To Trade or Not to Trade?
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Maintain the Tension
You may (or may not) have heard the advice to maintain the tension: Refrain from exchanging pawns and pieces, which would release the tension between them. This is something that International Master Josh Waitzkin (from the movie Searching for Bobby Fischer) professes in the old Chessmaster software series. I've also heard it from Grandmaster Daniel Naroditsky on one of his streams ("White made one transformation too many").
The advice to "maintain the tension" seems to lead us to the hypothesis that players should not trade pieces, and instead wait until their opponent initiates the exchanges themselves. In this article, we set out to test this hypothesis. We examine the question: Are players who initiate fewer trades than their opponent more likely to win?
The Data: 112k+ Online Games
To look at the effect of initiating trades on odds of winning, I've used the database of games played on lichess in May 2019. I sampled 200,000 games, and I only kept games that matched these criteria:
Normal termination (i.e., I removed games tagged with "abandoned game" and "rules infraction")
Decisive games ending with checkmate or resignation (i.e., I removed draws and timeouts)
Players were similarly rated (rated within 100 rating points of each other)
In total, I used 112,019 online games.
Captures and Trades
At each player's move, I looked at whether the move included a capture by noting the presence of an "x" in the algebraic notation (for example, dxc5 includes a capture, while Nf3 does not). To determine how many trades each player initiated during a game (up to 100 moves), I used the following criteria:
the player's move was a capture
this capture was not preceded by a capture (in other words, the opponent's previous move was not a capture)
the opponent's response was a capture
The difference in trades initiated between White and Black for each game is simply the difference between the number of trades White initiated minus the number of trades Black initiated during that game.
Initiating Trades and Odds of Winning
We're now ready to look at the effect of initiating trades on your odds of winning a game. (If you recall, we defined "initiating trades" as a capture that's also followed by a capture but not preceded by one.)
The following plot shows the percentage of games that White won (y axis) as a function of the difference in number of trades initiated between White and Black (x axis). The x axis is also from White's point of view:
a negative differential means White initiated fewer trades than Black
a positive differential means White initiated more trades than Black
a differential of 0 means White and Black both initiated as many trades
Note that I excluded games with a trade differential below -5 or above +5, since there were too few games outside of this range.
Amazingly, the relationship is almost perfectly linear! Keep in mind, this is not a linear model, those are the actual win percentages being plotted for each trade differential. And the effect of trade differential on odds of winning is large, too: When White initiates 5 fewer trades than Black, White can expect to win barely over 35% of their games. Contrast this with a situation where White initiates 5 more trades than Black: In that case, White can expect to win more than 65% of their games!
In other words, the more White initiates trades relative to Black, the more White is likely to win.
To Trade or Not to Trade?
So, what should we do anyhow? Do we maintain the tension or do we trade?
The plot above shows that players who initiate more trades than their opponents are much more likely to end up winning the game. This seems inconsistent with "maintaining the tension". Rather than maintaining the tension, the analysis above suggests that players should not fear initiating trades. Note that I also produced the plot separately for each rating group (not shown above), and the same pattern was maintained across all ratings. Similarly, retaining draws and timeouts also did not change the pattern displayed in the plot.
Why do you think these online games fail to support the advice to "maintain the tension"? Leave your ideas below.