Right you are, I do count the "wins" ^^.

1/e is a nice guess (theorized it myself in some point),
but the number I mentioned is very accurate (just doesn't include many digits so..).
bty, 1/e returns an average of about 1.08 +- 0.0001, while the mentioned number gives an average of about 1 +- 0.0001.

Any idea how to solve this thing ?