Investment process
It’s imperfect, but that’s what it’s all about
I’m not too proud to pick up ideas about investing wherever I can. Let’s call it thought diversification. We can get fresh ideas from other fields. We have to keep an open mind. In this post, I will take a look at what investors can learn from professional gamblers.
Expected value – Thinking probabilistically
Let’s start with something that might make your eyes glaze over.
In probability theory, the expected value is a generalization of the weighted average. Informally, the expected value is the mean of the possible values a random variable can take, weighted by the probability of those outcomes. Wikipedia
It this sounds obtuse, reflect on something Warren Buffett said at the Berkshire Hathaway Annual Meeting in 1989: “Take the probability of loss times the amount of possible loss from the probability of gain times the amount of possible gain. That is what we’re trying to do. It’s imperfect, but that’s what it’s all about.”
What Buffett is describing is expected value and probabilistic thinking. One other term to roughly describe it is risk/reward.
Nate Silver is an American statistician, writer, and poker player who analyzes baseball, basketball, and elections. He has written a couple of books, The Signal and the Noise, 2012, and On the Edge, 2024. The latter book is subtitled The Art of Risking Everything. For present purposes the thing we need to know is that for a number of years he worked as a professional poker player.
Silver offers the view that expected value is an absolutely foundational and central concept to poker, investing and a lot of fields of life. He describes it at the art of thinking probabilistically.
The reason this is important for investing is that the world is a complicated and uncertain place. Since we have to make decisions in the face of uncertainty, the only way we can make them is with probabilistic thinking. Probabilistic thinking leads one to expected values.
Gambling and investing share probabilistic thinking and expected value as central concepts. For investors, reading about how professional gamblers deal with expected value can be illuminating.
For this post it’s fair to say that Warren Buffett has summed it up. Expected value is a concept shared between gambling and investing. The devil is in the detail which can be dealt with elsewhere.
Game theory
Silver quotes one Doyle Brunson who says: “There’s never going to be a computer that will play World-Class Poker. It’s a people game.” (Silver, 2024) p39
That struck a chord with me. Investing is also a people game. The central players are you and Mr. Market.
We know that computers have mastered chess and several other games. What is different about poker? And what is different about investing. Let’s start with game theory, then chess, and then come back to poker and investing.
John von Neumann was a Hungarian and American mathematician, physicist, computer scientist and engineer. He died in 1957. He is perhaps best known known for his work in the early development of computers. He is also the father of game theory. Game theory is central to the nuclear deterrent concept of mutually assured destruction.
Annie Duke is a bestselling author, a former professional poker player and currently a consultant in the decision-making space. She also did graduate level research in psychology at the University of Pennsylvania. In her 2018 book Thinking in Bets, Annie Duke tells us that “game theory was succinctly defined by economist Roger Myerson (one of the game theory Nobel laureates) as ‘The study of mathematical models of conflict and cooperation between intelligent rational decision -makers’.
Duke goes on: “Game theory is the modern basis for the study of the bulk of our decision-making, addressing the challenges of changing conditions, hidden information, chance, and multiple people involved in the decisions.” (Duke, 2018) p20 She says that game theory is particularly applicable to poker.
Let’s go back to chess. Game theory doesn’t apply to chess. Von Neuman is quoted as saying: “Chess is not a game. Chess is a well-defined form of computation. You may not be able to work out the answers, but in theory there must be a solution, a right procedure in any position. Now, real games” he said, “are not like that at all. Real life is not like that. Real life consists of bluffing, of little tactics of deception, of asking yourself what is the other man going to think I mean to do. And that is what games are about in my theory.” (Duke, 2018) p20 This latter description certainly covers poker.
Duke concludes: “Chess for all it’s strategic complexity, isn’t a great model for decision-making in life, where most of our decisions involve hidden information and a much greater influence of luck” (Duke, 2018) p21
To see how game theory might apply to investing, let’s look at a quote from Maynard Keynes on the subject of what is called price discovery:
“It might have been supposed that competition between expert professionals, possessing judgment and knowledge beyond that of the average private investor, would correct the vagaries of the ignorant individual left to himself. It happens, however, that the energies and skill of the professional investor and speculator are mainly occupied otherwise. For most of these persons are, in fact, largely concerned, not with making superior long-term forecasts of the probable yield of and investment over its whole life, but with foreseeing changes in the conventional basis of valuation a short time ahead of the general public.” (Keynes, The General Theory of Employment, Interest and Money. 1936,2007) p154
This sounds a lot like game theory; looking for ways to maximize expected value while accounting for the actions of other investors. In poker, bluffing seems to be one of the sides of the action where game theory comes into play. It might be argued that there’s never going to be a computer that will invest like Warren Buffett.
