The BMW Method
Gambling, Investing, and Poker

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By Sand105
September 10, 2007

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Gambling, Investing, and Poker

There have been a couple of times that I have equated stock market investing and gambling to angry denunciations. This article is intended to show how they are related and how to leverage knowledge from games of chance into stock market success. This is a long read, so grab a cup of coffee and dig in. If you want to get to the nitty gritty, you can skip to the last section.

Definition of Game Types

Before we delve into the intricacies, it is important to understand what classes of games are out there - and yes, equity investing is a game. There are two basic types of games: logic based and trivia based. Logic games require only internal knowledge (i.e. read the rules, play the game) while trivia based games require external knowledge (Trivial Pursuit). Equity investing is a bit of both, however at its heart equities are a numbers game - a logic game. I offer this without proof and will backup with discussion below.

The subdivision goes further. What types of logic games are there? This is straightforward - there are four types of logic based games. Each requires its own set of critical thinking skills to master. Figure 1 shows the logic game matrix along with common examples of each. As can be seen the games are divided by whether or not they contain a random component and an informational component.

Figure 1

The top left are the most straightforward games - chess, go, etc. Not surprisingly these are the ones in which computers have become better than humans. Top right are those games that have an incomplete informational component, but no random component. Stratego is the most direct, recognizable example of this kind of game (Diplomacy is more fun, though). Bottom left are those games with randomness but complete information. Backgammon is the best example of this type (and the only popular one I can think of - of all the types I like this quadrant the least).

The bottom right contains the most interesting of logic games - those that have both incomplete information and randomness. The other three quadrants are additive into this quadrant and game theory used in the other three all apply here. Great examples of this include poker, many wargames (Advanced Squad Leader the prime example), and equity investing. (As a note I wanted to include women in this quadrant, but my wife whacked me over the head when she saw it. I offered that as proof of randomness and got whacked again. What's a guy to do?)

What are the predominant skill sets needed in each quadrant?

Non-random/complete information: This type of game is all about building a logic train that is superior to your opponent. Construct the highest quality logic train and you will win every time.

Non-random/incomplete information: This type of game has as its main component inferring the most logical content of incomplete information. It also involves anticipating the moves of an opponent by their past actions (part of which is assessing incomplete information).

Random/complete information: This type of game has as its main component odds calculation. Combine odds calculation with a logic train to achieve success in the long run.

Random/incomplete information: The skillset required in this game is the combination of the other three.

There are those out there that proclaim there is no randomness in the stock market - all movements are influenced by real, definable external forces. I would argue that while this may be true for the most part, most of these forces aren't easily knowable and that there are so many of them that, in effect, the short term movements of the market are indeed random. Some of the best work in this area was done by Benoit Mandelbrot, who found that the markets followed a definable chaotic walk and were able to be described using fractal analysis. He also found, however, that this fractal walk was describable once it occurred, but not predictable. That is random in my book.

The question remains, however, whether equity investing is "gambling". By corollary, are the games that have a random component gambling?

Randomness and Gambling

Does randomness = gambling? From the dictionary definition of gambling: to stake or risk money, or anything of value, on the outcome of something involving chance. By that definition any activity with a random component is gambling. For fun, let's see how the government views gambling:

State governments are very varied in their treatment of what is gambling and what isn't. A book could be written on this one. Some look at the amount of skill/randomness mix and some don't. California has many poker halls - it has defined poker, a game with a significant random component, as a game that is predominantly skillful and thus not gambling. New York, on the other hand, has found that those games with any random component are gambling and prohibit them. It, of course, blesses all stock market activities.

Federal government? Probably even more interesting. Congress in recent history has tackled the "problem" of internet gambling by passing a law that tried to strangle off funding mechanisms. It maintains that internet casinos, poker rooms, and sportsbooks are illegal. The area is actually pretty gray with the exception of sportsbooks. Those were expressly made illegal by the 1961 Wire Act. Their efforts at prohibition were aimed at internet bingo halls, casinos, sportsbooks, and poker rooms. It, however, made exceptions for horse racing, interstate casino jackpots (mostly Indian casinos), fantasy football, and (of course) lotteries. So according to the Feds gambling is bad unless you have a highly paid lobby - the NFL, pari-mutuels, casinos, etc. And, of course, the most regressive, destructive form of gambling - the lottery (50% profit cut with a near infinite variance) - is exempt. But this is evidently OK since the government runs that business.

