I've never memorized any games, but I would imagine it would be pretty easy if you took some time to understand why each move was played. Then when replaying the game from memory, rather than a memorized sequence of moves it would be more like "white played this threat, black responded to it like this, white had this idea", etc.
Memorizing famous games
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For me, at least, the memorizing of a famous game is an incidental result of pestering this or that person to look at the game.
"I couldn't replay any [game] although I could recognise quite a lot." - CM JamesColeman (~5 months ago)
"Good point. I could have replayed [1 e4 e5 2 Nf3 d6 3 d4 Bg4 4 dxe5 Bxf3 5 Qxf3 dxe5 6 Bc4 Nf6 7 Qb3 Qe7 8 Nc3 c6 9 Bg5 b5 10 Nxb5 cxb5 11 Bxb5+ Nbd7 12 0-0-0 Rd8 13 Rxd7 Rxd7 14 Rd1 Qd6 15 Bxd7+ Nxd7 16 Qb8+ Nxb8 17 Rd8#]. Also Reti-Tartakower [(1 e4 c6 2 d4 d5 3 Nc3 dxe4 4 Nxe4 Nf6 5 Qd3 e5 6 dxe5 Qa5+ 7 Bd2 Qxe5 8 O-O-O Nxe4 9 Qd8+ Kxd8 10 Bg5+ Ke8 11 Rd8#)] where White sacrifices his Q on d8 and then forces mate with a double check. So maybe 2. Both of those are rather short though." - CM JamesColeman (~5 months ago)
"Oh yeah, [1 d4 e6 2 Nf3 f5 3 Nc3 Nf6 4 Bg5 Be7 5 Bxf6 Bxf6 6 e4 fxe4 7 Nxe4 O-O 8 Bd3 b6 9 Ne5 Bb7 10 Qh5 Qe7 11 Qxh7+ Kxh7 12 Nxf6+ Kh6 13 Neg4+ Kg5 14 h4+ Kf4 15 g3+ Kf3 16 Be2+ Kg2 17 Rh2+ Kg1 18 Kd2#]. Maybe 3 then" - CM JamesColeman (~5 months ago)
"There are many many must-know games for general ideas and themes but not sure of the practical value of having all of them memorised move by move all the way through to resignation?" - CM JamesColeman (~5 months ago)
What's your process of memorizing famous games of chess? What are some strategies that help you retain better?