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Your description of the computer's suggestions doesn't quite match the position, but if you mean the computer suggests Nxe5, that is correct, as Bxe1Bxd1 leads to a variation of Legal's Mate.

  1. Nxe5 Bxe1 Bxd1
  2. Bxf7+ Ke7
  3. Nd4#Nd5#

If, instead,

  1. Nxe5 dxe5
  2. Qxg4

and white has won a pawn, and has a big lead in development.

Your description of the computer's suggestions doesn't quite match the position, but if you mean the computer suggests Nxe5, that is correct, as Bxe1 leads to a variation of Legal's Mate.

  1. Nxe5 Bxe1
  2. Bxf7+ Ke7
  3. Nd4#

If, instead,

  1. Nxe5 dxe5
  2. Qxg4

and white has won a pawn, and has a big lead in development.

Your description of the computer's suggestions doesn't quite match the position, but if you mean the computer suggests Nxe5, that is correct, as Bxd1 leads to a variation of Legal's Mate.

  1. Nxe5 Bxd1
  2. Bxf7+ Ke7
  3. Nd5#

If, instead,

  1. Nxe5 dxe5
  2. Qxg4

and white has won a pawn, and has a big lead in development.

2 added variation asked about in a comment
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Your description of the computer's suggestions doesn't quite match the position, but if you mean the computer suggests Nxe5, that is correct, as Bxe1 leads to a variation of Legal's Mate.

  1. Nxe5 Bxe1
  2. Bxf7+ Ke7
  3. Nd4#

If, instead,

  1. Nxe5 dxe5
  2. Qxg4

and white has won a pawn, and has a big lead in development.

Your description of the computer's suggestions doesn't quite match the position, but if you mean the computer suggests Nxe5, that is correct, as Bxe1 leads to a variation of Legal's Mate.

  1. Nxe5 Bxe1
  2. Bxf7+ Ke7
  3. Nd4#

Your description of the computer's suggestions doesn't quite match the position, but if you mean the computer suggests Nxe5, that is correct, as Bxe1 leads to a variation of Legal's Mate.

  1. Nxe5 Bxe1
  2. Bxf7+ Ke7
  3. Nd4#

If, instead,

  1. Nxe5 dxe5
  2. Qxg4

and white has won a pawn, and has a big lead in development.

1
source | link

Your description of the computer's suggestions doesn't quite match the position, but if you mean the computer suggests Nxe5, that is correct, as Bxe1 leads to a variation of Legal's Mate.

  1. Nxe5 Bxe1
  2. Bxf7+ Ke7
  3. Nd4#