So the government is no help - no surprise. But I digress.

The dictionary definition is accurate but it is incomplete. As with most things in real life, the issue much more nuanced. Games with a mixture of skill and randomness are not so easily pinned down. We'll talk about this more.

The Intricacies of Skill/Randomness

Now we need to define the nuances of games that combine randomness and skill. First let's look at how one can make money in a typical casino - the bastion of winning the randomness game:

1. Be the casino. Set the rules, make the money. In terms of equities, this is the NYSE or CBOE. These guys make money no matter the ups and downs. Making the game = profit.
2. Cheat. Always profitable, cheating and insider information will never go away. The downside is pretty harsh, though.
3. Play games in which the casino only arbitrates the action, rather than makes the rules. If you play a game that the casino doesn't have a direct interest in and if your skill set is better than other participants, there is an opportunity to make money. Equity investing naturally falls into this category, as does poker and backgammon. All have a skill/randomness mix and all can be beaten for a profit.

Casino games have two qualities: the profit curve and variance around that curve. Let's take the most common casino game as an example - blackjack. A typical good blackjack game has a fixed advantage for the casino of ~2%. If you play perfect blackjack the best you can do is -2%. Therefore, the profit curve for a player will be a -2% CAGR over the long haul. Blackjack also has a significant variance around that curve, however. Players who play over the short term may very well ride that variance to a win. That player is simply hoping to ride the lovely side of randomness to a profit. The casino wants to keep you playing over the long haul. The more hands the player partakes in, the closer to the true CAGR curve that player will get (casino = $$cha-ching$$). Thus the reason for the lack of clocks in casinos, betting limits, free drinks, etc.

Poker players and equity investors, done correctly, are the opposite. In these, if the skill sets are good enough, the CAGR is positive. However, both of these carry significant variance as we all know. Adherents of the BMW method know that many companies that have been around for a while tend to revert to an inherent CAGR and exhibit a variance around this natural return. In poker the same is true. In both if the game is played over the long haul and enough good decisions are made the return will conform to an innate growth rate. Investors and poker players (good ones) look to take the variance out of the equation by playing for the long haul.

So now we can get a bit better definition inside the category of gambling. Those players who attempt to ride variance are speculators. In the long run they have no expectation of having a positive expectation. This includes any casino game played against the casino, short term forex players, daytraders, etc. Those players playing in such a way to minimize the effects of variance are investors. These include long term investors and skillful players in games that have a skill/randomness combination (poker, backgammon, bridge, etc.).

One famous poker player, Phil Gordon, remarked in the introduction of his Little Blue Book: "Nearly every day people email me or stop me on the street and ask me: 'What's it like to be a professional gambler?' I invariable answer the same way each time: 'I've never gambled a day in my life.' I consider myself a strategic investor. For every $100 I put in the pot, I expect to take more than $100 back out. If I can succeed more times than not, hand after hand, tournament after tournament, year after year, I ensure a long term positive expectation. That positive expectation applied over thousands of trials is what makes me a winning player."

I quoted this because it simply can't be said any better. Technically every time someone puts money at risk (i.e. not a government backed treasury) they are gambling. Played properly over the long haul, however, a skilled player can overcome the variance and ensure a long term positive expectation.

Poker and Equity Investing

Now that we have defined what equity investing is and isn't, it remains to define why I believe the skill sets in poker and investing are pretty much the same. We know many of the mathematics around investing and gambling are the same (the Kelly Formula, for example). So how are poker and investing similar and dissimilar?


1. Most importantly, both games involve incomplete information and randomness. The skill sets developed in one apply directly over to the other. Developing a logic train, calculating odds, and accurately inferring conclusions from incomplete information are exactly what is needed to be successful in both.
2. Both are beatable over the long term. Poker is equivalent to playing one game of chess along with a couple die rolls. Over the short term the die rolls rule - over the long term the chess matches determine the expectation. Equity investing is essentially the same.
3. Both have inherent costs. Poker has rake (5% of each pot, give or take), investing has transaction and frictional costs.
4. Both see black swans occur. No matter the skill set, sometimes the incredibly unusual occurs. Knowing how to recover from these setbacks is a very valuable skill set.


