Predicting the Effectiveness of Chess Openings

Matthew Riordan
West Virginia University
First Published Online: April 20, 2026
AgEcon Search: https://ageconsearch.umn.edu/record/400136?ln=en&v=pdf

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Abstract

Introduction

Austrian chess master Rudolf Spielmann once famously said, "In the opening a master should play like a book, in the middlegame like a magician, in the ending like a machine."^[1]The opening of a chess game is typically limited to the first few moves, yet it often determines the style, development, and positional advantages of the entire game. Many games are won or lost within the first few moves, even when the players do not yet know it. For example, if a positionally strong player goes into a dynamic opening against a tactically strong opponent, it will likely end poorly for the positional player. Essentially, if a player enters an opening that plays to their strengths, they are much more likely to achieve a positive result. With the emergence of chess computers, top-level players have expanded chess theory, the common and best moves in openings, to the point where each grandmaster knows the best move and the critical ideas in the most popular openings. Due to this trend, many top-level players have used surprising, non-theoretical moves early in games to throw their opponents off their preparation and into unknown territory.

In this study, I examine the opening characteristics that predict whether a player will perform above their expected rating. I hypothesize that color will be the most significant predictor of opening effectiveness, and more popular and complex openings with higher win percentages will be associated with higher-than-expected performance. Players who choose to learn an opening that suits their playing style and strengths get an immediate and effective weapon for the rest of their chess career. With more experience, they will become increasingly familiar with the opening and the typical positions that arise from it. Increased familiarity contributes to the effectiveness of the player's opening. However, choosing the wrong opening can be costly. Players might spend hours studying lines that lead to game after game in which they are at a disadvantage. After going a while without improvement with a new opening, players might give up or try a different one. Both outcomes mean a player has wasted their time on something that is not useful to them. This paper aims to help players select effective openings by identifying which opening characteristics predict performance above the expected level. I measure the effectiveness of a given opening by calculating the difference between the average player rating and the average performance rating when employing that opening.

Recently, Marzo et al. (2023) used online chess data to construct large-scale networks to analyze similarities and differences among all chess openings. These networks could be very helpful for experienced players by identifying which openings are similar to those they already know. However, this is impractical for players with no experience in studying opening theory when choosing an opening. A further limitation is that their data came from online blitz games, where openings may have been played only sporadically by lower-rated players, leading to spurious connections where none exist. In this study, my objective is to provide more concrete solutions to the problems many players face when deciding which opening to learn. In addition, many young scholastic players often face similar problems in choosing openings. Many children learn to play chess in school, and it would be prudent for these new players to learn widely used openings in top-level chess.

In this study, I use three different regression techniques to predict the effectiveness of an opening: ordinary least squares (OLS), elastic net (ENET), and random forest regression. Using the two linear models, I find which specific openings are the best for each color in chess. This study makes three specific contributions to the existing literature. First, while prior work has focused on player behavior, decision-making, and network analysis, no study has examined which specific opening characteristics systematically predict above-expected performance, measured here as the difference between an opening's average performance rating and the average rating of players using that opening. Second, this study provides directly actionable recommendations for players by ranking openings based on their predicted effectiveness. Third, this study has implications that extend beyond chess. A farmer selects his crop variety based on observable characteristics rather than planting crops randomly. With this study, a chess player can use these findings to make informed decisions about which openings to learn. The cost of investing time in learning an ineffective opening is not just losing games, but also the time, energy, and sometimes money spent learning it. These resources could have been spent more productively on learning a more effective opening. At competitive levels of chess, marginal advantages often determine game outcomes, so selecting an opening that consistently outperforms expectations based on observable characteristics and data can provide a significant edge in a resource-constrained environment. Another important finding of this study is that risky openings that heavily rely on the other player making mistakes are ineffective. This has implications for trading strategies in the stock and commodity markets, suggesting that riskier strategies are typically less effective than strategies that deliver strong, reliable returns.

The next section reviews the literature in economics, sociology, and international studies that has used chess data to address a variety of research questions, and it motivates the need to examine the effectiveness of openings. Then, I describe the dataset construction and cleaning process, followed by the methods used to build and evaluate the three models. Next, I present and discuss the results of the three different modeling approaches and evaluations. The article concludes with a synthesis of findings and directions for future work.

