in a casino, you don't know the actual odds and edge you are playing with (because they move) which makes your Kelly ideal bet size a guess rather than a fixed number.

Here's more information: https://en.wikipedia.org/wiki/Kelly_criterion

Using new words for existing concepts shows a lack of interest to delve deep into the existing state-of-the-art. Anti-fragile is another example. Why not call it sturdy, robust, solid. Dude, English's been around long enough to have words for that concept!

Taleb's merits are more literally than substantial. He's - and I hesitate to say this - somewhat of a charlatan. He targets an audience that considers itself smart, casts experts outside as idiots or malicious hucksters (but not his readers of course, who, with his help, see through the ruse), uses a few TedX-ie rethorics to present a supposed alternative revolutionary idea (like using big words, or using unexpected multi-disciplinary comparisons), and all done with supreme confidence.

As long as he's selling books and talks, it's fine and fun, but I would never ask him to look after my laptop when going to the bathroom in Starbucks.

>Anti-fragile is another example. Why not call it sturdy, robust, solid. Dude, English's been around long enough to have words for that concept!

He literally addresses that point in his book "Antifragile." The point he was wanting to make is that the systems he talks about are not merely resilient or resistant to stress or damage -- but rather they are systems that get more robust or strong as a direct result of damage or stress. That's the property that is harder to find a nice concise English word for.

I did not know that, thank you.

Why are you willing to call him a charlatan or claim he lacks the character to look after your laptop when you haven’t even read the book you are criticizing?