Author: SK

Bond Market Liquidity and Selection Bias

I’ve long been a fan of Matt Levine’s excellent Money Stuff newsletter. I’ve mentioned this newsletter here several times in the past, and on one such occasion, I got a link back.

One of my favourite sections in Levine’s newsletter is called “people are worried about bond market liquidity”. One reason I got interested in it was that I was writing a book on Liquidity (speaking of which, there’s a formal launch function in Bangalore on the 15th). More importantly, it was rather entertainingly written, and informative as well.

I appreciated the section so much that I ended up calling one of the sections of one of the chapters of my book “people are worried about bond market liquidity”. 

In any case, the Levine has outdone himself several times over in his latest instalment of worries about bond market liquidity. This one is from Friday’s newsletter. I strongly encourage you to read fully the section on people being worried about bond market liquidity.

To summarise, the basic idea is that while people are generally worried about bond market liquidity, a lot of studies about such liquidity by academics and regulators have concluded that bond market liquidity is just fine. This is based on the finding that the bid-ask spread (gap between prices at which a dealer is willing to buy or sell a security) still remains tight, and so liquidity is just fine.

But the problem is that, as Levine beautifully describes the idea, there is a strong case of selection bias. While the bid-ask spread has indeed narrowed, what this data point misses out is that many trades that could have otherwise happened are not happening, and so the data comes from a very biased sample.

Levine does a much better job of describing this than me, but there are two ways in which a banker can facilitate bond trading – by either taking possession of the bonds (in other words, being a “market maker” (PS: I have a chapter on this in my book) ), or by simply helping find a counterparty to the trade, thus acting like a broker (I have a chapter on brokers as well in my book).

A new paper by economists at the Federal Reserve Board confirms that the general finding that bond market liquidity is okay is affected by selection bias. The authors find that spreads are tighter (and sometimes negative) when bankers are playing the role of brokers than when they are playing the role of market makers.

In the very first chapter of my book (dealing with football transfer markets), I had mentioned that the bid-ask spread of a market is a good indicator of market liquidity. That the higher the bid-ask spread, the less liquid a market.

Later on in the book, I’d also mentioned that the money that an intermediary can make is again a function of how inherent the market is.

This story about bond market liquidity puts both these assertions into question. Bond markets see tight bid-ask spreads and bankers make little or no money (as the paper linked to above says, spreads are frequently negative). Based on my book, both of these should indicate that the market is quite liquid.

However, it turns out that both the bid-ask spread and fees made by intermediaries are biased estimates, since they don’t take into account the trades that were not done.

With bankers cutting down on market making activity (see Levine’s post or the paper for more details), there is many a time when a customer will not be able to trade at all since the bankers are unable to find them a counterparty (in the pre Volcker Rule days, bankers would’ve simply stepped in themselves and taken the other side of the trade). In such cases, the effective bid-ask spread is infinity, since the market has disappeared.

Technically this needs to be included while calculating the overall bid-ask spread. How this can actually be achieve is yet another question!

Algorithms and the Turing Test

One massive concern about the rise of artificial intelligence and machine learning is the perpetuation of human biases. This could be racism (the story, possibly apocryphal, of a black person being tagged as a gorilla) or sexism (see tweet below) or any other forms of discrimination (objective looking data that actually represents certain divisions).

In other words, mainstream concern about artificial intelligence is that it is too human, and such systems should somehow be “cured” of their human biases in order to be fair.

My concern, though, is the opposite. That many of the artificial intelligence and machine learning systems are not “human enough”. In other words, that most present day artificial intelligence and machine learning systems would not pass the Turing Test.

To remind you of the test, here is an extract from Wikipedia:

The Turing test, developed by Alan Turing in 1950, is a test of a machine’s ability to exhibit intelligent behavior equivalent to, or indistinguishable from, that of a human. Turing proposed that a human evaluator would judge natural language conversationsbetween a human and a machine designed to generate human-like responses. The evaluator would be aware that one of the two partners in conversation is a machine, and all participants would be separated from one another. The conversation would be limited to a text-only channel such as a computer keyboard and screen so the result would not depend on the machine’s ability to render words as speech.[2] If the evaluator cannot reliably tell the machine from the human, the machine is said to have passed the test. The test does not check the ability to give correct answers to questions, only how closely answers resemble those a human would give.