Literature Review

In 1913, Ernst Zermelo first proposed his theorem, which states that "in chess, either white can force a win, or black can force a win, or both can force a draw" (Schwalbe & Walker, 2001). Many consider this to be the first formal proof in game theory, even though mathematicians would have considered it to be in set theory at the time. Economists today apply Zermelo's theorem more broadly than just the game of chess. As Schwalbe and Walker (2001) note, "the work of Zermelo, Konig, and Kalmar shows that these mathematicians were dealing with what we would now call two-person zero-sum games with perfect information." In these zero-sum games, Zermelo's theorem implies that once a player reaches a winning position, they can win with perfect play. There are many important economic applications of Zermelo's theorem. For example, two competing firms set their product prices, anticipating that their competitor's pricing will capture more market share.

In the mid-to-late twentieth century, chess increasingly became a research tool to advance computer science and artificial intelligence. In 1948, Alan Turing outlined a potential "paper machine" that would be able to exercise thought efficiently in translating languages, performing mathematical calculations, solving cryptographic problems, and playing games, such as chess (Turing, 1948). In the following decades, chess engines became much more capable and expansive. Famously, in 1997, the IBM computer Deep Blue defeated world chess champion Garry Kasparov in a six-game match with two wins, three draws, and one loss, signaling the beginning of AI domination in chess (Silver et al., 2018). Recently, the best human chess players have been unable to win a single game against top chess engines equipped with vast opening databases, neural networks, and reinforcement learning techniques.

In recent years, as online chess has gained increasing popularity, partly due to popular streamers and the Netflix show The Queen's Gambit, large amounts of data have been collected from these games. The COVID-19 pandemic also contributed to the resurgence of chess, bringing new players from non-traditional demographics into the game. Data from these games have been used in fields such as economics, sociology, and international studies. For example, Bilen et al. (2024) used recent data from Chess.com to compare how people interact with others from nations hostile to their own. They examined players from regions experiencing ongoing international conflicts, including Ukraine, Russia, Armenia, and Azerbaijan. There was a decrease in games played against the opposing nation after the start date, likely because people refused to play against those from hostile nations. In games between players from hostile nations, Bilen et al. (2024) found statistically significant differences in performance against hostile opponents. One finding was that people often adjust their play, particularly in the opening, to be safer and more persistent against those from hostile nations. That is, players are less likely to resign or abandon the game when playing someone from a hostile nation. Bilen et al. (2024) also found that more mistakes and blunders are made in games when opponents are from hostile countries. They noted that more mistakes were made by people from nations widely seen as aggressors in the conflict, namely, Russia and Azerbaijan. Gerdes and Gränsmark (2010) examined how people change their play styles by gender. Interestingly, they found that both men and women play more aggressively and take more risks when their opponent is a woman. The authors attribute the pattern to either male overconfidence or gender stereotypes, which would also explain its appearance among female players. The study also found that women are generally more risk-averse than men. Gerdes and Gränsmark (2010) also emphasized that their results were in line with previous studies on differences in psychological traits between men and women.

A recent economics study using chess data by Agarwal et al. (2022) examined decision-making in complex situations. To ensure that each position in the study was measurably complex, the authors focused on endgames with up to six pieces on the board, since chess has been solved by computers with six or fewer pieces. In the first part of the empirical analysis, Agarwal et al. (2022) examined how well experienced chess players could evaluate a move in an endgame as a win, loss, or draw. They found that evaluation success depended on the complexity of the position. Next, Agarwal et al. (2022) used endgame data from LiChess spanning 2013 to 2020 to test a "satisficing-with-evaluation-errors model". They found that players choose lower complexity most often for winning moves, whereas in a losing position, they tend to complicate the game more often. Then, the authors investigated whether players choose the objectively best move (maximization) or a satisfactory, simpler one (satisficing) when multiple winning options are available. They found that as the complexity of the best move increases, players tend to favor other winning moves—evidence against maximization and in favor of satisficing, with over 80% of individuals showing statistically significant departures from maximizing behavior. The last analysis by Agarwal et al. (2022) found that players spend more time analyzing complex positions and, when a losing move is played instead of a winning one, they usually take less time. Cero et al. (2019) used opening gambits to test the generalized matching law in behavioral analysis. They found that chess data supported the generalized matching law. Another study using chess data was by Bertoni et al., which examined the relationship between age and mental productivity. Critically, they account for the fact that many chess players stop playing when they are not good enough by using a repopulated sample. The study found that productivity peaks in early adulthood and then declines steadily with age. Linnemer and Visser (2016) examined amateur participation in the World Open, focusing on factors such as player experience level and prize money. They found that players near the top of their rating section are overrepresented, and those near the bottom are underrepresented. The authors also found that these patterns become more pronounced as the prize fund increases.

