Today I faced the rare Levitsky attack in Live chess, an opening I don't think I had faced before (nor ever heard of until I looked it up afterward). I responded with what I considered an interesting though questionable gambit.

After all, I couldn't let him play an opening he presumably knew well and I clearly did not.

So I sacrificed a pawn for some development. I ended up winning the game quickly after white responded poorly to a queenside attack, but that doesn't have much bearing on how good the gambit is. What do you think?

An instructive example.  Yes, Black has some play for his pawn.  Let's count the tempi first.

We only count tempi on the board.  Moves made by pieces no longer on the board don't count.  We consider a tempo in this respect to be any move of a piece besides the King off of the back rank, an e- or d-pawn advanced to the frontier, a castled King, a Rook on a half-open or open file, and add an extra tempo for a Knight on the 4th or 5th rank (since it takes two moves to get there).

By this standard, Black has three evident tempi - both Ns and the Pd4 - while White has only one in his Bh4 (his d-pawn moved to the frontier, but is now vanished and doesn't count).  This gives Black a net of +2 tempi, but we know a pawn is worth 3 tempi, so Black does not have evident compensation.  That's okay - it is what makes it a true "gambit," the risk involved.

But Black does have some play, and this could lead to an advantage or attack for him if White isn't careful.  The first rule for White is "time is of the essence."  White cannot afford to waste any time at all.  No preventative pawn moves or speculative forays.  It's a sure path to disaster when Black's only compensation is time (tempi), and White gives him even more for free.

So how should White proceed?  Next we visualize what our optimum set-up might be, and then how to get there as quickly and safely as possible.  Obviously we need to secure our King by castling early, because the gambiteer knows his edge in time is a fleeting thing, and given enough moves on each sides he will usually have to give some time back sooner or later, so he wants to strike, or threaten to strike, ASAP to apply maximum pressure from the start.

Okay, but which side?  Black has the half-open f-file, so that's one strike against the King's side, but Queenside castling is essentially "looser"  and White will usually find it necessary to move the K to b1 for full protection, and this wastes time.  Also it is going to be hard to prevent Black from attempting to open the position further with ...d5-d4 if he wishes, so there is uncertainty in that respect.

So King's side it must be, so we need to develop the Kingside pieces right away.  We will play Nf3 and e2-e3, followed by Bf1-b5 or perhaps d3 or e2, depending, and then 0-0.

Now this does neglect our Nb1, which we would normally want to get out early, but we have a pawn in the bank and paid for it with time, so someone must wait.  It's not a bad thing in this case, since it isn't clear where it should go yet.  Nbd2 blocks the d-file, making the ...d4 thrust even easier.  Nc3 invites a pin with ...Bb4, while leaving the Nb1 at home permits such a move to be repulsed with c2-c3.  Na3 is unlikely to be good here, so waiting to deploy this piece makes good sense.

With a calm approach, resolute in the determination not to lose further time if at all possible, White should emerge with a completely defensible position, good squares for his pieces, and a pawn in the bank growing interest.  No need to fear here!

Still, I have to wonder why you would play 2 Bg5 after 1 d4 d5 anyway.  It's just not a serious attempt at advantage.  As the late SM Charles Powell and others pointed out, Black can virtually equalize vs the Trompowsky after 1 d4 Nf6  2 Bg5 d5!, and he could just as easily do that in your line as offer a speculative gambit. 

Thanks for your comment. I guess I'll go from the top down.

Your tempi counting is something I feel like I have seen before but don't know much about. In particular, I don't understand why a pawn is worth just three tempi so early in the opening. It seems like the Evans Gambit and the Half Danish both sacrifice a pawn for two tempi, though I understand both openings are very studied and black usually must give the pawn back.

You are certainly correct that white can develop the kingside fairly normally, though I think black can create pressure by castling queenside and playing Rf8. The biggest question is how black should start an attack on the castled position, or if that is even the correct way to proceed. I admit that as black I didn't have a clear plan here.

As for why white played 2. Bg5 (the Levitsky Attack), I imagine he probably did expect to transpose into the Trompowski and from there probably the Torre Attack. Every authority I can find online suggests or states that this squanders white's advantage, but I don't think this is a fair assessment at lower levels. (And it still gets played by some GMs too, so it hardly seems fair to criticize weaker players for using it.)

As far as the envisioned continuation goes fro your gambit, White can simply play Bxf6 and your Kingside is ruined with your King still in the center. 

I don't believe it's so easy for Black to equalize in the Trompowsky. 2.d5 does give Black the Bishop pair, but also an inferior pawn structure.

Since black will be castling queenside, I don't see Bxf6 as a very strong move. If black plays Qd7 it is of course a reasonable option, but it doesn't give any obvious advantage, and if black plays Qd6 or Be7 instead it looks very bad.

Duh! The Queen can just re-capture...haha sorry...I haven't had my morning coffee yet.

This gambit is almost certainly unsound.

And how do I know this?

Firstly as estragon has already pointed out black doesn't really have enough tempi for hes pawn and when you doesn't enough tempi you really need to have some concrete ideas behind your sacrifice and in this position I don't such ideas for black.

As you pointed out there are "similar" gambits where black sacrifices a pawn for less than three tempi but in all those situations there is usually a kind of positional idea combined. Some examples:

But if we look at this gambit black doesn't really seem to have these kind of ideas and white doesn't seem to have that much problem finishing hes development.

An example:

The "pawn = 3 tempi" is primarily a rule of thumb.  In chess, of course, the exact position is everything and can change the value of material and time.  For instance, in a position where both sides threaten mate on the move, a single tempo could be worth more than a Queen because it lets you mate first.

But the same is true for the point values assigned to every piece.

The 3-tempi rule of thumb has been around a long time, though, and seems to fit more often than not.  Remember that a real "gambit" is one where the player does NOT have full compensation for his pawn right away: if he does, there is no risk in the sacrifice and it is not a true gambit.

This makes sense, thanks.

Conzipe, I'm not sure the fact that white can complete development necessarily proves the gambit is unsound. The same could be said of the Danish Gambit, for example (though black usually has to give back one pawn). As long as there is some persistent initiative, the pawn might still be worth it.

I mean, you might be right about the opening, but I just don't think you can come to that conclusion so quickly.

But the problem is that black doesn't seem to have any "persistent initiative" going for him especially when the both sides will end up castling on the same side.

Note that in the danish gambit white actually has some very clear targets.