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Na6 against d4?

I know an international master who used to play 1...Na6 against everything. He continued ...c6, ...Nc7. He did not want to waste his time on opening theory, wanted to play original chess and scored well with it.
After Na6 black can choose between Benoni style setups (c5, e6, exd5), Non-Mar del Plata Kings Indian Style setups (c6, d6, e5) and Old Indian style setups (c5, d6, e5, like in the game). In all these setups white is slightly better due to his space. Na6 is missing on d7 in some lines, where it defends against e4-e5 (In the Benoni) or (if Old Indian) f4 and f4xe5. Still Na6 is played often in the Benoni (in all of these openings) but i would prefer to first fianchetto my bish to g7 on move 2, or play d6 (if i want to develop the bish to e7), then i still can choose where to put the knight.
regarding the game, the bishop is not well placed on g5 in this pawn structure (it is actually rarely well placed there in Kings Indian/Benoni pawn structures, it does a better job fighting for b4/c5/f4/e5, not e4/d5). Especially exchanging it on f6 followed by f4 is terrible.

White should instead play h3, Be3, Nf3-d2, a3-b4 and then, depending on how black plays, play on b-file (supported by a4-a5) and/or break through with f4 in the moment when black has no good control over e5. This structure is known to be passive for black. Its closed nature makes it easy for white to prevent blacks counterplay, it is too slow.
Also in the Leningrad Dutch i.e. ...f5, ...g6, ...Bg7 the knight often goes ...Nb8-a6-c7-e6, where it supports the push ...f4 and can sometimes attack from g5.
In the Caro-Kann ...Na6-c7 allows to maintain the central tension after Nc3 or Nd2: black is not obliged to capture ...dxe4.

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