Data

Figure 1. The positions reached in the top eight most common openings Figure 2. Histogram of Number of Games Played per Opening Figure 3. Difference Between Performance Rating and Average Rating Plotted Against Win Rate for an Opening

I used an opening dataset available from Chess Tempo^[2], which contains performance data on more than 2000 opening variants, though this number was reduced during data cleaning. I combined it with an open-source dataset from LiChess^[3] that contains the names and moves of every documented chess opening. The columns from Chess Tempo provided information on several aspects of the opening, from the color it is played by to the frequency with which each opening was used in the sample of games. Using these columns, I was able to draw inferences about opening characteristics and their association with player performance. The dataset was constructed using games from various online game databases. The dataset comprises more than 2,000 opening variations that high-level players in this database have played more than 100 times. These conditions helped ensure that the openings were both common and well-played. A well-played opening is crucial if one is to consider it a contributing factor in the game's outcome. Furthermore, using only common openings is important to avoid outliers with a minimal number of games played from skewing the data.

As shown in Figure 2, the distribution of the number of games played per opening is very skewed. The mean number of games played per opening in the dataset is 2,805, with a standard deviation of 4,757 and a median of 1,026. The lower quartile bound is 369, and the upper quartile bound is 3,152 games. Figure 1 shows the eight most common chess openings in the database. Many of them lead to vastly different positions, despite having similar moves. The plots were generated in Python using information about moves from the Lichess dataset and the Python chess library.

Another critical variable in the dataset was the difference between the average performance rating with an opening and the average player rating with that opening. In chess, a player's strength is measured by an Elo rating, and the performance rating of an opening over many games can be calculated using the Elo formula. The formula is:

Performance = (∑_i=1n  Elo_{oppenent i}  +  400 results_i) / n  

where n is the number of games played for a given opening, and the result is a {1, 0, −1} for a win, draw, or loss. Elo_oppenenti represents the ith opponent's Elo rating.

One would expect a player to typically get a performance rating equal to their Elo. So, if an opening consistently gets players to perform above their Elo, it would be an effective opening. In Figure 3, I plotted effectiveness against win percentage for each opening and overlaid the opening color. In this graph, there is a clear positive relationship between the win percentage and the difference between the performance rating and the average player rating when white plays the opening. However, when an opening is played with the black pieces, there appears to be a negative relationship between the two variables.

In the next section, I used these relationships to create a linear model with the difference between the average performance rating and the player rating as the dependent variable. The predictive variables were the win rate and draw rate of an opening, the color with which it is played, the popularity of the variation, and the number of theory or book moves in the opening. The number of moves of theory is a sign of how complex the opening is, and the draw rate can signal how stale or boring an opening is. The popularity of the variation was measured by dividing the number of games that use that variation by the number of games that use that general opening group. Using this model, I can assess which factors make an opening effective and then predict which openings will be most successful. Then I attempt to determine whether the model's effectiveness differs when using only popular opening variations.

Methods

I used several linear and nonlinear regression models to analyze and predict the effectiveness of chess openings. I chose to use ordinary least squares (OLS), elastic net regression, and a random forest regressor. The first step in making these models was to choose the predictors. As stated earlier, the win percentage, the draw rate, the number of theoretical moves, the popularity of an opening variation relative to related variants, and the color by which the opening is played are the predictors. The predictors were then scaled and standardized. Because of this standardization, the coefficient values in the data will be comparable, allowing me to identify which predictors are most and least important.

