Breaking Down The Final Chess Match In The Netflix Miniseries ‘The Queen’s Gambit’
A guide to understanding chess in the final episode.
They’re always real moves and it’s always very accurate. You can freeze-frame anything, and it’s a real chess setup. There’s even a whole sequence where you never see the board, but they’re still actually moving the pieces where they’re supposed to. ― Writer/Director Scott Frank
Given the accuracy of the chess setups in “The Queen’s Gambit”, we can use our background knowledge of the characters and data from chess engines to gain a deeper appreciation of what happened in the final scenes of the show.
Notation
Prior to the 1980s, chess literature used a descriptive system — versus modern algebraic notation — to record chess games. Each player begins with eight named pieces (King, Queen, two rooks, two knights, two bishops) and eight pawns. The King and Queen can each be thought of as being supported by three officers (Rook, Bishop, Knight) and four soldiers (pawns). In descriptive notation, the squares on which the King and Queen are placed are called the “King’s square” and “Queen’s square”, respectively. The pieces and squares on either side are named accordingly — for example, the Rook on the King’s side is the King’s Rook, with the square on which it resides the King’s Rook square. The eight pawns are named according to whom they stand in front of: King’s Rook Pawn, King’s Knight Pawn, King’s Bishop Pawn, King’s Pawn, Queen’s Pawn, Queen’s Bishop Pawn, Queen’s Knight Pawn, and Queen’s Rook Pawn.
The eight rows on a chessboard are styled as ranks, while the eight columns are distinguished as files. The rank containing the eight pieces when the game starts is called the “royal line”; the ranks are also numbered from one to eight, with one being closest to the player. Each file is named for the piece occupying its first square at the start of the game. Thus, the King’s Rook square is the first in the King’s Rook file — and the King’s Rook Pawn begins on the second square of the King’s Rook file. All sixty-four squares are named based on the intersection of their file and rank. Thus, the fourth square in Queen’s Bishop’s file is called the Queen’s Bishop’s fourth square or Queen Bishop four. Each of the squares retains its name throughout the duration of the game, regardless of whether the original piece still occupies it or not.
Note: For historical accuracy, the show uses descriptive notation. However, as all of the modern computational tools for chess use algebraic notation and it would be quite burdensome to convert it all, I will be using algebraic notation.
First-Move Advantage In Chess
Historical texts have used a frequentist approach to show that players who make the first move win roughly 55% of games played. Because White always goes first, this translates to saying White has an inherent advantage. Other theoretical explanations of why White tends to win were similarly opaque, however, so I decided to review the data and come up with my own theory.
After studying how Google DeepMind’s AlphaZero plays, my theory is that, by making the first move, you are able to position your pieces to constantly keep the opponent’s King under attack, thereby forcing the opposing player to move their King and reducing the number of turns that can be used to stage a counterattack. This can be seen by looking at the design features of AlphaZero’s strategies. AlphaZero favors openings that clear a path for the Queen; sacrifices pawns early to create weaknesses in the opponent’s King position; and is able to place the opponent’s King in check earlier and more frequently than most human players. This has enabled AlphaZero to achieve previously unseen win rates for White.
The Queen’s Gambit
An opening is a named, initial sequence of moves by both players. A gambit is an opening where a player attempts to sacrifice a piece in the hopes of gaining a future advantage. The Queen’s Gambit is one of many possible openings, described in the dialogue of the show:
Elizabeth Harmon plays pawn to Queen four. Borgov plays pawn to Queen four. Harmon plays pawn to Queen Bishop four. The Queen’s Gambit.
Early on in the show, Mr. Shaibel—a custodian at the orphanage where Elizabeth Harmon, the series’ heroine, grows up, who becomes her first chess teacher — stresses to Harmon that she needs to learn the Sicilian Defense, which leads her, in the early episodes, to open King four (e4) when White.
The Sicilian is really best thought of as a large collection of systems and variations, all of which begin with 1.e4 c5. ― Garry Kasparov
But — per the novel on which the show was based — prior to the final match against Russian world champion Vasily Borgov, Harmon tells her friend and fellow chess prodigy Benny that she wants to avoid Borgov’s Sicilian — and that, if she were to draw White, she would play the Queen’s Gambit to do so. In the final match with Borgov, this is the first time that Harmon opens with Queen four (d4), while in every other match, she opened with King four (e4).
Borgov Takes Non-Standard Line
Borgov declines, moves pawn to King four. The Albin Counter-Gambit. Borgov’s second move is a bit of a surprise. Normally, Borgov would do something more solid, but here, he’s going against his own style and playing a rare line to win.
After Harmon (White) makes the Queen’s Gambit, the opening will subsequently fall into one of two categories, depending on Borgov’s (Black) response: accepted or declined.
If Black takes the pawn at Queen Bishop four (c4), the response is defined as accepted, since Black allows White to sacrifice the pawn.
