So, I'm watching Take Me Out To The Holosuite on the YouTubes.
I won't bother going over it because this being STO I'm pretty confident you're familiar with everything DS9. But the question in the comments was posed, "Where was Garak?" since he had all of the traits required for sports: Cunning, tough, willing to cheat his butt off.
My theory was that Sisko asked him, he suggested poisoning the Vulcans before the game, and Sisko decided to go with Rom after all. You?
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Sisko hired him to plant a bomb on the Vulcan's ship while everyone was at the game and then alter the records to say the Niners won.
It was just done offscreen
The Foundry Roundtable live Wednesdays at 7:30PM EST/4:30PM PST on twitch.tv/thefoundryroundtable "I would rather take a chance on getting a change made to the game through positive engagement than know for sure that I got a change made by complaining" -drogyn1701, May 14, 2014.