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Why would white play 6.Nc4.

Oh I see is this position called anything.

NC4 THREATENS CHECKMATE ND6

It is Mortimers Trap... A good one! There are several good traps for the Black side of a Ruy Lopez. If White had played 6.Bc4, instead of hoping for the  Smothered Mate, 6... Qa5+ wins the Horse.

 can you notate all of them on this forum with the name next to it.

The only problem with this trap is that if the opponent knows it, or sees it, black has just made an odd, anti-developing tempo-wasting move which white can exploit with quick development. Fortunatly, 4.d3 is pretty irregular (c2-c3 followed by d2-d4 is superior), so chances are if your opponent plays this they won't know about the Mortimer trap. If they do, however, moving your knight from e7 to g6 in front of your kingside sets up a nice defence and a strong attack, assuming white castles kingside. So, Ne7 isn't a total waste of a move. Clever trap regardless.

 lol... No, but I will give you another good one!

The 'Noah's Ark Trap'... I think because it is that old! I have used this several times, even against Strong players, as I like the 'Deferred Steinitz Defence' against the Ruy Lopez

 Do you know the name of the trap in his other forum.

There's another trap in the Ruy Lopez, known as the Fishing Pole Trap:

Thanks for sharing...

Never knew the name of it, I have used it tho' and other variations of it.

It is a good one as you still have a good game if your opponent knows it.

I usually get there from here...(Deferred Steinitz Defence)