If Black does not take the pawn at Queen bishop four (c4), the response is defined as declined, since Black does not take White’s sacrifice. In the case of a decline, the standard (Orthodox Line) move for Black is to move a pawn to King three (e6), providing defense for the pawn at Queen four (d5). The Albin Counter-Gambit is an uncommon defense of the Queen’s Gambit in which Black moves a pawn to King four (e5).
Harmon’s response was a complete deviation from the Albin, which must’ve surprised him right back, whilst allowing her to get out into the open.
In the scene, after a few moves occur off-camera, we see that Borgov’s pawn at King four (e5) is still on the board, meaning Harmon has declined to take the Albin Counter-Gambit —the main line would be to play your knight to Queen Bishop three, but she first plays her pawn to King four, allowing space for her bishop, then plays Knight to Queen Bishop three. Such a divergence from the main line is called a “deviation”.
Who was winning when the game was adjourned?
To determine this, I input the board position — that is, which pieces are still on the board, with the coordinates of each piece — into the Stockfish chess engine, which output a score of the match. The position is written and stored using the Forsyth-Edwards Notation (FEN) to record the state of the board.
The Queen’s Gambit FEN:
rnbqkbnr/ppp1pppp/8/3p4/2PP4/8/PP2PPPP/RNBQKBNR b KQkq c3 0 2
You can copy and paste the string above into any chess diagram creator that accepts FEN; all standard notations are determinant, meaning they will produce the same output across all compatible programs.
The chess engine score is a single value: either a signed number indicating which player has the advantage on the board, or a signed alphanumeric combination indicating how many moves it will take the winning player to force a checkmate. A positive (“+”) sign indicates the score is with respect to White, and a negative (“-”) means the score is with respect to Black.
To calculate the score, the chess engine considers a number (depth) of possible moves both players can take in the future based on the board’s current position. As a signed number, the score indicates how many points ahead a player is; the unit of measure is the pawn. A score of +2.25 or -2.25 indicates that White or Black, respectively, leads by 2.25 pawns. A score of +M3 means that White can force a checkmate in three moves, and vice versa.
There is a strong correlation between the chess engine’s score and the proportion of victory for each player. MIT Media Lab took the chess engine score of 120,000+ positions and the proportion of victory for each position from an archive of 750,000 games, finding a best-fit line to approximate the relationship to win percentage. Given a chess engine score, you simply multiply the value by 100 to match the units — appropriately named centipawns — of the graph below, then you can find the probability of a win for either side using the best-fit line.
In the (non-realistic) example above, where only three Black pieces remain, the chess engine computes a score of +87.92, which means that White has an advantage of 87.92 pawns. To find the win probability, we can convert the score to get 87.92 x 100 = 8792 CP (centipawns). Although this x-value falls far outside the window of the graph, the best-fit line indicates that it would produce a y-value of ~1.0, also known as a 100% chance of victory for White.
In the example above, where the only White piece remaining is the king, the chess engine outputs a score of -M6. This means that Black can force a checkmate in six moves. Due to the unbounded (because ultimate) value of the King, you can assume that for any mate score, the CP score is +/- infinity.
It is worth noting that, in World Chess Championships, the pawn differential is typically small.
Considering the board before Borgov’s last move prior to adjournment, the Stockfish calculation puts him 0.71 pawns ahead of Harmon, with the optimal move for him being Rook to a2.
Instead, Borgov moves his knight to e6.
If Borgov had moved his Rook to a2, he could have maintained his lead; by moving his Knight to f6, he gives Harmon the opportunity to tie the match.
Harmon moves her pawn to h3, the calculated optimal move. Borgov requests to adjourn and must seal his next move, to be played when the game resumes. They adjourn at a tie.
Strategizing
During the adjournment, both players seek advice from their chess fellows. When Harmon speaks to Benny and Harry on the phone, they each play through different possible outcomes of the game, to offer strategies whatever Borgov might do. Benny’s advice applies to the board only after Harry’s because, given the board after Borgov retreats his Queen (image above), the King’s Rook’s Pawn is not near either of Harmon’s knights, and the bishop is not under attack. Harry discusses a possible line Harmon should take, which becomes the actual play of the game following the retreat of Borgov’s Queen.
Everything Goes According To Plan… Until It Doesn’t
Looking at the board prior to Borgov moving his pawn to d5, we see that it is possible for Borgov to move his “knight to Rook four”, and the “King Knight pawn” has relevance in this scenario. So, given this board, the probable plan that the group was devising involved everything that happens after this point.
If Borgov moves his knight to Rook four, I think their plan looked like the simulation below using the King’s Rook and King’s Knight Pawn:
When Borgov moves his pawn to d5, Harmon becomes unnerved because they had analyzed every line of play except this one. Staring at the ceiling, Harmon uses the chess engine in her head to calculate. Then she makes her move.
Borgov Offers Draw
Harmon Receives A Promotion
Borgov Resigns
