I used to think the following draw by repetition looked optimal for complicated reasons (detailed below), but now I doubt it. White may well have a winning strategy, involving putting Black in zugzwang on both sides. See Stephen's answer.

[FEN "8/pppk4/8/8/8/8/4KPPP/8 w - - 0 1 "]
  
1. h4  a5  2. h5 Ke7 3. h6 Kf6 4. g4 a4 5. Kd2 Kg6 6. g5 a3 7. Kc2 b5 8. Kb3 b4 9. Ka2 Kh7 10. Kb3 Kg6 ½-½

Neither player can advance the ♟c/♙f, or will end up in zugzwang.

#If White advances the ♙f, Black wins.

[FEN "8/2p5/6kP/6P1/1p6/pK6/5P2/8 w - - 8 9"]
  
  9. f3 c6 10. f4 c5 (9. f4 c5) 11. f5+ Kh7 12. Ka2 (12. f6 Kg6 -+) c4 13. Ka1 b3 14. Kb1 c3 15. Ka1 c2 (13. Kb1 b3 14. Ka1 c3 15. Kb1 b2 16. Ka2 c2 17. Kxa3 c1=Q -+(16. Kc2 a2 17. Kxc3 a1=Q -+)) 16. g6+ Kxh6 17. g7 c1=Q# (15. Kc1 a2 -+)

#If Black advances the `♟c`, White wins. Notice how it falls back to White playing `♙f4` with reverse colors. [FEN "8/2p5/6kP/6P1/1p6/pK6/5P2/8 w - - 8 9"] 9. Ka2 c6 10. f4! c5 (9... c5 10. f3! c4 11. f4 +- see Wf4) 11. Kb3 c4+ 12. Ka2 +- I wouldn't call that a full analysis, especially as the first moves are played so hastily, but I don't think neither player is in zugzwang *from the start*, as back-and-forth moves on columns seem free. As neither the rush of pawns work, nor helping one's pawns with one's king (which must stay in the opponent's far-pawn's square), I think the position is symetrical enough to be a fair draw.

I used to think the following draw by repetition looked optimal for complicated reasons (detailed below), but now I doubt it. White may well have a winning strategy, involving putting Black in zugzwang on both sides. See Stephen's answer.

[FEN "8/pppk4/8/8/8/8/4KPPP/8 w - - 0 1 "]
  
1. h4  a5  2. h5 Ke7 3. h6 Kf6 4. g4 a4 5. Kd2 Kg6 6. g5 a3 7. Kc2 b5 8. Kb3 b4 9. Ka2 Kh7 10. Kb3 Kg6 ½-½

Neither player can advance the ♟c/♙f, or will end up in zugzwang.

#If White advances the ♙f, Black wins.

[FEN "8/2p5/6kP/6P1/1p6/pK6/5P2/8 w - - 8 9"]
  
  9. f3 c6 10. f4 c5 (9. f4 c5) 11. f5+ Kh7 12. Ka2 (12. f6 Kg6 -+) c4 13. Ka1 b3 14. Kb1 c3 15. Ka1 c2 (13. Kb1 b3 14. Ka1 c3 15. Kb1 b2 16. Ka2 c2 17. Kxa3 c1=Q -+(16. Kc2 a2 17. Kxc3 a1=Q -+)) 16. g6+ Kxh6 17. g7 c1=Q# (15. Kc1 a2 -+)

#If Black advances the `♟c`, White wins. Notice how it falls back to White playing `♙f4` with reverse colors. [FEN "8/2p5/6kP/6P1/1p6/pK6/5P2/8 w - - 8 9"] 9. Ka2 c6 10. f4! c5 (9... c5 10. f3! c4 11. f4 +- see Wf4) 11. Kb3 c4+ 12. Ka2 +- I wouldn't call that a full analysis, especially as the first moves are played so hastily, but I don't think neither player is in zugzwang *from the start*, as back-and-forth moves on columns seem free. As neither the rush of pawns work, nor helping one's pawns with one's king (which must stay in the opponent's far-pawn's square), I think the position is symetrical enough to be a fair draw.

For complicated reasons (detailed below), the following draw by repetition looks optimal.

[FEN "8/pppk4/8/8/8/8/4KPPP/8 w - - 0 1 "]
  
1. h4  a5  2. h5 Ke7 3. h6 Kf6 4. g4 a4 5. Kd2 Kg6 6. g5 a3 7. Kc2 b5 8. Kb3 b4 9. Ka2 Kh7 10. Kb3 Kg6 ½-½

Neither player can advance the ♟c/♙f, or will end up in zugzwang.

#If White advances the ♙f, Black wins.

[FEN "8/2p5/6kP/6P1/1p6/pK6/5P2/8 w - - 8 9"]
  
  9. f3 c6 10. f4 c5 (9. f4 c5) 11. f5+ Kh7 12. Ka2 (12. f6 Kg6 -+) c4 13. Ka1 b3 14. Kb1 c3 15. Ka1 c2 (13. Kb1 b3 14. Ka1 c3 15. Kb1 b2 16. Ka2 c2 17. Kxa3 c1=Q -+(16. Kc2 a2 17. Kxc3 a1=Q -+)) 16. g6+ Kxh6 17. g7 c1=Q# (15. Kc1 a2 -+)

#If Black advances the `♟c`, White wins. Notice how it falls back to White playing `♙f4` with reverse colors. [FEN "8/2p5/6kP/6P1/1p6/pK6/5P2/8 w - - 8 9"] 9. Ka2 c6 10. f4! c5 (9... c5 10. f3! c4 11. f4 +- see Wf4) 11. Kb3 c4+ 12. Ka2 +- I wouldn't call that a full analysis, especially as the first moves are played so hastily, but I don't think neither player is in zugzwang *from the start*, as back-and-forth moves on columns seem free. As neither the rush of pawns work, nor helping one's pawns with one's king (which must stay in the opponent's far-pawn's square), I think the position is symetrical enough to be a fair draw.

I used to think the following draw by repetition looked optimal for complicated reasons (detailed below), but now I doubt it. White may well have a winning strategy, involving putting Black in zugzwang on both sides. See Stephen's answer.

[FEN "8/pppk4/8/8/8/8/4KPPP/8 w - - 0 1 "]
  
1. h4  a5  2. h5 Ke7 3. h6 Kf6 4. g4 a4 5. Kd2 Kg6 6. g5 a3 7. Kc2 b5 8. Kb3 b4 9. Ka2 Kh7 10. Kb3 Kg6 ½-½

Neither player can advance the ♟c/♙f, or will end up in zugzwang.

#If White advances the ♙f, Black wins.

[FEN "8/2p5/6kP/6P1/1p6/pK6/5P2/8 w - - 8 9"]
  
  9. f3 c6 10. f4 c5 (9. f4 c5) 11. f5+ Kh7 12. Ka2 (12. f6 Kg6 -+) c4 13. Ka1 b3 14. Kb1 c3 15. Ka1 c2 (13. Kb1 b3 14. Ka1 c3 15. Kb1 b2 16. Ka2 c2 17. Kxa3 c1=Q -+(16. Kc2 a2 17. Kxc3 a1=Q -+)) 16. g6+ Kxh6 17. g7 c1=Q# (15. Kc1 a2 -+)

#If Black advances the `♟c`, White wins. Notice how it falls back to White playing `♙f4` with reverse colors. [FEN "8/2p5/6kP/6P1/1p6/pK6/5P2/8 w - - 8 9"] 9. Ka2 c6 10. f4! c5 (9... c5 10. f3! c4 11. f4 +- see Wf4) 11. Kb3 c4+ 12. Ka2 +- I wouldn't call that a full analysis, especially as the first moves are played so hastily, but I don't think neither player is in zugzwang *from the start*, as back-and-forth moves on columns seem free. As neither the rush of pawns work, nor helping one's pawns with one's king (which must stay in the opponent's far-pawn's square), I think the position is symetrical enough to be a fair draw.