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Investing is a Solved Game

Updated: Sep 9, 2023

Chess is one of the oldest and most popular board games in the world, with a rich history that spans more than a thousand years. Today, chess is played by millions of people worldwide and is recognized as a game of skill and strategy that requires mental discipline, creativity, and perseverance.


I enjoy playing chess and was the captain of my school’s second team.


A monumental event occurred in 1997. A chess program “Deep Blue”, capable of analyzing 200 million positions a second, beat the reigning world champion Garry Kasparov 2-1 over a series of 6 games, in a rematch. Since then, chess programs have become much stronger than human players and the current best software named “Stockfish” can analyze billions of moves a second. However, the number of possible chess games is estimated to be at least 10^120 so the game remains “unsolved” and continues to evolve and adapt, with new variants and variations constantly being developed and explored.


For many people, investing is often seen as a risky, complicated and unpredictable endeavor. While investing can be challenging, it is by no means a game without rules. However, unlike chess, investing can be considered a “solved game”.


Let’s explore why investing is a solved game and what it means for investors.


Firstly, it is important to understand what is meant by a "solved game." A solved game is a game in which the optimal strategy has been determined and any deviation from that strategy will result in suboptimal outcomes. In other words, a solved game is one where there is a clear path to success, and any attempt to deviate from that path is likely to result in failure.


Secondly, there are numerous academic studies, backed up with logical proofs and supported by empirical evidence that show the optimal strategy of investing. Harry Markovitz introduced the “Modern Portfolio Theory” in a 1952 essay in which he was later awarded a Nobel prize. William Sharpe showed logically that low cost index funds provide higher returns than active funds over the long term which is also consistently backed up by empirical evidence from SPIVA (S&P Indices versus Active).


Thirdly, there is also a clear set of principles and strategies that have been shown to be replicable and repeatable by investors that consistently produce superior results. For example, the “buy and hold” strategy involves investing in a diversified portfolio of low-cost index funds and holding them for the long term. This strategy has been shown to produce solid returns over time and is recommended by many financial experts


Finally, we have a well defined framework that anyone can use to duplicate the same optimal investing success for themselves. Vanguard provides a fantastic framework based on four simple principles (free pdf download):

  1. Define clear goals

  2. Invest with balance and diversification

  3. Minimize cost

  4. Stay disciplined over the long term

On a similar theme, the Bogleheads Investment Philosophy provides people with clear steps to be successful as investors:


Prepare to invest

  • Live below your means

  • Develop a workable plan

  • Never bear too much or too little risk

  • Invest early and often

Create a portfolio

  • Diversify

  • Invest with simplicity

  • Use index funds when possible

  • Minimize costs

  • Minimize taxes

Maintain discipline

  • Never try to time the market

  • Stay the course

From all of this, we can see that investing is actually a very simple endeavor, even for the average person without a degree in finance. Research, knowledge, and experience has shown us the exact path to achieve our financial goals. Fear can be eliminated and no luck is required.


Happy investing everyone.

a screenshot of "Deep Blue" beating Gary Kasparov. Unlike chess, learning how to invest is easy.
Unlike chess, learning how to invest is easy.


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