I came across this fantastic article about maximizing a slight edge: “When Blackjack Meets Investing—A Look at the Power of a Small Edge.” This is relevant to trading because if you expect to have a huge advantage in the trading game, you are making a big mistake. Most of the time, we can only find small advantages that can be consistently exploited. This article clearly explains the importance of maximizing a slight advantage and encompasses many of the principles we believe in here at MMR.
By using card counting, a blackjack player can gain a 1.5% edge over the casino. Even though this may seem small, accumulating that edge over many hands and long periods can result in impressive outcomes. To get started, a player needs to learn the basic strategy, which still makes it a -EV game of -0.5%. If you can't play the basic strategy perfectly, you will lose all the edge you gained from learning how to count and the necessary deviations to play based on the true count of the game. Trading and investing are no different; learning the "basic strategy" of the markets is the essential foundation needed so that you can recognize when you have a strategy that has an edge and can define the strategy’s edge.
However, having an edge, no matter how small, is not enough. Both markets and Blackjack are subject to high variance, and return predictability is nearly impossible. To realize your edge, you need more than just an advantage-you need confidence in your system, proper risk management, and a large enough sample size to weather the ups and downs of the market. In their article, they simulated a game of Blackjack played by one card counter with a 2% edge.
“We will pretend to sit down at the blackjack table, simulate multiple hands given a small implied edge of 2% in our favor, and analyze the overall results from a capital return and risk perspective. Assuming we have a starting base capital account of $1,000 and bet on average $50 per hand, let’s take a look at our potential gains and losses after 100, 500, 1,000, and 5,000 hands of blackjack. Figures 1-a through 1-d show the results of these simulated blackjack hands and their effect on our overall account.”
Figure 1: Profit & Loss Curves from Blackjack Simulation
Figure 1-a: 100 Hands
Figure 1-b: 500 Hands
Figure 1-c: 1,000 Hands
Figure 1-d: 5,000 Hands
Figure 2: Return & Risk Metrics from Blackjack Simulation (5,000 hands)
Despite consistently having an advantage, the player experienced some significant losing streaks. On average, there would be a 20% swing in the bankroll for every 100 hands played. There would be periods of 200 hours where the player faced losses and bad beats, despite always having the edge over the casino. To overcome this variance in the single player's advantage, a solution was devised. The solution involved betting on multiple players ($200 per play instead of $1000 on one player) across various games. This "team play" strategy reduces risks and helps the card counters reach their long-term expectancy with less hours of play.
“To analyze this concept further, we will re-run the 5,000 simulations for each of five individual players, and then compare their performance to our overall performance (which is the investment of $200 we make in each of the five players, totaling $1,000). By taking this approach, we can explore the outcomes associated with deploying multiple players across multiple games.”
Figure 3: Blackjack Simulation (5,000 Hands) for Five Players & Team Account
Figure 4: Return & Risk Metrics from Blackjack Simulation (Five Players & Team Account)
Please take note that the volatility has decreased to 7%, and the maximum drawdown has been reduced from 74% to 15%. Most importantly, the risk-adjusted return has improved by 70%, increasing from 1.37 to 1.63, due to diversification across players and games.
Although Blackjack is a closed system, I believe it is closely related to understanding the importance of diversifying one's edge. Searching for small uncorrelated advantages, employing proper risk management, minimizing execution errors, and perfecting basic strategy is necessary to achieve superior results in trading and investing not just Blackjack.