2
[FEN "r3kb2/pp3pp1/8/2P5/1qN3p1/3Qp2r/P4P1P/5RK1 w KQkq - 0 1"]

1. Qe4+ Be7

In this position why is Be7 the best move for black after Qe4+, given that black will instantly lose its queen afterwards (Knight d6)? For example Kd8 would not immediately lose the queen (still losing the game though).

3

This is a very loosing position for Black .I am not evaluating it from a Computer perspective .In this position Be7 is a better move though it looses the Queen because Kd8 allows Rd1+ check . Now it was only Queen & Knight who were attacking the King and after Kd8 Rook joins the attack .

The Black King has only two valid squares . Kc7 & Kc8 . The Black King is left wide open and the Queen, two Rooks and Bishop cannot come in between to intercept the attack . True after Rd1+ the Queen can intercept in between but anyways it is getting killed either by Knight or the Rook .On Kc8 White can take the g4 pawn and the rook on h3 will fall .

Be7 only provides an escape square for the King on f8 and King is not subjected to plenty of checks .

So the Queen and Rook falls leaving White with Knight/Rook and the Queen and with an unstoppable attack .A GM at this position would throw in the Towel if he/she were at Black's position.

4

While Be7 loses the queen in three moves, Kd8 will lose the queen in the end as well. This kind of position contains a lot of forcing moves (checks, mating threats) and can be analyzed quite deeply by engines like Stockfish. They will evaluate the position at the end of their search tree, which is often >15 moves deep. For the engine, it doesn't matter if you lose your queen in one move or in 15 (though losing the queen sooner increases the chance of losing more material) - it's the end result that counts.

2

Because the black queen will get lost anyway. Fire up your engine and see what happens after

  1. Qe4+ Kd8

  2. Rd1+ Kc7

    (2. ... Kc8?? 3. Qf5+ Kc7 (3. ... Kb8 4. Rd8+ Kc7 5. Qd7#) 4. Qd7+ Kb8 5. Qd8#)

    (2. ... Bd6?? {is futile})

    (2. ... Qd2? {loses the Queen})

  3. Qe5+ Kc6 (3. ... Kc8?? {is the same #3}) (3. ... Bd6?? {is again futile})

  4. Qd5+ Kb5 (4. ... Kc7?? 5. Qc7+ Kb8 6. Qd8#)

  5. Qxb7+ Kxc4 (5. ... Ka4?? 6. Qa6+ Qa5 7. Qxa5#) (5. ... Kxc5?? 6. Qd5#)

  6. Rc1+ Qc3 {any king move loses the queen directly, hoping for 7. Rxb3+? Kxb3, but}

  7. Qb3+ {the black queen is pinned and definitely lost.)

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