The test was introduced by Turing in his paper, “Computing Machinery and Intelligence“, while working at the University of Manchester (Turing, 1950; p. 460).

Think of any recommender system, for example. With some effort, it is easy for a reasonably intelligent human to realise that the recommendations are being made by a machine. Even the most carefully designed recommender systems give away the fact that their intelligence is artificial once in a while.

To take a familiar example, people talk about the joy of discovering books in bookshops, and about the quality of recommendations given by an expert bookseller who gets his customers. Now, Amazon perhaps collects more data about its customers than any such bookseller, and uses them to recommend books. However, even a little scrolling reveals that the recommendations are rather mechanical and predictable.

It’s similar with my recommendations on Netflix – after a point you know the mechanics behind them.

In some sense this predictability is because the designers possibly think it’s a good thing – Netflix, for example, tells you why it has recommended a particular video. The designers of these algorithms possibly think that explaining their decisions might given their human customers more reason to trust them.

(As an aside, it is common for people to rant against the “opaque” algorithms that drive systems as diverse as Facebook’s News Feed and Uber’s Surge Pricing. So perhaps some algorithm designers do see reason in wanting to explain themselves).

The way I see it, though, by attempting to explain themselves these algorithms are giving themselves away, and willingly failing the Turing test. Whenever recommendations sound purely mechanical, there is reason for people to start trusting them less. And when equally mechanical reasons are given for these mechanical recommendations, the desire to trust the recommendations falls further.

If I were to design a recommendation system, I’d introduce some irrationality, some hard-to-determine randomness to try make the customer believe that there is actually a person behind them. I believe it is a necessary condition for recommendations to become truly personalised!

Python and Hindi

So I’ve recently discovered that using Python to analyse data is, to me, like talking in Hindi. Let me explain.

Back in 2008-9 I lived in Delhi, where the only language spoken was Hindi. Now, while I’ve learnt Hindi formally in school (I got 90 out of 100 in my 10th boards!), and watched plenty of Hindi movies, I’ve never been particularly fluent in the language.

The basic problem is that I don’t know the language well enough to think in it. So when I’m talking Hindi, I usually think in Kannada and then translate my thoughts. This means my speech is slow – even Atal Behari Vajpayee can speak Hindi faster than me.

More importantly, thinking in Kannada and translating means that I can get several idioms wrong (can’t think of particular examples now). And I end up using the language in ways that native speakers don’t (again can’t think of examples here).

I recently realised it’s the same with programming languages. For some 7 years now I’ve mostly used R for data analysis, and have grown super comfortable with it. However, at work nowadays I’m required to use Python for my analysis, to ensure consistency with the rest of the firm.

While I’ve grown reasonably comfortable with using Python over the last few months, I realise that I have the same Hindi problem. I simply can’t think in Python. Any analysis I need to do, I think about it in R terms, and then mentally translate the code before performing it in Python.

This results in several inefficiencies. Firstly, the two languages are constructed differently and optimised for different things. When I think in one language and mentally translate the code to the other, I’m exploiting the efficiencies of the thinking language rather than the efficiencies of the coding language.

Then, the translation process itself can be ugly. What might be one line of code in R can sometimes take 15 lines in Python (and vice versa). So I end up writing insanely verbose code that is hard to read.

Such code also looks ugly – a “native user” of the language finds it rather funnily written, and will find it hard to read.

A decade ago, after a year of struggling in Delhi, I packed my bags and moved back to Bangalore, where I could both think and speak in Kannada. Wonder what this implies in a programming context!

Generalist and specialist managers

A really long time ago, I’d written this blog post about “comparative advantage” versus “competitive advantage” employees. A competitive advantage employee is better at a particular kind of task or skill compared to the rest of the team, and he is valued for that kind of skill.

A comparative advantage employee, on the other hand, is “dominated” by at least one other person in the team – in the sense that someone else is better than this person at everything required for the job. In that sense, the value that the comparative advantage employee adds is by taking load off his colleagues, and allowing them to do more (and focus on the more productive parts of their jobs).

Thinking about it now, I realise that a similar classification exists from the manager’s perspective as well. And this is broadly correlated with whether the manager manages a “generalist” or a “specialist” team.

A specialist manager manages a team all of whose members work on and excels at one specialist task. This task could come from any part of the organisation – it could be sales or a particular kind of operations, or some financial activity or whatever. The defining feature of this kind of task is that it is usually repetitive and needs to be done in high volumes. Such tasks also offer high “returns to experience”.

