Evan's Gambit or Deutz Gambit?

Hi, I'm somewhat of a beginner and I've recently picked up studying the Italian Game more in-depth because it's one of my favorite openings. Besides the main line, two of my favorite options after the Giuco Piano are the Evan's Gambit and the Deutz Gambit, the latter being an opening some people don't really know much about.

The Evan's Gambit goes like this:

After 4. b4, black can either accept the gambit or decline it by taking their bishop to safety. If 4... Bxb4, then 5. c3 and after this move, there are numerous variations that can arise based on black's response. I will not go into detail because most people already know about this and there are plenty of resources on the Evan's Gambit online for people who don't.

The Deutz Gambit, in short

The Deutz Gambit, on the other hand, arises from the Giuco Piano, only after white castles and black plays Nf6, after which white will play d4. Unlike in the Evan's Gambit Accepted, which has many variations, black only has 3 choices in the situation: Nxd4, exd4 or Bxd4. The first one (in which the knight takes the pawn) is the worst of the bunch because the following will happen:

After 6. Nxe5, black has to defend the weak f7 square, otherwise white's knight will fork the queen and the rook. Therefore, 6... Qe7, after which 7. Bxf7+ Kf8, the knight retreats, the king takes the bishop and so on like in the diagram. The result is a quite busted position for black because the king has been weakened and white has numerous attacking possibilities, such as Qh5.

5... exd4 is black's second best choice, basically transferring into the Max Lange attack. The most logical move for white in this scenario is 6. e5, attacking black's knight on the f6 square. Black now has no choice but to give up his knight and advance his d-pawn to the 5th rank, attacking white's bishop (so, basically, offering an exchange). Now, you might be wondering, why can't black just move his knight? Because wherever it will go, a worse situation for black will arise.

• Nd5 is obviously a dumb move because white can then simply take the knight with the bishop.
• Ng8 is just a waste of tempo and puts the knight back in its starting position, which only really handicaps black.
• Ne4 might seem like a good move because it (seemingly) takes the knight to safety and further advances into white's territory, but white can play Qe2, once again attacking the knight, after which the knight doesn't have a single safe square to go to. In this case, black has done nothing but given white a free knight and helped them develop their queen (somewhat).
• Ng4 is what you might often see black play, but this move is very bad too because: 7. Bxf7+ Kxf7, 8. Ng5 Kg6 and 9. Qxg4. In this scenario, both sides are equal in material but white has a far, far better position and black has basically lost the game.
• Nh5 is black's last alternative, but once again, this move is also bad because white can play Ng5, attacking the f7 square and threating to fork black's queen and rook. Even if black defends with a move like Qe7, white still has an advantage because black has essentially pushed his own knight to the side of the board, which is never good, and allowed white to take up more space in black's side.

I won't attach a diagram to illustrate or the scenarios I detailed above. If you want to properly understand or study these variations, feel free to do so yourself. We've established that after 5... exd4 and 6. e5, black is better off playing 6... d5 because moving the knight is bad. The following happens:

This line of moves is, as far as I know, best for both players. However, not everyone will play like this and there are several places where black can go wrong, so keep an eye out. Even after all these moves, white clearly has the upper hand. For this reason, 5... exd4 is not the best response to the Deutz Gambit.

The best response to the Deutz Gambit is 5... Bxd4 and the continuation to it is this:

Black now has many moves to choose from. The most common ones are b5, Be6 and Qe7. b5 is the worst here, but it's sometimes played in this position which is why you should know how to counter it:

As shown above, b5 is best followed by Bxe5+, after which 10... Nxb5, then a queen exchange - 11. Qxd8+ Kxd8 - and then Rxf6 by white. Black will be tempted to take the rook with the g-pawn, but if they do that, white can play Bxf6, forking black's king and rook, so black should just ignore the rook. Whatever else black plays next, such as Ke8 for example, white can simply take his rook to a safe position such as f3.

Qe7 - and not b5 - is the best response to the position shown previously and also the hardest to punish. At this point, white's best bet is to just be careful and develop their other pieces like this:

Obviously, at this point both players have reached a point well after opening theory, so your opponent's next moves after Qe7 and then Na3 by white will vary greatly. This is, for the most part, a hypothetical ideal series of moves from both players for reasons I won't really go into. If you want to know the "why"s of each move, you could read up more on the Deutz Gambit online or watch Hanging Pawns' video on it, which I would rather recommend. 

The point is black has played perfectly so far. They have a slight advantage which is only natural after 17 moves of perfect play. This is the only possible line in the Deutz Gambit where white doesn't have the advantage and the worst case scenario you could face when playing this gambit. (Even after all the moves shown above, white can still do well, given the fact that black now has doubled pawns on the f file, or that white can take the pawn on b5 and so on.) However, most players do not know how to properly play against it. Even if they respond to it with Bxd4, they just make other mistakes along the way which give white the upper hand. Given all the possible ways that black can blunder, I think this gambit is more than justified, and I would even go as far as to call it a competitor to Evan's Gambit, which brings us to the point of the entire post.

Evan's Gambit vs. the Deutz Gambit

The pros of the Deutz Gambit are that there are only 3 main variations that can arise after you play it, unlike in the Evan's Gambit where there are many possible lines and defenses. There is much more theory to it than there is to the Deutz Gambit, which is why I found the latter more suitable for me, as a beginner. The main pros of Evan's Gambit, evidently, are that black will have a hard time trying to equalize (among others, depending on the different possible variations). What do you guys prefer? Which one would you typically go for and which one do you think is better or safer for white? Would you just go with Evan's Gambit after the Giuoco Piano, or would you castle and hope for black to play the Two Knights Defense (Nf3) so you can pull out your secret weapon, the Deutz Gambit?

The deutz isn't good. I don't know much analysis of it, but after Nxd4 Nxe5 can't black play Ne6, defending f7 via interference?

In the ...Bxd4 line, after Nxd4 taking with the pawn is best. after exd4 e5 Ne4 it finds a safe square on c5.

The evans, on the other hand, may be more complicated, but it is much more sound despite having less traps.

I think that would be even worse than Qe7, because this would happen:

(Black can't take the bishop with the d-pawn because that would trigger a queen exchange and then Nxf7, forking black's king and rook). Now black can play either d6 or Nxe4. If black chooses Nxe4, white can play Nxc5, then Nxc5 once more from black, and then white can fork the king and the knight with Qh5, so black would clearly be in a losing position. d6 is a better response, but even so...

...after these few moves, white already has a better position.

As for your second idea, in the Bxd4 line, exd4 would be worse because after Ne4, white can play Qg4, threatening the knight you just placed on e4, as well as the undefended g7 square, so you need to guard one of them. This is, once again, a winning position for white if they know what they're doing.

true. 

Took a longer think, the Bxd4 is good for black.

Black is better in that position. Doubled pawns on the f-file simply open the g-file, while white doesn't have any attack on the queenside.

You're right, black has a slight advantage in that situation. I covered this position in my post and I didn't deny this fact. But I think the Deutz Gambit especially in more casual play, where people don't know how to counter it. I personally really like it, at least at my humble ~930 rating level