1. Madhura Gajendragadkar Tianqi Wang
White versus Black
Madhura Gajendragadkar
Tianqi Wang

2. Hypothesis In this project, we focus on the following questions:
Does White play better than Black in most games?
Does the first move advantage affect subsequent moves?
Does Elo rating affect the first move advantage?

3. Does White play better than Black?
Weaver Adams and Vsevolod Rauzer claimed that White is winning after the first move 1.e4, while Hans Berliner argued that 1.d4 may win for White
 Grandmaster (GM) András Adorján wrote a book series: "Black is OK!", arguing that the general perception that White has an advantage is founded more in psychology than reality
Jonathan Rowson wrote that “the conventional wisdom is that White begins the game with a small advantage and, holding all other factors constant, scores approximately 56% to Black's 44%”

4. The first move advantage
The first-move advantage in chess is the advantage of the player (White) who makes the first move in chess.
There are differing opinions on whether the advantage actually leads to a win or has no significant impact on the outcome.
This is what we explore in this project.

5. Related studies
‘Do Initial Strategies or Choice of Piece Color Lead to Advantages in Chess Games?’ by Sameer Ponnaluri and Mary J King investigates popular opening moves like King’s Pawn, King’s Indian Attack, Queens Gambit, and English.
They concluded that opening and defense strategies affect the outcome.
‘Move-by-Move Dynamics of the Advantage in Chess Matches Reveals Population- Level Learning of the Game’ by Ribeiro et. al. studies chess matches spanning 150 years.
They conclude that the average advantage of White is 0.17 pawns and is exponentially increasing due to the increasing abilities of chess players over the years.

6. Bias in the dataset
White has an advantage bias in the current dataset we are using
However, we are not studying the outcome, but rather the effectiveness of each move made by both players
We consider the ASD and IPR values rather the win, loss, or draw scenario
This also takes into account the level of play which may or may not be at expected level according to the Elo rating of the player (off days, careless mistakes, errors in judgement)

7. What is elo rating?
The Elo rating system is a method for calculating the relative skill levels of players in zero-sum games like chess.
A player's Elo rating is represented by a number which increases or decreases depending on the outcome of games between rated players.
Our dataset contains Elo ratings from 1025 to 2800 which we have analyzed over an interval of 25 points

8. What is asd? ASD stands for the Average Scaled Difference
This is the difference between the evaluation of the top move that the engine predicts and the actual move made by the player
It is averaged over all the moves in the game

9. What is ipr? IPR stands for Intrinsic Performance Rating
We chose to use IPR because it analyzes individual moves rather than the outcome of the game
It is a metric that measures accuracy

10. IPR and asd comparison
We conducted a small experiment where we compared the ASD and IPR values for players of all Elo ratings
The results are represented as line graphs and scatter plots that depict:
X-axis: Elo ratings
Y-axis: ASD/IPR values for white and black

11. Scatter plot: asd comparison

12. ASD Mean difference Source SS df MS F Prob>F
Groups
Error
Total

13. Observations for asd
The ASD decreases exponentially with increase in Elo rating
This says that players at a higher level make moves closer to the engine’s best move predicitons
There are no significant differences between White and Black in terms of the ASD

14. zASD comparison

15. Observations for zASD We observed the following:
The zASD for White was significantly greater than that for Black between the 1600 to range of Elo ratings
It was also greater for a few observations around the 2500 Elo rating
For other ratings, the zASD values are interspersed with no marked difference for White or Black

16. Zasd Q-Q PLOT

17. Zasd white

18. Zasd black

19. Scatter plot: ipr compariosn

20. Ipr mean difference Source SS df MS F Prob>F
Groups
Error
Total

21. Observations We observed the following:
The IPR exponentially increases with increase in Elo rating
The values are extremely close for White and Black and show no significant difference for any particular Elo rating

22. conclusion
White or Black has no significant impact on the IPR or ASD and it remains very close for all Elo ratings
The zASD is greater for White most noticeably around the 1600 to 2000 Elo range
Overall, the first move advantage does not drastically impact the outcome of the game in terms of IPR or ASD but does hold some sway over the zASD

23. References
Papers:
‘Rating Computer Science Via Chess’ by Kenneth W. Regan
‘Do Initial Strategies or Choice of Piece Color Lead to Advantages in Chess Games?’ by Sameer Ponnaluri and Mary J King
‘Move-by-Move Dynamics of the Advantage in Chess Matches Reveals Population- Level Learning of the Game’ by Ribeiro et. al.
Links:
Graph tools:

24. The turning point in my career came with the realization that Black should play to win instead of just steering for equality
-Bobby Fischer