The average employee of a specialist team is usually a “comparative advantage” employee. In most cases, such an employee is likely to be “dominated” by the manager, and the value he adds is by taking the load off the manager and allowing him to do more. Over the course of time, he becomes good enough at the job to become a manager himself, and the cycle continues – he will manage a team of people who are mostly inferior to him in the job.

Due to managers dominating direct reports, such teams end up being largely hierarchical, and there can be a tendency for the manager to micro-manage – if you are better at the task than the person actually doing it, you can do worse than giving specific instructions.

Generalist managers, on the other hand, manage teams that involve at least a few competitive advantage employees. What this implies is that there is a set of people who are better than the manager at certain parts of the business. The manager’s role in such a team is more of a facilitator, in terms of bringing the team together and coordinating in a way that they can maximise the team’s effectiveness.

Generalist managers seldom micromanage, since usually their team members know better (literally). They are also usually open-minded, since extracting full value from the team means recognising each member’s strengths (and consequently their own weaknesses). They learn the art of asking questions and verifying insights and work of the team in a cheap manner (remember from complexity theory that the complexity of verifying a solution can be much lower than the complexity of finding a solution).

Regular readers of the blog might have anticipated this paragraph – the trouble comes when a generalist manager has to manage a specialist team or the other way round.

A generalist manager managing a specialist team may not offer as much as he can to the team based on his experience. He might be too hands-off and team members used to more handholding and direction might feel lost. And so on.

A specialist manager managing a generalist team can be more damaging – not appreciating that some members might know more about some parts of the business might limit the performance of the team (since what the team can do is limited by what the manager knows). Also too much micromanagement on employees who know better about some parts of the business than the manager can result in disillusionment and ultimately backfire on the manager.

I wonder if this has something to do with the Peter Principle!

Bollywood movies and Rajputs

Bollywood movies and rajputs are in the news because of the recent stalling of this movie called “padmavati” thanks to threats of violence from goons who claim to represent Rajputs. This blog post is not about that, though, for there are better things to talk about, such as one Rajput movie from Bollywood that did see light of day, and become a huge hit.

I’m talking about the Imran Khan and Genelia D’Souza starrer Jaane Tu Ya Jaane Na. This released back in 2008, when I used to actually watch movies, and go to theatres to watch them (this one was at Inox Lido in Bangalore, and I even wrote what now appears to be an atrocious blog post about the experience).

Most of the story doesn’t matter here, except that the protagonist (Jai, played by Imran Khan) is a Rajput. And he’s no ordinary Rajput – he’s a Ranjhor ka Rathore. If you insist, he’s an excellent review of the movie by Baradwaj Rangan, and he’s a fascinating post about the geopolitical implications of the movie by Dr. Boris Bhartiraj Pandey.

So the main character in the movie (the way I saw it) is played by Naseeruddin Shah, and he appears as a portrait. For he is dead. But he comes alive to talk to his wife Savitri (played by his real-life wife Ratna Pathak Shah) at strategic times, offering advice which she is usually dismissive of.

There’s one scene in the movie that I still remember (as I commented a few months later, Bollywood movies can indeed by thought provoking). In that, Savitri chides her husband (in portrait mode, of course) for exhibiting the kind of false bravado that got him killed.

His reply (from the portrait), in my mind, encapsulates everything that I’ve read and seen about Rajputs in life. He starts off by saying that he’s a real Ranjhor ka Rathore who died an honourable death. And then goes on to say (ok I’m paraphrasing here) that it might be true that he got killed in the fight, but that before he got killed, he managed to slap each and every one of the opponents who killed him (exact context of the fight I’m not sure of – not even sure the movie dwells over that).

So people talk about the Rajputs’ culture of honour. One great example of this is the first battle of Tarain in 1191 when Prithviraj Chauhan, in a doubtless honourable gesture, decided to let go of the captured Mohammad Ghori. Ghori duly returned a year later and in the second battle of Tarain in 1192, not only defeated Prithviraj, but also killed him. He (Ghori) was perhaps not as honourable. But this led to the establishment of what we know as the Delhi Sultanate. Prithviraj being an honourable man was in a way responsible for this. But then he was honourable, and went down fighting, so we still revere him.

It is this very kind of honour that is illustrated by Naseeruddin Shah’s character in Jaane Tu Ya Jaane Na. It doesn’t matter that you get killed (going down fighting is honourable, right?). What matters more is that you manage to slap a few people before you got killed.

And in illustrating this so effectively, Jaane Tu Ya Jaane Na is in my opinion one of the best Bollywood movies about an Indian ethnic group!

 

Ratings revisited

Sometimes I get a bit narcissistic, and check how my book is doing. I log on to the seller portal to see how many copies have been sold. I go to the Amazon page and see what are the other books that people who have bought my book are buying (on the US store it’s Ray Dalio’s Principles, as of now. On the UK and India stores, Sidin’s Bombay Fever is the beer to my book’s diapers).

And then I check if there are new reviews of my book. When friends write them, they notify me, so it’s easy to track. What I discover when I visit my Amazon page are the reviews written by people I don’t know. And so far, most of them have been good.

So today was one of those narcissistic days, and I was initially a bit disappointed to see a new four-star review. I started wondering what this person found wrong with my book. And then I read through the review and found it to be wholly positive.

A quick conversation with the wife followed, and she pointed out that this reviewer perhaps reserves five stars for the exceptional. And then my mind went back to this topic that I’d blogged about way back in 2015 – about rating systems.

The “4.8” score that Amazon gives as an average of all the ratings on my book so far is a rather crude measure – since one reviewer’s 4* rating might differ significantly from another reviewer’s.

For example, my “default rating” for a book might be 5/5, with 4/5 reserved for books I don’t like and 3/5 for atrocious books. On the other hand, you might use the “full scale” and use 3/5 as your average rating, giving 4 for books you really like and very rarely giving a 5.

By simply taking an arithmetic average of ratings, it is possible to overstate the quality of a product that has for whatever reason been rated mostly by people with high default ratings (such a correlation is plausible). Similarly a low average rating for a product might mask the fact that it was rated by people who inherently give low ratings.

As I argue in the penultimate chapter of my book (or maybe the chapter before that – it’s been a while since I finished it), one way that platforms foster transactions is by increasing information flow between the buyer and the seller (this is one thing I’ve gotten good at – plugging my book’s name in random sentences), and one way to do this is by sharing reviews and ratings.

From this perspective, for a platform’s judgment on a product or seller (usually it’s the seller, but for products such as AirBnb, information about buyers also matters) to be credible, it is important that they be aggregated in the right manner.

One way to do this is to use some kind of a Z-score (relative to other ratings that the rater has given) and then come up with a normalised rating. But then this needs to be readjusted for the quality of the other items that this rater has rated. So you can think of some kind of a Singular Value Decomposition you can perform on ratings to find out the “true value” of a product (ok this is an achievement – using a linear algebra reference given how badly I suck in the topic).

I mean – it need not be THAT complicated, but the basic point is that it is important that platforms aggregate ratings in the right manner in order to convey accurate information about counterparties.

Freelancing and transaction costs

In the six years of running my own consulting business, I’d forgotten about an essential part that you need to endure as part of a job – piecemeal work. It is fairly often when you’re working for someone else that you get work that is so tiny or insignificant that you can hardly take ownership of it. The best strategy for dealing with it is to quietly get it over with and hope you won’t get such stuff again.

However, sometimes you can get caught in a rut of continuously getting this kind of work, and start wondering what you actually signed up for. And this is one thing I hadn’t expected to encounter when I got back to full time working earlier this year.

Thinking about why I never had to encounter such stuff during my consulting life, I realised there’s a fairly simple explanation – transaction costs.

Being a consultant is high transaction cost business. Every time you need to take on a new piece of work, you need to go through the charade of negotiating specifics with the client, pricing and drawing up a contract. All put together, the effort is not insignificant.

Moreover, in the line of work that I used to do, there was this massive overhead cost of understanding, cleaning and getting comfortable with the client’s data  – the effort involved in that meant that after a particular point in time I stopped taking work that wasn’t chunky enough. For a while I started refusing such work, but then got smarter and started pricing myself out of such work (though some clients were generous enough to meet that price to get their little tasks done – effectively I’d passed on the transaction costs to them).

The downside of this, of course, was that there was a fair amount of money I could have made taking up small works which I didn’t since the transaction cost was too high – this can be thought of as potential lost revenues. The upside was that whatever work I did was of high quality and (hopefully) made a big impact on the client’s business.

