I was very surprised to see that two 400 game matches could have a 6% difference in winrates (the winrates were 33% and 39%, with the same parameters)
To be sure that the results of these two 400 game matches were within reasonable probabilistic limits, I set up a 100000 throws match of "Heads or Tails". The result comes in seconds, so, this "heads or tails" experiment can be run several times.
Bottom line is :
For a 100000 throws game,
After 400 throws the winrate is anywhere between ~44% and ~56%
After 1000 throws the winrate is usually between ~46% ~54%
After 10000 throws, it's within 1-2 % of 50%
and at 100000 throws, it's usually very close to 50%
It's really a surprise to me that 400 games gives so little information !
Below, two graphs, in each , the 4 pictures describe the same game, after 400, 1000, 10000 and 100000 throws
PS. I'm running a third (and last) 400 game match between #196 and 92297ff