There are two gambits in the BDG family that are older than the Diemer's idea of 4.f3. One is the Blackmar Gambit 3.f3 and the other is Von Popiel with 3.Nc3 Nf6 4.Bg5. When put side by side they look like this:
1.d4 d5 2.e4 dxe4 3.f3 - The Blackmar Gambit from the 1880s.
1.d4 d5 2.e4 dxe4 3.Nc3 Nf6 4.Bg5 - Von Popiel from early 1900s.
1.d4 d5 2.e4 dxe4 3.Nc3 Nf6 4.f3 - Blackmar-Diemer from 1930s.
The BDG thematic postal tournament that ran from 1968 to 1975 with 21 players was won by Georg Danner. In a quick glance at his games was White from that era, I count 9 times he played 4.Bg5 and 6 times he played 4.f3. Probably the starting position for that event required just 3.Nc3 Nf6, since 4.f3 was not played in every game. Below is a recent well played game from Poland between Szadkowski and Aglave in the Von Popiel 4.Bg5.
Szadkowski (2184) - Aglave (2113), 28th Gniot Mem 2013 Police POL (7.12), 16.07.2013 begins 1.e4 d5 2.Nc3 Nf6 3.d4 dxe4 4.Bg5 Bf5 5.Qe2 [5.f3!? and 5.Bxf6 are alternatives.] 5...c6 6.0-0-0 [6.Bxf6 exf6 7.0-0-0=] 6...e6 [Black could try 6...Nbd7 7.f3 exf3 8.Nxf3 e6 9.d5 Qa5=/+] 7.f3 exf3 8.Nxf3 Be7 9.Ne5 Nd5 [9...Qc7!?] 10.Bd2 [10.Bxe7 Qxe7=] 10...Nxc3 11.Bxc3 0-0?! [11...Qd5 12.Kb1 Nd7=] 12.g4 Bg6 13.Kb1 Nd7? [Now White has a great attack. 13...Bh4!? is a creative way to slow the h4-h5 advance. 14.Be1=] 14.h4 Nf6 15.Bg2 h5 [If 15...Nd5 16.h5 Bxc2+ 17.Kxc2 Nf4 18.Qe4+-] 16.Nxg6! fxg6 17.Qxe6+ Kh7 18.gxh5 gxh5 19.d5 cxd5 20.Rxd5 [Or 20.Rhe1!+- ] 20...Nxd5 21.Be4+ 1-0
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