In the nature of the firm, Ronald Coase wrote that the purpose of the corporation was that transaction cost of dealing with co-workers can be eliminated. But then, I realise that sometimes this transaction cost can also be a good thing!

Oh, and obligatory plug here – my book Between the buyer and the seller deals with transaction costs, among other things. It’s available for sale (both in print and digital) on Amazon.

 

The (missing) Desk Quants of Main Street

A long time ago, I’d written about my experience as a Quant at an investment bank, and about how banks like mine were sitting on a pile of risk that could blow up any time soon.

There were two problems as I had documented then. Firstly, most quants I interacted with seemed to be solving maths problems rather than finance problems, not bothering if their models would stand the test of markets. Secondly, there was an element of groupthink, as quant teams were largely homogeneous and it was hard to progress while holding contrarian views.

Six years on, there has been no blowup, and in some sense banks are actually doing well (I mean, they’ve declined compared to the time just before the 2008 financial crisis but haven’t done that badly). There have been no real quant disasters (yes I know the Gaussian Copula gained infamy during the 2008 crisis, but I’m talking about a period after that crisis).

There can be many explanations regarding how banks have not had any quant blow-ups despite quants solving for math problems and all thinking alike, but the one I’m partial to is the presence of a “middle layer”.

Most of the quants I interacted with were “core” in the sense that they were not attached to any sales or trading desks. Banks also typically had a large cadre of “desk quants” who are directly associated with trading teams, and who build models and help with day-to-day risk management, pricing, etc.

Since these desk quants work closely with the business, they turn out to be much more pragmatic than the core quants – they have a good understanding of the market and use the models more as guiding principles than as rules. On the other hand, they bring the benefits of quantitative models (and work of the core quants) into day-to-day business.

Back during the financial crisis, I’d jokingly predicted that other industries should hire quants who were now surplus to Wall Street. Around the same time, DJ Patil et al came up with the concept of the “data scientist” and called it the “sexiest job of the 21st century”.

And so other industries started getting their own share of quants, or “data scientists” as they were now called. Nowadays its fashionable even for small companies for whom data is not critical for business to have a data science team. Being in this profession now (I loathe calling myself a “data scientist” – prefer to say “quant” or “analytics”), I’ve come across quite a few of those.

The problem I see with “data science” on “Main Street” (this phrase gained currency during the financial crisis as the opposite of Wall Street, in that it referred to “normal” businesses) is that it lacks the cadre of desk quants. Most data scientists are highly technical people who don’t necessarily have an understanding of the business they operate in.

Thanks to that, what I’ve noticed is that in most cases there is a chasm between the data scientists and the business, since they are unable to talk in a common language. As I’m prone to saying, this can go two ways – the business guys can either assume that the data science guys are geniuses and take their word for the gospel, or the business guys can totally disregard the data scientists as people who do some esoteric math and don’t really understand the world. In either case, value added is suboptimal.

It is not hard to understand why “Main Street” doesn’t have a cadre of desk quants – it’s because of the way the data science industry has evolved. Quant at investment banks has evolved over a long period of time – the Black-Scholes equation was proposed in the early 1970s. So the quants were first recruited to directly work with the traders, and core quants (at the banks that have them) were a later addition when banks realised that some quant functions could be centralised.

On the other hand, the whole “data science” growth has been rather sudden. The volume of data, cheap incrementally available cloud storage, easy processing and the popularity of the phrase “data science” have all increased well-at-a-faster rate in the last decade or so, and so companies have scrambled to set up data teams. There has simply been no time to train people who get both the business and data – and the data scientists exist like addendums that are either worshipped or ignored.

Firecrackers and the Hindu religion

There was massive controversy in India last month when the Supreme Court banned the sale of firecrackers in and around Delhi, in an ostensible Move to cut pollution.

As one might expect, the move drew heavy criticism on the grounds that the court was ruling against a fundamental tenet of Hindu religion. In return, other people pointed out that bursting firecrackers on the occasion of Deepavali is a rather recent tradition, and thus has nothing to do with the “fundamental tenets of Hinduism”.

As it happened, the ban continued to stay, though reports say that both noise and air pollution levels in Delhi were unaffected by the ban. Here’s my humble attempt to argue that why modern traditions such as bursting firecrackers is important to religion,

As I’ve mentioned several times on this blog, religion in general and festivals in particular are memes, in the traditional Richard Dawkins sense of the term.

