For single seasons, From 1901 to 2007, (requiring W=6, L=6, and GS=6), sorted by smallest GS

  Cnt Player            **GS**  W  L Year Age Tm  Lg  G  CG SHO GF  W-L% SV   IP   H   R   ER  BB  SO   ERA  ERA  HR  BF   AB  2B 3B IBB HBP  SH  SF GDP  SB CS Pk BK WP   BA   OBP   SLG   OPS  OPS   Pit  Str
 ----+-----------------+------+--+--+----+---+---+--+---+--+---+--+-----+--+-----+---+---+---+---+---+------+----+--+----+----+--+--+---+---+---+---+---+---+--+--+--+--+-----+-----+-----+-----+----+----+---- 
    1 John Butcher         6    6  6 1983  26 TEX AL  38  1   1 14  .500  5 123   128  50  48  41  58   3.51  114  8  522  474 22  1   4   1   4   2  11   2  3  0  0  4  .270  .328  .371  .699   95           
    2 Rudy May             6    6  6 1982  37 NYY AL  41  0   0 22  .500  3 106   109  43  34  14  85   2.89  137  4  438  409 24  1   5   1   9   5   3   4  2  0  0  2  .267  .289  .359  .648   77           
    3 Doug Bird            6    6  6 1978  28 KCR AL  40  0   0 13  .500  1  98.2 110  63  58  31  48   5.29   73  8  434  387 19  5   5   2   8   6   5   8  2  0  2  9  .284  .336  .421  .757  108           
    4 Dick Hall            6    6  6 1962  31 BAL AL  43  1   0 14  .500  6 118.1 102  31  30  19  71   2.28  162  9  468  443 24  4   2   0   4   2   6   2  5  0  0  0  .230  .261  .363  .624   76           
    5 Steve Swetonic       6    6  6 1930  26 PIT NL  23  3   1 14  .500  5  96.2 107  53  48  27  35   4.47  111  7  420                  0                        0  1                            0           
    6 Vic Aldridge         6    6  6 1917  23 CHC NL  30  1   1 13  .500  2 106.2 100  52  37  37  44   3.12   93  1  445                  2                        0  5                            0           

Seasons/Careers found: 6.

 Photos from the George Grantham Bain Collection at the Library of Congress.