So, obviously the filename of the log on goko is something like
log\.[0-9a-z]{24}\.[0-9]*\.txt
The [0-9a-z]{24} is non-unique, I was wondering what it means, and it is probably encodes the username (tested for 2 different numbers on a single day, so what can possibly go wrong?). So if you are looking for your games, you probably only need to find out your hash (or whatever this is) and look for these games.
The [0-9]* is also not unique but doesn't have many dublicates, on 20130320 I have 47817 different numbers on 47859 games.
edit: The number is probably the timestamp, on 20130320 I have two games with 1363763058763 , both dated to 20-Mar-2013 07:04, and 1363763058 is 20-Mar-2013 07:04:18 unixtime (according to wolfram alpha), so that would mean they would finish the same millisecond. Which is not unlikely to have 40times/day with 50k games and birthday paradox.
Edit2: Assuming uniform distribution over the day of finishing of the games you would expect on average ~14 collisions for 50k games. As uniform is clearly not realistic, and every other distribution should give a higher rate of collision, 40 collsions a day sounds fine.