To merge the two datasets, several methods were employed to match openings by name. The merging of the datasets was critical to obtain a variable for the complexity of an opening in the regressions. To merge them, I first removed all punctuation, capitalization, and unusual characters from the names in each dataset, then merged the data by the opening names. However, because many openings have multiple name variants, only slightly more than half were initially matched. The first method used was fuzzy matching. If the highest fuzzy matching score exceeded 90, the opening would be assigned to its corresponding PGN. Fuzzy matching compares two strings and scores their similarity based on patterns, partial matches, and edits, rather than requiring exact identity. It uses algorithms that account for spelling differences, missing characters, and word rearrangements to identify the closest match. After using fuzzy matching, many openings still lacked a sufficient match. Because of that, I decided to use only the Levenshtein distance to get the final matches. The Levenshtein distance measures the minimum number of single-character edits needed to transform one string into another. Using a threshold where less than 10% of characters in a string required changing, the vast majority of the remaining openings were matched to their opening moves. After that, 1,222 openings were successfully matched. The matches were manually verified after Levenshtein and fuzzy matching.

Before modeling, the variables were scaled to have a mean of 0 and a standard deviation of 1, following a standard normal distribution. This is done using the simple z-score formula of z=x-μσ for each variable. After scaling the variables, the different regression fits were applied to the training set. Although color is a binary variable with a heavy skew, scaling is appropriate if the proportion p-hat is between 0.3 ≤ p-hat ≤ 0.7 (Gelman, 2008). Then, I used that model on the testing set. Both linear models produced similar results on both the training and testing sets.

Table 1. Descriptive Statistics
Statistic	Effectiveness	Color	Win_Pct	Popularity	Complexity	Draw_Pct
Count	1222.00	1222.00	1222.00	1222.00	1222.00	1222.00
Mean	-0.38	0.67	0.41	0.03	9.29	0.26
Std Dev	37.97	0.47	0.07	0.09	4.39	0.08
Min	-122.01	0.00	0.18	0.00	2.00	0.06
Q1	-29.80	0.00	0.37	0.00	6.00	0.21
Median	-0.18	1.00	0.41	0.01	9.00	0.25
Q3	29.10	1.00	0.45	0.03	12.00	0.30
Max	149.69	1.00	0.75	1.00	27.00	0.66

 

The aim is to fit the following linear regression equation for the ordinary least squares model:

Effectiveness_i = β₀ + β₁winpct_i + β₂complexity_i + β₃color_i + β₄popularity_i + β₅drawpct_i + ϵ_i.

In this equation, each β represents the coefficient for each predictor, and each i represents an opening. The variable εi represents the random error of the model. Because all the variables have approximately the same mean and standard deviation after scaling, the coefficients indicate which variables are most important for the model's predictions.

The OLS regression aims to minimize the following loss:

Lβ = ∑_i=1ⁿ (y_i - ŷ_i)²

where yᵢ is the true value of effectiveness for an opening and ŷᵢ is the predicted value of effectiveness for the opening. The estimated coefficients β̂ are found by minimizing this loss function.

Elastic net regression differs from OLS in that it penalizes the coefficients to yield a parsimonious model. There are two penalties in elastic net loss, L1 and L2, that differentiate it from OLS loss. The penalties are added to prevent overfitting, to shrink coefficients for feature selection, and to handle multicollinearity. The L1 penalty is based on the absolute values of the model's coefficients. This is the penalty that handles feature selection. The L2 penalty squares the coefficient values to induce a penalty. The equation for the elastic net loss vector is the following:

Lβ = ∑_i=1ⁿ (y_i - ŷ_i)²+ λ [α ∑_j=1^p |β_j| + (1 - α) ∑_j=1^p β_j²]

Then, to get the predictions, ŷ is calculated by ŷ=Xβ̂ where X is the matrix of predictor variables, including the intercept, β̂  is the vector of adjusted coefficients, and ŷ is the vector of model predictions.

The last modeling approach I used was random forest regression. Random forest regression employs a complex network of decision trees trained on randomly selected subsets of the data, each making independent predictions. Once each tree has made its prediction, the final prediction is obtained by averaging all the predictions. Due to its predictive power, random forest regression excels at identifying nonlinear patterns in data. However, random forest regression is best suited to larger datasets than the one used.

To assess the predictive ability of the models, I split the data into training and test sets. The training set contained 90% of the data, while the testing set contained 10%. The split was done pseudo-randomly with a fixed seed. Splitting data into training and test sets is crucial to combat overfitting. After that, I used the model on the testing set. As discussed in the next section, the test set results were very similar to those of the training set. Then, permutation tests were performed on each model's test set to determine whether the data points came from the same distribution or different distributions. If the models are statistically significant, then they perform measurably better than random choice. The final test of model viability was to bootstrap 95% confidence intervals for the coefficients of both linear models. For this, no train/test split was performed. Rather, the coefficients were obtained from bootstrapped samples of size n = 1,222, run 1,000 times. This method is robust for both the unbiased OLS model and the biased elastic net model.

