SumGames - Zero Sum Games, Winner's Games, Loser's Games

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 summarizes and compares the numbers, probabilities, and odds of the common investments, speculations, and gambles that people often face. Throughout the history of Wall Street, analogies comparing investing and the stock market to gambling and speculation have been common. Definitions vary and discussions are included in numerous articles, studies, and books including many investment classics.

Questions touched on at include

The distinction between investment and speculation in common stocks has always been a useful one and its disappearance is a cause for concern. We have often said that Wall Street as an institution would be well advised to reinstate this distinction and to emphasize it in all dealings with the public. Otherwise the stock exchanges may some day be blamed for heavy speculative losses, which those who suffered them had not been properly warned against.
Benjamin Graham in "Investment versus Speculation" - the first chapter of The Intelligent Investor.

     Casino games are generally negative sum games. Yet there are professional gamblers that consistently (or persistently) make money at the expense of other gamblers. This occurs only in games of skill like Poker, where weak or suboptimal players provide enough of an opportunity for professionals to overcome the vigorish or costs. But there are no professional gamblers in negative sum games that don't involve skill (like craps and roulette). Definitions - See also Investment, Speculation, and Gambling at

Investing - allocating funds with a positive expected return. Investing in securities or property for the purpose of generating a reasonable rate of return in addition to return of the original investment, commensurate with the risk. The investment should have a logical theory as to why it should have a reasonable return in addition to the return of the principal, and preferably historical data supporting the theory. Participating in a positive sum game is investing.

Speculation - allocating funds with an even (or insignificantly negative) expected return, but also some underlying rational for potential gain relative to other participants. Participating in a zero-sum game is speculating.

Gambling - allocating funds with a negative expected return, but some possibility of substantial gain. Gambling also frequently involves the intentional assumption of risk, in other words risk is sought, rather than avoided as in investing. Gambling is also sometimes associated with some morally questionable activities. Participating in a negative sum game where no skill is involved is gambling (unless it is for insurance purposes, which is a separate, but related discussion).

     Gamblers intentionally assume risk for thrill, excitement, or other reasons. Speculators only assume risk when they believe they have identified an advantage (or weakness in their opponents) that compensates for the risk and their costs or vigorish. Or alternatively, gamblers and speculators get some pleasure or value from the process of speculating which compensates for the negative expected returns. Investors avoid risk and don't allocate any entertainment value to the process.

     Here at, the intent is not to encourage you to gamble, but to help clarify the smart way to play the various games to maximize your expected return. In gambling you should only logically play for entertainment purposes (there may be other logical reasons as well) rather than in the expectation of profiting. Aside from entertainment, it only makes sense to speculate or gamble if you can identify opponents that are making predictable mistakes. For instance, there are many psychological reasons for profit opportunities in investment markets. Or it can make sense to participate in certain casino games such as poker for instance, if you can identify less than optimal judgment or motives among opponents.

In game theory and economic theory, zero-sum describes a situation in which a participant's gain or loss is exactly balanced by the losses or gains of the other participant(s)."

     Another goal of is to help you minimize the vigorish (the houses advantage in gambling, and investment costs in investing). Active investing (trying to beat a benchmark) is a zero-sum game. Trading is a zero-sum game, but market makers and arbitrageurs only participate in markets if they have a positive expectation, thus market making is a positive sum game.

     Investors face a choice - invest passively, or actively. Visitors to casinos also face a choice when they walk through a casino floor - get some chips and gamble, or keep walking. Choosing to fully diversify is the highest expected return/lowest risk option for investors and choosing to index an asset class (like the stock market) is effectively choosing not to play a negative sum game (negative because being less than fully diversified increases risk and has costs). Although there is another related discussion regarding investing risks (see discussions related to Fundamental Anomalies and Market Cap Effects).

The profits and losses of all players in a zero-sum game sum exactly to zero. The winners' profits are the losers' losses.
Lawrence Harris in The Winners and Losers of the Zero-Sum Game

     The creation of index funds and the subsequent evolution of ETFs have made passive, fully diversified investing available (at relatively low costs) to anyone with a brokerage account. Passive management in investing is similar to walking through a casino and never playing a penny. Both (1) passive investing and (2) walking through the casino and watching but not playing allow you to watch and smell the action, without lowering your expected payout and increasing your risk.

