Chess-playing computer programs have made considerable advances in the past 40 years. Early programs used what is called “brute-force searching” to make their moves. 1) Simply put, a brute-force search looks at all possible legal moves in a position and decides which move is best. One problem with brute-force searching is that the game of chess is complex – some researchers estimate there could be more than \(10^{120}\) possible games.

In practical terms, the complexity of the game 2) had meant that a computer program can only “look ahead” by a limited number of moves. Computer programs have advanced by working smarter (not wasting time on unlikely or foolish moves) and faster (as computer power increases, brute-force searching can look farther ahead). 3) Due to these advances, even the best computer programs 4) cannot search beyond a tiny fraction of all possible games.

1) Simply put, a brute-force search looks at all possible legal moves in a position and decides which move is best.

The author is considering deleting the underlined sentence. Should the author do so?

Chess-playing computer programs have made considerable advances in the past 40 years. Early programs used what is called “brute-force searching” to make their moves. 1) Simply put, a brute-force search looks at all possible legal moves in a position and decides which move is best. One problem with brute-force searching is that the game of chess is complex – some researchers estimate there could be more than \(10^{120}\) possible games.

In practical terms, the complexity of the game 2) had meant that a computer program can only “look ahead” by a limited number of moves. Computer programs have advanced by working smarter (not wasting time on unlikely or foolish moves) and faster (as computer power increases, brute-force searching can look farther ahead). 3) Due to these advances, even the best computer programs 4) cannot search beyond a tiny fraction of all possible games.

2) had meant

Chess-playing computer programs have made considerable advances in the past 40 years. Early programs used what is called “brute-force searching” to make their moves. 1) Simply put, a brute-force search looks at all possible legal moves in a position and decides which move is best. One problem with brute-force searching is that the game of chess is complex – some researchers estimate there could be more than \(10^{120}\) possible games.

In practical terms, the complexity of the game 2) had meant that a computer program can only “look ahead” by a limited number of moves. Computer programs have advanced by working smarter (not wasting time on unlikely or foolish moves) and faster (as computer power increases, brute-force searching can look farther ahead). 3) Due to these advances, even the best computer programs 4) cannot search beyond a tiny fraction of all possible games.

3) Due to

Chess-playing computer programs have made considerable advances in the past 40 years. Early programs used what is called “brute-force searching” to make their moves. 1) Simply put, a brute-force search looks at all possible legal moves in a position and decides which move is best. One problem with brute-force searching is that the game of chess is complex – some researchers estimate there could be more than \(10^{120}\) possible games.

In practical terms, the complexity of the game 2) had meant that a computer program can only “look ahead” by a limited number of moves. Computer programs have advanced by working smarter (not wasting time on unlikely or foolish moves) and faster (as computer power increases, brute-force searching can look farther ahead). 3) Due to these advances, even the best computer programs 4) cannot search beyond a tiny fraction of all possible games.

4) cannot

Because of these limitations, researchers evaluated positions from a different perspective – the endgame. While each opening position is likely to have over 30 possible 5) moves endgame options are much more limited. Because of the dearth of pieces, endgame positions with a given structure 6) transposes into each other, and positions that are like others are often easy to relate to each other. This means that a computer can “brute force search” more moves ahead when only a few pieces remain on the chessboard.

Using these innovations, computer chess experts utilize programs to evaluate positions 7) that no one has ever considered. This strategy 8) has allowed researchers to consider “solutions” to every legal chess position with 7 or fewer pieces on the board. These few endgame positions 9) provide insights to human chess competitors of all abilities. 10)

5) moves endgame

Because of these limitations, researchers evaluated positions from a different perspective – the endgame. While each opening position is likely to have over 30 possible 5) moves endgame options are much more limited. Because of the dearth of pieces, endgame positions with a given structure 6) transposes into each other, and positions that are like others are often easy to relate to each other. This means that a computer can “brute force search” more moves ahead when only a few pieces remain on the chessboard.

Using these innovations, computer chess experts utilize programs to evaluate positions 7) that no one has ever considered. This strategy 8) has allowed researchers to consider “solutions” to every legal chess position with 7 or fewer pieces on the board. These few endgame positions 9) provide insights to human chess competitors of all abilities. 10)

6) transposes

Because of these limitations, researchers evaluated positions from a different perspective – the endgame. While each opening position is likely to have over 30 possible 5) moves endgame options are much more limited. Because of the dearth of pieces, endgame positions with a given structure 6) transposes into each other, and positions that are like others are often easy to relate to each other. This means that a computer can “brute force search” more moves ahead when only a few pieces remain on the chessboard.

Using these innovations, computer chess experts utilize programs to evaluate positions 7) that no one has ever considered. This strategy 8) has allowed researchers to consider “solutions” to every legal chess position with 7 or fewer pieces on the board. These few endgame positions 9) provide insights to human chess competitors of all abilities. 10)

7) that no one has ever considered.

Which of the following best maintains the paragraph’s focus?

Because of these limitations, researchers evaluated positions from a different perspective – the endgame. While each opening position is likely to have over 30 possible 5) moves endgame options are much more limited. Because of the dearth of pieces, endgame positions with a given structure 6) transposes into each other, and positions that are like others are often easy to relate to each other. This means that a computer can “brute force search” more moves ahead when only a few pieces remain on the chessboard.

Using these innovations, computer chess experts utilize programs to evaluate positions 7) that no one has ever considered. This strategy 8) has allowed researchers to consider “solutions” to every legal chess position with 7 or fewer pieces on the board. These few endgame positions 9) provide insights to human chess competitors of all abilities. 10)

8) has allowed

Because of these limitations, researchers evaluated positions from a different perspective – the endgame. While each opening position is likely to have over 30 possible 5) moves endgame options are much more limited. Because of the dearth of pieces, endgame positions with a given structure 6) transposes into each other, and positions that are like others are often easy to relate to each other. This means that a computer can “brute force search” more moves ahead when only a few pieces remain on the chessboard.

Using these innovations, computer chess experts utilize programs to evaluate positions 7) that no one has ever considered. This strategy 8) has allowed researchers to consider “solutions” to every legal chess position with 7 or fewer pieces on the board. These few endgame positions 9) provide insights to human chess competitors of all abilities. 10)

9) provide

Because of these limitations, researchers evaluated positions from a different perspective – the endgame. While each opening position is likely to have over 30 possible 5) moves endgame options are much more limited. Because of the dearth of pieces, endgame positions with a given structure 6) transposes into each other, and positions that are like others are often easy to relate to each other. This means that a computer can “brute force search” more moves ahead when only a few pieces remain on the chessboard.

Using these innovations, computer chess experts utilize programs to evaluate positions 7) that no one has ever considered. This strategy 8) has allowed researchers to consider “solutions” to every legal chess position with 7 or fewer pieces on the board. These few endgame positions 9) provide insights to human chess competitors of all abilities. 10)

10) The author is considering adding the following sentence to conclude the passage. Should the author do so?

“These programs have increased the popularity of betting on virtual chess games.”