Results and Discussion

Figure 4: Value of Average Coefficients in the OLS Model Figure 5: Value of Average Coefficients in the Elastic Net Model

The results from the two linear models, OLS and elastic net, were remarkably similar. As shown in Table 2, the R² values are very similar for both the training and test sets. These metrics indicate that the two models were nearly equally successful, suggesting that the L1 and L2 penalizations did not improve predictive performance. This is further evidenced by the model coefficients shown in Figures 4 and 5. Although all OLS coefficients are slightly larger, penalization has barely affected the coefficient values and, therefore, the model. Even though the coefficients for the number of moves of theory (complexity) and the popularity of a variation are very close to 0, they are approximately just as close in both linear models. Furthermore, they have the same statistically significant and nonsignificant predictors, as indicated by the 95% bootstrapped confidence intervals. The penalties likely did not affect the elastic net model because the regularization strength, λ, is moderately close to 0, with λ = 0.0618 found by cross-validation. This indicates little multicollinearity among the predictors, as evidenced by the lack of coefficient shrinkage. This was also verified by VIF values ranging from 1.1 to 7.1, all below the conventional threshold of 10, suggesting no problematic multicollinearity among the predictors. Figure 6 shows the residual plots for both linear models on the training and testing sets. Both models show a clear two-cluster structure in the residuals, representing white and black openings, respectively, reflecting the inherent advantage of moving first. Within each cluster, the residuals appear to be randomly scattered around zero, suggesting that the linearity and homoskedasticity assumptions are approximately satisfied.

The coefficients of both models indicate an advantage for the white player, with the opening color being the most important predictor. The model coefficients suggest that complex and popular openings played by white are typically the most effective. This can be observed in professional chess, where players have been delving deeper into obscure, complicated lines more frequently to draw their opponents into unfamiliar territory and beat them there.

 

Table 2. Model Performance Summary
Model	Avg Train R²	Avg Test R²	Avg Perm. p-value	Prop. Sig. (p<.05)
RFR	0.915	0.402	0.0000	1.00
OLS	0.248	0.238	0.0000	1.00
ENET	0.247	0.238	0.0000	1.00

 

Table 3. 95% Bootstrap Confidence Intervals — OLS vs. Elastic Net
Feature	OLS CI Low	OLS CI High	ENET CI Low	ENET CI High
color	18.0834	19.1050	17.3123	18.6533
win_pct	0.8894	2.6947	0.8687	2.5991
popularity	0.2804	1.5135	0.1866	1.4036
complexity	0.2528	1.7163	0.2840	1.6189
draw_pct	-0.8660	0.7592	-0.8265	0.5505

 

Figure 6: Residuals of the linear regressors for the final training and testing split Figure 7: Residuals of the random forest regressor for the final training and testing split

The random forest model is very different from the other linear models. As seen in Table 2, the random forest model performed very well on its training set. The R² of the random forest testing set is higher than that of both linear models. However, the random forest regressor showed overfitting, with a large gap between its training R² (0.915) and test R² (0.402). The R² for the testing set is significantly lower than for the training set. The overfitting is likely due to insufficient data (n = 1,222). Random forest regression performs best with large datasets, which this dataset is not. The linear models were still worse at prediction than the random forest regressor, but the differences in predictive capacity were not as extreme as for the training data. Figure 7 shows that there is greater variation in the residuals of the test set, as expected, and that the random forest model has a significantly lower R² value. Furthermore, there is clear heteroskedasticity in the training residuals, but none in the test set. In the training set, as the actual effectiveness increases, the average error decreases.

According to both linear models, the best opening variation is the famous Fried Liver variation of the Italian Game. The best general opening category for white, according to the models, is the Englund Gambit, which is considered a poor choice for black. For the black pieces, the models deem the Neo-Grünfeld Defense, Goglidze Attack to be the best. This variation has a high win rate, is popular, and is fairly complex, so it makes sense that the model rated it very effective. The models' suggestions show the advantage white has in the opening of a chess game. In both models, white plays eight of the ten openings with the highest predicted effectiveness.

