While he was in charge of Terok Nor during the war, Dukat never seemed to let go of that ball. Surely he must have had a slip of curiosity to see how that ball connected with the rest of the "baseball" phenomena.
So if this so... Who did Dukat play?
Historical figures or Sisko?
Or did he play along side Sisko as best friends on the same team?
And after the Federation retook the Station, did Dukat leave a holographic team of himself and "friends" to challenge Sisko?