I played a game on lichess recently. Afterwards, I used the analysis feature, including the "learn from your mistakes" feature, and it said that 6. a3 by white was a mistake, with 6. Qa4+ as best. I'd like to know why, as I don't understand why 6. Qa4+ is superior.
[After Qa4+ , it seems to me black can play 6. Nc6, and if the white queen captures the black knight, 7. Qxc6, it seems to lead to a draw as the white queen cannot escape capture threats starting with 7. Bd7 by black.]
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1. d4 d5 2. e3 { D00 Queen's Pawn Game } a6 3. c4 b6?! { (0.12 ? 1.07) Inaccuracy. Best move was e6. } (3... e6 4. Nf3 c5 5. cxd5 exd5 6. Nc3 Nf6 7. Bd3 c4 8. Bc2) 4. Nc3?! { (1.07 ? 0.50) Inaccuracy. Best move was cxd5. } (4. cxd5 Nf6 5. Nf3 Bb7 6. Be2 Qxd5 7. Nc3 Qd6 8. O-O Nbd7 9. Nd2 e5 10. Bf3 c6) 4... e6 5. Nf3 Bb4? { (0.17 ? 1.63) Mistake. Best move was Bb7. } (5... Bb7 6. b3 Nf6 7. Bb2 Bd6 8. Bd3 O-O 9. O-O Nbd7 10. h3 c5 11. cxd5 exd5 12. Ne2) 6. a3? { (1.63 ? 0.59) Mistake. Best move was Qa4+. } (6. Qa4+ Nc6) 6... Bxc3+ 7. bxc3 f6?! { (0.65 ? 1.60) Inaccuracy. Best move was Nf6. } (7... Nf6 8. cxd5 exd5 9. Be2 Nbd7 10. O-O O-O 11. a4 c5 12. c4 Bb7 13. Bb2 Rc8 14. Nd2) 8. Qc2 g6 9. cxd5 exd5 10. c4 Ne7?! { (1.74 ? 2.43) Inaccuracy. Best move was Bf5. } (10... Bf5 11. Bd3) 11. cxd5 Qxd5 12. e4?! { (2.47 ? 1.93) Inaccuracy. Best move was Bc4. } (12. Bc4 Qd6 13. O-O Be6 14. d5 Bf7 15. Rd1 b5 16. Ba2 Nd7 17. e4 O-O 18. Be3 g5) 12... Qd6 13. Be2 Bg4? { (2.31 ? 3.33) Mistake. Best move was Bb7. } (13... Bb7) 14. Bb2?! { (3.33 ? 2.57) Inaccuracy. Best move was O-O. } (14. O-O Nd7 15. Rd1 h5 16. h3 Bxf3 17. Bxf3 Kf7 18. a4 Qc6 19. Qd3 Qe6 20. Bf4 c6) 14... Nbc6?! { (2.57 ? 3.07) Inaccuracy. Best move was Nd7. } (14... Nd7 15. O-O O-O 16. Rfd1 c6 17. a4 Rfe8 18. Ba3 Qb8 19. Qb3+ Kh8 20. Bc4 Kg7 21. Bf7) 15. d5? { (3.07 ? 1.98) Mistake. Best move was O-O. } (15. O-O) 15... Bxf3 16. Bxf3 Ne5 17. Be2 b5 18. O-O O-O 19. Bd4 Rac8?! { (2.29 ? 3.12) Inaccuracy. Best move was f5. } (19... f5 20. Bc5 Qd7 21. Rfd1 Nf7 22. exf5 gxf5 23. d6 cxd6 24. Qb3 d5 25. Qg3+ Ng6 26. Bxf8) 20. f4? { (3.12 ? 1.35) Mistake. Best move was Bc5. } (20. Bc5 Qd7) 20... Nc4? { (1.35 ? 3.56) Mistake. Best move was Nd7. } (20... Nd7) 21. Bxc4 bxc4 22. Qxc4 c5 23. Be3 Kg7? { (3.59 ? 4.87) Mistake. Best move was f5. } (23... f5 24. Rac1 fxe4 25. Bxc5 Qxd5 26. Qxd5+ Nxd5 27. Bxf8 Rxf8 28. g3 Nf6 29. Rc6 a5 30. Ra6) 24. Rac1 f5? { (4.67 ? 6.59) Mistake. Best move was Qd7. } (24... Qd7 25. Bxc5 a5 26. Qc3 a4 27. Qd4 Rfd8 28. Rc4 Qe8 29. Rfc1 Qf7 30. Rxa4 Nxd5 31. exd5) 25. Bxc5 Rxc5?! { (5.89 ? 6.59) Inaccuracy. Best move was Qd7. } (25... Qd7 26. Qc3+) 26. Qxc5 Qxc5+ 27. Rxc5 fxe4 28. d6 Nf5 29. d7 Rd8 30. Rd1 e3 31. Kf1 Ne7?! { (6.49 ? 7.39) Inaccuracy. Best move was Kf8. } (31... Kf8 32. Ke2 Nh6 33. Ra5 Ke7 34. Rxa6 Ng4 35. a4 Nf2 36. Rd4 Ng4 37. h3 Nf6 38. Kxe3) 32. Ke2 Nf5? { (7.22 ? Mate in 10) Checkmate is now unavoidable. Best move was Kf7. } (32... Kf7 33. g4 a5 34. a4 h5 35. gxh5 gxh5 36. Rxa5 Ng6 37. Kxe3 h4 38. Rad5 Ke7 39. a5) 33. Rc8 Rxd7?! { (24.96 ? Mate in 8) Checkmate is now unavoidable. Best move was Kh6. } (33... Kh6) 34. Rxd7+ Kf6 35. Rc6+ Nd6 36. Rcxd6+?! { (Mate in 2 ? Mate in 2) Not the best checkmate sequence. Best move was g4. } (36. g4 a5 37. Rcxd6#) 36... Kf5 37. Kxe3?! { (Mate in 2 ? Mate in 4) Not the best checkmate sequence. Best move was Kf3. } (37. Kf3 g5 38. Rf7#) 37... Kg4 38. Rxh7 g5 39. fxg5?! { (Mate in 3 ? Mate in 4) Not the best checkmate sequence. Best move was Ke4. } (39. Ke4 a5 40. Rg6 a4 41. Rxg5#) 39... Kxg5 40. Rc7 Kf5 41. Rc5+ Kg4 42. Rd4# { White wins by checkmate. } 1-0 *