The Englund Gambit is an opening that black chooses to enter. However, there are certain variations that white plays into. These are the variations counted here for the best white opening. These variations are counted in the general opening category data for white. The Englund Gambit is widely regarded as an unsound and very risky opening for Black. However, this risk is different in nature from the calculated risks masters take when preparing their openings. Rather, it is known to rely primarily on tricks and traps to lure the white player into. Most gambits aim to gain a specific strategic or tactical advantage at the cost of a pawn, rather than hoping white will play a bad move. The Englund Gambit's high effectiveness for white shows that taking unnecessary risks in the hope of a rare payoff is not a good strategy, which is applicable to trading strategies.

Conclusions

In this study, I examined the characteristics that make an opening effective using ordinary least squares, elastic net regression, and random forest regression, and found that color is the most important characteristic in linear models. The results also show that popularity, complexity, and win rate are significant predictors of an opening's effectiveness. The models suggest that the Fried Liver Attack and variations of the Englund Gambit are the best openings to play as white. The Englund Gambit is a gambit played by the black pieces, yet the variations white can play into are modeled to be the most effective. Despite strong training performance, the random forest regressor underperformed on the test set. In the future, this could be remedied through hyperparameter tuning by reducing the number of trees, the maximum tree depth, or the minimum number of samples per leaf node. The random forest model also showed heteroskedasticity in its training-set residual plot, a pattern not observed in the test set. Both linear models, the ordinary least squares and the elastic net, performed very similarly on both the training and testing sets. They also had two clear groups in their residual plots. The groups represent the color of the opening, white or black, and indicate the advantage that the white player enjoys in chess. The L1 and L2 penalties had minimal impact on the results, with little difference between OLS and the elastic net model. The lack of difference between the two models is likely due to the low regularization strength and the absence of multicollinearity.

One limitation in the analysis is that it was conducted at the opening level. Move-level data would allow for more inferences and predictions about chess openings. Without move-level data, it is challenging to select many features. Furthermore, game-level data could allow for the interpretation of common opening mistakes and the kinds of mistakes they lead to in the middlegame and the endgame. It would also allow inferences about game theory and how players prepare for specific opponents. For example, looking at how players counter known aggressive players could be very useful for players at all levels. Another limitation of this project is the limited feature set in the models, particularly the elastic net model. Elastic Net is effective at selecting which features are most and least important for prediction. Therefore, when a model has a limited number of features, elastic net regularization provides little advantage over OLS. The small R² values of approximately 0.25 indicate that a substantial portion of the variance in an opening's effectiveness remains unexplained. Some omitted variables, such as time controls, the rating range of the player pool, and a better measure of complexity, likely could account for some of the unexplained variance. All of these may systematically affect performance with a given opening and represent avenues for future work.

Another limitation of the analysis is endogeneity among an opening's win rate, draw rate, and effectiveness. My analysis does not allow me to make claims that the win rate causally increases effectiveness. However, if interpreted as a descriptive model, the multivariate associations between different opening features and effectiveness can be characterized. The remaining three predictors, color, popularity, and complexity, do not share this mechanical relationship with the outcome and are therefore more amenable to causal interpretation, provided that unmeasured confounders are absent. An additional limitation is survivorship bias. Because only openings played more than 100 times by high-level players are included, openings that were tried and abandoned due to poor performance are excluded, which likely truncates the left tail of the effectiveness distribution and may overstate the average effectiveness of included openings.

The first and most obvious implications of this work are chess-related. Players can take the findings into account for their preparation by knowing which openings to use and which to avoid. An edge in the opening can be crucial in games between high-level players, and this paper could give that edge to someone. It could also aid chess coaches by offering ideas for teaching children new to chess openings. However, this work has implications that go beyond chess. As mentioned above, farmers use observable crop characteristics to decide what crop varieties to plant. Similarly, policymakers could evaluate a given bill by examining the observable characteristics of similar laws in other areas to predict its effects in their district, state, or nation. Furthermore, the Englund Gambit, being so highly rated for white, shows that highly risky openings are not effective. This is analogous to strategies across many fields, where safer approaches often yield more consistent and effective results over time. In particular, in a highly leveraged commodities market, tried-and-tested strategies tend to outperform speculative bets over time.

