It's called the Philidor Defence, and is a sound defence (3: ... Bg4?! is not sound)
1. e4 e5 2. Nf3 d6
I think your move 5.Bb5+ a minor mistake. You do not want to trade off your very nice light squared bishop in this type of postion. After 5. Bb5+ Bd7 what is your follow up? So possibly Black could have played a better move on his 5th move.
Hello Victor, Yes, I knew it was the Philidor Defense. My surprise was that I am in the process of writing a blog on that very defense and here it shows up in a live blitz game. I live near where Paul Morphy grew up and I taught a Summer class at the college where he graduated.
Hello Ponz111, I usually bring the Bishop back. In a Blitz game, I might trade. Thank you for your reply. I will search for something better than 5. Bb5+ for White so if it arises again I will be ready. If you have a suggestion, I would like to try adding it to my list.
Just 5. Nc3 developing and protecting you e pawn would be better.
and then Black will probably play 5. ...Be7 and then there are several lines of play for White inculding 6. Bc4 and 6. Be2 and maybe 6.g3
I am in the process of posting a blog on the famous game played by Paul Morphy (White) VS The Duke of Brunswick and Count Iousard which was played in Paris in 1858. Meanwhile, today in a 10 minute blitz game, I was surprised to see the same 2...d6 that Morphy's opponents played in that game. I think Black's biggest mistake was allowing White's Bishop the post on e6. This short game was as follows: