I'm not working with Python on a daily basis. You can find any reference or tutorial pages that will tell you how to use files.
However, I'll tell you a simple logic (with pseudo-code) of how to handle your problem
function WhenGameBegins
if CanOpen([in] saveFileName, [out] saveFile)
winCount = ReadWinCountFrom(saveFile)
else
winCount = 0
function WhenGameEnds
WriteWinCountInto([in] saveFile, [in] winCount)
So the point is that when the user plays for the very first time, no save file exists, so you know that your winCount is 0. Any other time, you can read it from this save file.
When the game ends, you save the winCount into a save file (even if it is 0, though if it's the only thing you store there, there isn't much difference between saving and not saving -- see why above). The next time the user plays, the value can be accessed from the file.