Importance of process
The following quote from Annie Duke applies equally to investing and poker. “What makes a decision great is not that it has a great outcome. A great decision is the result of a good process, and that process must include an attempt to accurately represent our own state of knowledge. That state of knowledge, in turn, is some variation of ‘I’m not sure.’” (Duke, 2018) p.27
There are several points here. Good process is one. Acknowledging the limits of our knowledge and even our skill, are critical. For investors, in a world of intuiting probabilities and risk/reward, recognizing our limits, makes for better decisions. This kind of thinking is what Annie Duke calls ‘Thinking in Bets’.
Experience leads to better learned intuitions and better outcomes. Duke says: “…if we follow the example of poker players by making explicit that our decisions are bets, we can make better decisions and anticipate (and take protective measures) when irrationality is likely to keep us from acting in our best interest.’ (Duke,2028) p43 Which brings us back to expected value and probabilistic thinking.
Optionality
Nate Silver suggests that optionality is one of the key concepts in poker and in many other facets of life. He writes: “Optionality is a term use in game theory and finance to describe the value of being able to take advantage of future opportunities that might arise.” (Silver, 2024) p.76
We can compare this with Warren Buffett’s thoughts. Alice Schroeder wrote an authorized biography of Buffett titled The Snowball: Warren Buffett and the Business of Life published in 2008.
A newspaper article in 2012 about the book suggested that to Mr. Buffett, cash is not just an asset class that is returning next to nothing. It is a call option that can be priced. When he thinks that option is cheap, relative to the ability of cash to buy assets, he is willing to put up with super-low interest rates. “He [Buffett] thinks of cash differently than conventional investors,” Ms. Schroeder says. “This is one of the most important things I learned from him: the optionality of cash. He thinks of cash as a call option with no expiration date, an option on every asset class, with no strike price.”
Silver generalizes and says: “A heuristic way of thinking of optionality is this: when you face a close decision, make the choice that will keep the most options open”. Investors can reflect on this advice.
In blackjack gamblers can sometimes gain an edge by counting cards. Silver relates how one benchmark card counting strategy executed perfectly “will net you about 60 cents for every $100 you bet – meaning a player edge of just 0.6%. This is razor thin. But edge is critical in gambling, as in investing. “‘Edge’ means having a persistent advantage in gambling – consistently making +Expected Value bets.” (Silver 2024) p22
In poker it seems the edge comes from bluffing and game theory.
The term +Expected Value means positive expected value. In investing, an edge can come about in various ways. In my own investing I rely on a behavioral edge. I have no informational edge. I have no insights beyond other investors.
Financial swings and volatility
Silver tells us that “…betting sports – or almost anything else – requires a tolerance for financial swings that isn’t for everyone.” (Silver, 2024) p179 That sounds to me a lot like investing.
Inefficient markets
In sports betting there are real issues around efficient markets. I am not a sports bettor. I’m writing here from what I have read, as far as I understand it. Apparently, making money in sports betting is not about picking winners. Bookmakers will set various types of betting odds based on the amount of money being staked on an event by the public. Money bet is a kind of market that will clear at a price that determines odds. Making money at sports betting is about finding odds that are wrong i.e. are inefficient. If a lot of dumb money is bet on a particular side, this creates +Expected Value for smart bettors who can take advantage of an inefficient market. This is much like what happens in the stock market.
Cool under pressure
Silver says that the best poker players are those who can execute with a level head when the going gets tough. (Silver 2024) p221
This is true in spades, so to speak, when investing. Pressure exacerbates and causes all sorts of behavioral biases and cognitive errors to surface. Humans are neither fully rational nor fully selfish. Readers not sure how important investment psychology is to successful investing are invited to read my post Investment psychology explainer for Mr. Market – introduction
Duke tells us that in poker and gambling circles, becoming emotionally unhinged is called ‘tilt’, as in pinball machines. Losing it emotionally happens in investing. Anyone who can’t take a deep breath and restabilize should not be investing.
Waiting for the right pitch
In poker, the players are typically dealt two cards. There are apparently 1,326 combinations of starting hands. Most of these combinations are not worth betting on. An experienced player will fold and not bet if the first two cards are poor. Annie Duke suggests that an experienced player will choose to play only about 20% of the hands they are dealt. That means that 80% of the time an experienced player will be simply watching other players play. (Duke, 2018) p97
Compare this with Warren Buffett’s advice. In his 1994 Chairman’s Letter to Berkshire Hathaway shareholders, he explains why one has to wait for the right pitch:
“Ted Williams, in The Story of My Life, explains why: ‘My argument is, to be a good hitter, you’ve got to get a good ball to hit. It’s the first rule in the book. If I have to bite at stuff that is out of my happy zone, I’m not a .334 hitter. I might be only a .250 hitter.’ Charlie [Munger] and I agree and will try to wait for opportunities that are well within our own ‘happy zone.’” (Buffett W. E., The Essays of Warren Buffett: Lessons for Corporate America. 1998) p208 That’s the only way to become a good hitter.