1. By its nature, poker is a negative expectation game if no players are better than one another (due to the rake). Investing naturally has a long term ~10% positive tilt due to the nature of the markets.
2. The inherent costs in investing are lower. As long as the investor doesn't have huge turnover, transaction costs and frictional costs are well under the cost of rake in poker.
3. More often than not, choosing to do nothing in investing is the right choice. Poker typically requires more risk taking events.
4. The variance in investing is lower than poker. For every $1 I have made in poker over the long haul there has been a ~$10 standard deviation in those results (i.e. for every $1 there is a 67% chance my result will actually be from -$4 to $6 and a 95% chance it will actually be from -$9 to $11.) This type of variance isn't typical of the equity markets.
5. In poker, to win in the long term a player simply tries to ride out the variance. An investor, however, can use variance to their benefit. BMW has talked about this extensively. Figuring out to what price an equity is likely to jog down to in the short term can greatly juice overall returns.

Lessons Learned:

As a person who has played over 1,000,000 hands of poker in the last few years and been involved in the markets for 15+ years, there are some things that I have learned that I hope folks will find useful.

Pretty much in the order I think they are important, these are lessons I think provide for success in both poker and equity investing:

1. Emotional control. Yep, after all the talk about logic trains and odds, I firmly believe emotional control has the most effect on long term results. This is multifaceted. The primary emotion one needs to regulate is tilt ("fear"). Selling in panic is very, very often the exact wrong thing to do. Yet even very experienced investors have it happen. It can't be stomped out completely - however minimizing it will do wonders for an investor's return. On the flip side of the coin boredom can be almost as damaging. Playing a hand one shouldn't or making a trade just because you haven't had anything enticing float by in a while is usually a mistake. Coincidentally, Whatismyoption has just posted an excellent thread on this subject.

2. Recognize that once you buy and equity or put your money into the pot, that money should be treated as if it is no longer yours (in poker it actually is no longer yours). Most people base decisions on selling an equity based on whether or not it has been performing for them. This is wrong! It doesn't matter if the equity has lost a bunch or gained a bunch since ownership - it is the prospects for the future, the odds that one will see a rise from that price point, that count. In a game sense, when you buy an equity you give your money to Mr. Market. He then takes it and walks around with it - you have no direct control over that walk at all. You are simply betting on the overall direction of his travels. All decisions should be based on that premise. Since most investors feel the loss of money as near physical pain (lots of studies out there on investor psychology), they watch their returns like a hawk and decide to sell based on past performance. Sell decisions should be based on changes in how speculative a stock is, changes in fundamentals, tax loss harvesting, finding a better opportunity, etc. Price by itself, and your buy point relative to that price, is irrelevant.
3. Recognition of high probability situations. Dhandho, in other words. Figure out how to get your money into play with a 60-40 advantage over and over and riches will follow. In investing there are choices every day to hold, buy or sell. Most of the time this will be to hold, but when the high probability situations roll by, grab on and get a piece.
4. The corollary to #3. Don't bet unless you have lopsided odds. Taking those 51-49 bets, though positive, leads to very high variance. Leave that to the institutional investor who has the bankroll to spread those bets around in enough places to get to the long term. Most individual investors will never get there.
5. Playing games, chess, poker, etc keep the mind agile and greatly assist in both business and investing. Mental cross training. Learning emotional control. Recognizing that both poker, investing, business, and other difficult-but-satisfying-activities are lifelong pursuits and ones in which there is always something new to learn and improvements to be made.

I have been thinking about this subject for a while. Hopefully the article makes sense and adds to the group. It is a bit long, for which I apologize. I wanted to get this down on paper for myself as much as to put out there, though. I truly enjoy both the game of poker and investing (as well as wargames like ASL). Having two out of three hobbies actually make money keeps me off the streets and the wife happy - a great combination. It is my ambition and goal to parlay these two hobbies into a 10 year decrease in my time to retirement. A lofty goal, for sure. Even if that doesn't work out, it will be a fun journey.

Take care.