Religion and festivals are basically ideas that compete in an ideas marketplace, and people propagate the ideas that they like the most. In one sense people like what they find useful – which is why imagined orders such as democracy or public limited companies continue to propagate and thrive.

At a more personal level, though, people will choose to associate with and propagate ideas that they simply like, and at a very basic level, enjoy. In other words, the more fun people find a concept, the more heavily they’ll adopt and propagate it.

Hence religions evolve, and (in what can be seen as parallels to mutation), pick up ideas from outside that can make them more fun. So the American Christians picked up and appropriated thanksgiving from the red Indians. Even further back Christianity picked up and amalgamated the idea of Christmas. Hare Krishna people picked up wild dancing. Bombay people picked up Ganesha processions. And so on.

By incorporating fun practices from outside, religions make themselves fitter, as they open up leeway’s for new recruits (such as kids). Short of coercion, without fun practices there’s little chance that religion can pick up new recruits.

Crackers on Deepavali, or colours on Holi, are aspects that have come into the hindu religion that have made it more fun. That theee aspects make the religion more fun mean that it’s easier to co-opt new recruits, especially the young kind. This makes the meme that is the hindu religion fitter.

So it doesn’t matter how ancient a practice is – as long as it’s fun, and increases the memetic fitness of a religion, it remains a fundamental part of the religion.

Without firecrackers the idea of Deepavali might lose its identity and people might stop celebrating it. And it being one of Hinduism’s most celebrated festivals, a weakening Deepavali meme leads to a weakening hindu meme.

So the banning of firecrackers in Delhi on the occasion of Deepavali was indeed injurious to the hindu religion.

Just keep in mind that culture (using memes) evolves much much faster than organisms (which use genes)!

Lessons from poker party

In the past I’ve drawn lessons from contract bridge on this blog – notably, I’d described a strategy called “queen of hearts” in order to maximise chances of winning in a game that is terribly uncertain. Now it’s been years since I played bridge, or any card game for that matter. So when I got invited for a poker party over the weekend, I jumped at the invitation.

This was only the second time ever that I’d played poker in a room – I’ve mostly played online where there are no monetary stakes and you see people go all in on every hand with weak cards. And it was a large table, with at least 10 players being involved in each hand.

A couple of pertinent observations (reasonable return for the £10 I lost that night).

Firstly a windfall can make you complacent. I’m usually a conservative player, bidding aggressively only when I know that I have good chances of winning. I haven’t played enough to have mugged up all the probabilities – that probably offers an edge to my opponents. But I have a reasonable idea of what constitutes a good hand and bid accordingly.

My big drawdown happened in the hand immediately after I’d won big. After an hour or so of bleeding money, I’d suddenly more than broken even. That meant that in my next hand, I bid a bit more aggressively than I would have for what I had. For a while I managed to stay rational (after the flop I knew I had a 1/6 chance of winning big, and having mugged up the Kelly Criterion on my way to the party, bid accordingly).

And when the turn wasn’t to my liking I should’ve just gotten out – the (approx) percentages didn’t make sense any more. But I simply kept at it, falling for the sunk cost fallacy (what I’d put in thus far in the hand). I lost some 30 chips in that one hand, of which at least 21 came at the turn and the river. Without the high of having won the previous hand, I would’ve played more rationally and lost only 9. After all the lectures I’ve given on logic, correlation-causation and the sunk cost fallacy, I’m sad I lost so badly because of the last one.

The second big insight is that poverty leads to suboptimal decisions. Now, this is a well-studied topic in economics but I got to experience it first hand during the session. This was later on in the night, as I was bleeding money (and was down to about 20 chips).

I got pocket aces (a pair of aces in hand) – something I should’ve bid aggressively with. But with the first 3 open cards falling far away from the face cards and being uncorrelated, I wasn’t sure of the total strength of my hand (mugging up probabilities would’ve helped for sure!). So when I had to put in 10 chips to stay in the hand, I baulked, and folded.

Given the play on the table thus far, it was definitely a risk worth taking, and with more in the bank, I would have. But poverty and the Kelly Criterion meant that the number of chips that I was able to invest in the arguably strong hand was limited, and that limited my opportunity to profit from the game.

It is no surprise that the rest of the night petered out for me as my funds dwindled and my ability to play diminished. Maybe I should’ve bought in more when I was down to 20 chips – but then given my ability relative to the rest of the table, that would’ve been good money after bad.