We want to know when to hold ‘em and when to fold ‘em, and when to walk away, Annie Duke’s 2022 book is titled Quit – The Power of Knowing When to Walk Away. It deals with a lot more than poker and gambling. From her poker experience she offers the view that great players know when to fold and when to walk away from a game.
Duke writes: “Deciding which hands are worth playing and which hands are not, is the first and most consequential choice a player makes.” Where an experienced player will stick with only 20% or so of their hands, amateurs will stick with half. Amateurs seem to fear missing out on a pot.
Two investing parallels come to mind. Inexperienced investors swing too often. They suffer from a fear of missing out (FOMO). As well, when inexperienced investors find themselves in a losing situation, they are reluctant to sell and take the loss.
Walking away
Duke points out that great poker players will walk away from a game they are not comfortable with. She writes: “When experts are in a game, they are more likely than other players to recognize when the game conditions aren’t favorable or when they’re not playing well. And given that they recognize those things, they are more likely to quit the game because of it.” (Duke, 2022) p20 Investors might take this advice to heart.
Kill criteria
Often when we are in a losing situation, we tend to double down rather than cutting our losses. Duke offers the idea of making decisions ahead of time as to when we will take action. (Duke, 2022) p115-121 In a stock situation it might be a price below cost when we commit to bail out of the position. Or it might be a time, say three years, by which the bargain basement stock we bought should be fully priced by the market. This allows the decision to be made ahead of time when emotions and behavioral biased don’t warp our view of things. I’m not a great fan of this idea. But it might make sense for less experienced investors.
Conclusion
I began this post with the thought that I’m not too proud to pick up ideas about investing wherever I can. Professional gambling provides a living for some. Learning about their edge and how they do it can be illuminating for investors. I am not suggesting for a moment that investing is a form of gambling; Quite the contrary. I do believe that reading about how professional poker players go about it is of interest as professional gambling is actually a near cousin of investing and can provide insights for investors.
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I have written other posts that touch on various aspects of gambling and what investors can learn from gambling. Interested readers might check out these posts:
Coping with luck – good and bad
Investors must keep in mind the ‘gamblers’ fallacy’. This is the tendency of gamblers on a losing streak to up the ante, to take more risks. That is, they become risk seeking.
A lottery is simply a gamble where the potential reward doesn’t justify the risk. There is a name for it. It’s called risk seeking behavior.
Gambling, trading, risk intolerance and investing
When you are placing bets at a casino, the house has an edge. In probability terms, the bettor’s wager has a negative expectation. As Poundstone points out, almost everyone who gambles goes broke over the long run. It’s called Gambler’s Ruin. Professional gamblers will only gamble if they have an edge. They are, technically speaking, investing not gambling.
Haghani and Dewey devised a simulated coin flipping game to determine whether a group of finance and economics students and young professionals at finance firms could successfully take advantage of odds of 60/40 in their favor on each and every flip of the coin. The edge in the odds on each flip was explained to the subjects before the experiment. They were each given a $25 starting stake and could bet any amount on any simulated flip of the coin. The game lasted 30 minutes.
The paper notes with genuine disbelief: “We were surprised that one third of the participants wound up with less money in their account than they started with. More astounding still is the fact that 28% of participants went bust and received no payout.”
The betting errors made by the subjects included over-betting, under-betting, erratic-betting and betting based on previous flips. The authors write: “Without a Kelly-like framework to rely upon, we found that our subjects exhibited a menu of widely documented behavioral biases such as illusion of control, anchoring, over-betting, sunk cost bias, and gambler’s fallacy.”
What we learn from this simulated 60/40 coin flipping experiment is that a speculative, erratic approach can lose even a winning game.
Lessons from the world of gambling
What it means to not lose money
Gamblers often call it bankroll management.
Investors can learn from gamblers about the optimum size of particular investments in a portfolio. The money and betting management system is also called ‘betting your beliefs.’ The system tells the gambler the optimum amount to wager on each bet. The magic sauce is the use of the geometric mean of the return expectations, as opposed to the arithmetic mean.
The math is calculated by taking the ‘mathematical expectation of winnings’ on each bet, say ten bets in a ten-horse race, multiplying them together and then taking the tenth root of the product. This gives the geometric mean of the ‘expectation of winnings’ of each bet.
It’s called the Kelly system or as it is sometimes, the Kelly Criterion. The key insights from the Kelly system for common stock investors are as follows:
1. The optimum strategy is the one that gives the highest compound return over the long haul with no risk whatsoever of going broke.
2. A corollary to not going broke is that no position is ever so large that it imperils the portfolio; this is a significant constraint on concentration.
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You can reach me by email at rodney@investingmotherlode.com
I’m also on Twitter @rodneylksmith
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