     In the July/August 1975 issue of Financial Analysts Journal, Charles Ellis published The Loser's Game (or here), which was followed by his classic book (Investment Policy: How to Win the Loser's Game). Ellis cited Simon Ramo's analysis of tennis, in which he argued that professional tennis is a winners game (where the winner tends to be the player that can hit winning shots), while amateur tennis tends to be a losers game (where the winner is the player that makes the fewest unforced errors or mistakes). Therefore in a loser's game the goal should be to keep the ball in play until your opponent makes a mistake, rather than trying to hit unreturnable winners. Ellis then compared tennis to investing (specifically active investors) and argues that investing has become a loser's game. Thus the logical goal for investors should be to use passive strategies, keep costs to a minimum, and avoid mistakes, rather than trying to beat the market. continues and elaborates on that discussion. Thanks to the wonderful features of the internet, it's never been easier to explain and link to the various explanations and guides (there are also plenty of free online games and tools available for those that want to test their skills and luck).

     Is buying a stock an investment, a speculation, or a gamble? A very strong argument can be made that buying a stock is part investment, part speculation. The percentage investment and percentage speculation is determined by the stock's correlation with the stock market itself. In other words, buying the entire stock market (Wilshire 5000) is investing because both theory and historical evidence confirm that returns over time are significantly above that of risk free bonds (aka the risk premium). But individual stocks over a given period have a wide variation of returns (with some multiplying and some going to zero). The correlation of the stock with the market is the investing part, while the deviation from the market return is the speculation part. This applies to any deviation from the full index of an investment category or asset class.

     These are not new arguments. There are many proofs and prior writings of these conclusions. For instance, this argument was nicely summarized by Professor Steven Thorley in The Inefficient Market Argument for Passive Investing or more recently by Richard Ferri in his Forbes article titled Active Investing is Uncompensated Risk. They follow among others William Sharpe's The Arithmetic of Active Management. See References and Martin Fridson's discussion and definitions in Exactly What Do You Mean By Speculation? (summarized at Investment, Speculation, and Gambling.)

The stock market may be somewhat of a casino, but is better than Las Vegas because the odds are in your favor. In addition to the stock marketís long-term uptrend, financial markets have become more efficient over the past 30 years as a result of more participation by institutions, greater influence from hedge funds, and the variety of new derivatives in use. Thanks to these factors, investors holding broadly diversified portfolios indexed to the market should earn returns equal or superior to those achieved by the experts. On the other hand, active management, especially of hedge funds, serves a useful purposeógetting new information into the market in a timely fashion. In addition, professional investment managers can offer valuable advice in specific circumstances. . . Although the stock market may be somewhat of a casino, itís a lot better than Atlantic City or Las Vegas because the odds are in your favoróthereís a long-term uptrend in the stock market. Do I buy some individual stocks? Yes, because itís fun. I also go to Las Vegas and Atlantic City. But as a trustee for family trusts, or a member of foundation investment committees, and in my own 403(b) account, I believe in indexing stocks, bonds, and real estate.
Burton G. Malkiel in Market Efficiency and Active Management

It is not easy to get rich in Las Vegas, at Churchill Downs, or at the local Merrill Lynch office.
Paul Samuelson

Games of chance must be distinguished from games in which skill makes a difference. The principles that work in roulette, dice, and slot machines are identical, but they explain only part of what is involved in poker, betting on the horses, and backgammon. With one group of games the outcome is determined by fate; with the other group, choice comes into play. The odds--the probability of winning--are all you need to know for betting in a game of chance, but you need far more information to predict who will win and who will lose when the outcome depends on skill as well as luck. There are cardplayers and racetrack bettors who are genuine professionals, but no one makes a successful profession out of Craps. Many observes consider the stock market itself little more than a gambling casino.
Peter Bernstein in Against the Gods

Wall Street investment banks are like Las Vegas casinos. They set the odds. The customer who plays zero-sum games against them may win from time to time but never systematically, and never so spectacularly that he bankrupts the casino. Yet John Paulson had been a Wall Street customer. . . The casino has misjudged, badly, the odds of it's own game, and at least one person noticed.
Michael Lewis in The Big Short: Inside the Doomsday Machine





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