Complex attack

Game this week between two student players:

The younger of the two (playing white) launched into a brilliant attack which led to the position above.  Here, white can reach a solid endgame with 1. Nxf5+ which forces Qxf5 (or else mate) 2. Qxf5 gxf5 and once the white bishop retreats, white is up two pawns, with a supported outside passed pawn to boot.

However, white instead played 1. g4, looking to deflect the f5 bishop guarding against mate on g6.  It looks like it should work, but black countered with 1. ..Be4 with the idea that if the bishop is taken with 2. dxe4 then  Qxg4+ and the critical g6 square is still covered.  White assumed (incorrectly) that black could get a perpetual from this check, declined to take the bishop, and lost from the ensuing complications.

Does white have a finish from here, and if so is 1. g4 the beginning of it?  Or is the simplification outlined above the best play?

Stockfish says g4 is much better than the simplification play. It gives g4 a + 7.25 evaluation versus only a +2.5 evaluation for 1. Nxf5+.

Maybe you don't have the little computer analysis icon as a basic member.

I get slightly different results running it on a phone.

You are right, I don't have the computer analysis icon.  I suspected g4 was the stronger play, but the opponent reply (Be4) is more troublesome OTB than the engine response Bxd3.  The engine's move may be objectively better with perfect play, but black creates a mating threat of his own (namely Qxg4# on the next move), and a tempo check to play if the bishop is taken.

When trying to swindle your way out of a loss (and +2.5 from the simplification play looks like a losing continuation, too), the best tactics muddy the waters.  As an Expert who used to frequent this club once taught me, unclear is better than lost.  The engine treats certain losses which can be forestalled over the horizon as OK, but human players with endgame experience often know better.  The student who played black in this game understood that, and so I consider his response to 1. g4 to be more reasonable than the engine's.  This is the basic danger of engine analysis, they follow lines humans wouldn't play, and sometimes those humans have a valid reason for not playing those lines.

In any event, thanks for the analysis.  I'm sure these students will find it helpful.

In either case, there doesn't appear to be an immediate forced mate, which answers the first question.  Again, thanks!

A good point - it will take black at least two moves to do anything about the threat of Nxf5, so there's little reason not to make productive use of the spare tempo in the meantime.  Even the pin-breaking 1. ..Kh7 doesn't really solve black's problem, as 2. Nxf5 still needs to be met with ..Qxf5 (..gxf5 3. Qg6+ Kh8 4. Qh6#, or ..Rxf7 3. Qh4+ Kg8 4. Nh6+, etc.).

They say Bobby Fischer used2 say that 1. h4 is best by test.

A "student player" is a player of scholastic age.  No permit required.  I am not a professional coach, mind you, though I do give informal lessons (free of charge of course, as I'm nowhere near good enough to be worth paying for it) in one of my local clubs.

The two players in this game are both very good for their respective ages, but without a really good player to push them (they're frankly about even with me already), I'm worried that their abilities may stagnate.  Of course, I enjoy analyzing interesting positions to begin with, so this helps me get better, too (my own tournament results have been improving of late).

The line that hasn't been analyzed yet here is 1. g4 Be4, which was what was actually played.  It looks like white can just play 2. dxe4 (Nxe4 allows Qxf7), but after Qxg4+ 3. Kh1, Nd7 looks like it complicates matters.  Black doesn't have a perpetual because the white queen guards f3, but this also means that white has to worry about queen deflection plays.

Got a chance to review the 1. g4 Be4 line last night - doesn't work either, but is also complicated.  After 2. dxe4 Qxg4+ 3. Kh1 Nd7 doesn't work because of 4. Nf5+ Qxf5 (or else mate) 5. exf5 Nxf6 6. fxg6 is hopeless for black, especially in light of the open g-file.  Black can't move the king after 4. Nf5+ because ..Kh7 falls into 5. Qg7# and ..Kh5 fails to the pretty 5. Bxg6+!! Qxg6 6. Qh4#.