I remember several players claiming rare results on this.
However... most of the times seems just a chance question.
If 100 players throw a coin 6 times (i e the option during 6 years on 50/50)
3 of these players get those results (i.e all faces)... As we play a lot of games sure some of us get those results.
If both players do the option during 3 years is the same 3%.
Sure cheating is posible unfortunately

... Unless you run the turn, then it is somewhat hard, (perhaps the Masters of Athena?...if they cared

)