LiChess puzzle 87510: How much calculation would a strong player do before playing Bg4+ when white has a range of (all losing) responses?

Question

LiChess puzzle 87510 has the following position:

[FEN "r1b1k3/pp4R1/2q3RQ/4p3/5P2/bP2P3/2P1K2P/8 b - - 0 1"]

The solution is 1...Bg4+, after which white has 6 legal moves:

• 1...Bg4+ 2. Rxg4 Qxh6, which is the computer solution (possibly followed by 3. Rg8+ Bf8),
• 2. Kd3, which is mate in 7,
• 2. Kd2, which is mate in 8,
• 2. Ke1, which is mate in 5,
• 2. Kf1, which is mate in 4, and
• 2. Kf2, which is mate in 4.

I feel like a human player in a tournament would not calculate the whole decision tree, and probably just intuit that 1...Bg4+ is going to win since black can continue with a range of powerful moves Qf3, Qc2, Rd8, and Bb4, and at least one of them is with check, depending on white's response.

Question: How much calculation would a strong player (say an FM+) perform before playing 1...Bg4+?

It's a dangerous move: black begins with an exposed king (with mate threats and a possible rook skewer) and queen attacked, and black responds by creating an undefended bishop. If the checks ended, black would probably lose.

Answer 1

I'm an FM, and my calculation process would be as follows:

1) See that after 2.Rxg4 Qxh6 2.Rg8 Bf8, I'm clearly winning and White has no follow up.

2) Look at White's king moves to get out of check. Immediately Kd1, Kd2, Kd3 can be discarded since they just let me play ...Rd8+ for free. Also, Kf1/Kf2 lead to the same thing after I play 2...Qf3+. So I'd just look at Ke1 and Kf2.

3) Everything looks good, so I'm done.

If I were in time trouble, I'd play 1...Bg4+ seconds after seeing it. Since 2.Rxg4 doesn't work, there's no practical risk to playing it.

Answer 2

I'm no FM, but here's how I would look at it logically, while keeping in mind that calculation can overrule logic.

Black's move pretty much must be a check, given the mate threat and the threat to Black's queen. Four of the checks look really bad because they immediately lose the queen for no discernible benefit. This leaves only two choices: ...Bg4+ and ...Qxc2+.

While ...Bg4+ puts the bishop en prise, it is easy to see (a two-ply calculation) that taking it would be disastrous for White, even though, according to the engine, it is White's best move! If White doesn't take, even without doing a lot of calculation, you can have a "feeling" that there are mating chances now that you have your bishop and queen cooperating in the attack and the possibility of adding the other bishop, as well as the rook, which is now free to move to the open file.

With ...Qxc2+, the problem is that the only attacking piece is the queen, which on its own gives you perpetual check at best. Now that your queen isn't pinning White's rook against the queen, there is no good way of bringing the light-square bishop into the attack.

The problem is that if it so happened that ...Bg4+ didn't work after all (something which you can't know for sure without further calculation), it could well be that a draw is the best result for Black, which would make ...Qxc2+ the better choice! So "logic" can give you an indication of which move is likely to be better, but it is not foolproof. How much a FM would calculate probably depends on how much time they have. I would be interesting to hear from an actual FM. :-)

Answer 3

With enough time (let's say a couple of minutes), a strong player would most certainly do all the calculations (down to mate) before deciding on a move here.

Doing the calculations here is actually not all that difficult because of several factors:

1. As pointed out, because of white's threats against the black king, black is basically forced to check and obviously has only two good candidate moves to do so: Bg4+ or Qxc2+. If playing for a win, Bg4+ is more attractive because it adds another attacker to the game, so one might as well start calculating the consequences of Bg4+ only.
2. All moves are forced and many of the longest mating sequences all follow the same pattern: basically black capturing the e3 pawn with check opening more diagonals for activating the dark-squared bishop.
3. While Kd2 and Kd3 lead to the longest theoretical mates from the position, they are quite obviously lost after Rd8+, when white has the option of prolonging the game by sacrificing all his pieces or getting mated immediately (e.g. after easy-to-see Kd2, Rd8+, Ke1, Rd1+, Kf2, Qf3++). Of course once white loses all his pieces there is no point calculating the shortest route to mate.

So in summary, the mates after Bg4+ boil down to calculating something like a mate in 4 where black gives check at every move. Not at all difficult even for sub-FM players like me (around 2200 strength).

In addition to calculating the mates, one would also have to decide that 1. Qxc2+ does not lead to mate (quite obviously because black is only attacking with the queen) and that Bg4+, Rxg4, Qxh6 is winning for black (also obvious because of the large material advantage).