In the future, there is still work to be done on chess openings. I believe that more inferences can be drawn from opening analysis to inform learning by new and experienced players alike. Additional analysis could examine how chess opening selection affects players' decision-making in the later stages of the game. For instance, one could examine whether players who play the Queen's Gambit make safer, more satisfactory moves than those who play the Sicilian Defense. Analyzing decision-making at the opening of chess games could provide valuable insights into the behavioral aspects of the game of chess.

References

Bertoni, M., Brunello, G., & Rocco, L. (2015). Selection and the age–productivity profile: Evidence from chess players. Journal of Economic Behavior and Organization. https://doi.org/10.1016/j.jebo.2014.11.011

Bilen, E., Doghonadze, N., Khubulashvili, R., & Smerdon, D. (2024). Nationalism in online games during war. SSRN Working Paper. https://doi.org/10.2139/ssrn.4833809

Campbell, M., Hoane, A. J., & Hsu, F. (2002). Deep Blue. Artificial Intelligence, 134(1), 57–83. https://doi.org/10.1016/S0004-3702(01)00129-1

Carow, J., & Witzig, N. M. (2024). Time pressure and strategic risk-taking in professional chess (Gutenberg School of Management Discussion Paper Series). https://doi.org/10.1016/j.jebo.2025.107218

Cero, I., & Falligant, J. (2019). Application of the generalized matching law to chess openings: A gambit analysis. Journal of Applied Behavioral Analysis. 10.1002/jaba.612

Collins, C., & Le Mercier, A. (2024). Chess openings [Data set]. Kaggle. https://doi.org/10.34740/KAGGLE/DSV/8075830

de Marzo, G., & Servedio, V. D. P. (2023). Quantifying the complexity and similarity of chess openings using online chess community data. Scientific Reports. https://doi.org/10.1038/s41598-023-31658-w

Fiekas, N. (2024). python-chess: A chess library for Python. https://python-chess.readthedocs.io/en/latest/

Gelman, A. (2008). Scaling regression inputs by dividing by two standard deviations. Statistics in Medicine, 27(15), 2865–2873. https://doi.org/10.1002/sim.3107

Gerdes, C., & Gränsmark, P. (2010). Strategic behavior across gender: A comparison of female and male expert chess players. Labour Economics. https://doi.org/10.1016/j.labeco.2010.04.013

Glickman, M. (1995). A comprehensive guide to chess openings. American Chess Journal.

Linnemer, L., & Visser, M. (2016). Self-selection in tournaments: The case of chess players. Journal of Economic Behavior and Organization. https://doi.org/10.1016/j.jebo.2016.03.007

Miric, M., Lu, J., & Teodoridis, F. (2020). Decision-making skills in an AI world: Lessons from online chess. SSRN. https://doi.org/10.2139/ssrn.3538840

Salant, Y., & Spenkuch, J. L. (2025). Complexity and satisficing: Theory with evidence from chess. Review of Economic Studies. https://doi.org/10.1093/restud/rdaf041

Schwalbe, U., & Walker, P. (2001). Zermelo and the early history of game theory. Games and Economic Behavior, 34(1), 123–137. https://doi.org/10.1006/game.2000.0794

Silver, D., Hubert, T., Schrittwieser, J., Antonoglou, I., Lai, M., Guez, A., Lanctot, M., Sifre, L., Kumaran, D., Graepel, T., Lillicrap, T., Simonyan, K., & Hassabis, D. (2018). A general reinforcement learning algorithm that masters chess, shogi, and Go through self-play. Science, 362(6419), 1140–1144. https://doi.org/10.1126/science.aar6404

Turk, J. (2024). Jellyfish: A Python library for approximate and phonetic matching of strings (Version 1.2.1). https://pypi.org/project/jellyfish/

Turing, A. (2004). Intelligent machinery. In B. J. Copeland (Ed.), The essential Turing (pp. 395–432). Oxford University Press

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^[1] Rudolf Spielmann: The Last of the Romantic Era, www.chess.com/blog/Bogo-IndianaJones/rudolf-spielmann-the-last-of-the-romantic-era

^[2] ChessTempo (2025) chesstempo.com/game-database/chess-openings/

^[3] LiChess Community (2025) github.com/lichess-org/chess-openings