At the 2009 BAT Dinner, guests received a cool gift - a DVD case featuring 1) Game 2 of the 1995 American League Division Series between the Mariners and Yankees and 2) Game 3 of the 1986 National League Division series between the Astros and Mets.
They really are both outstanding games; I didn't watch the '95 game live because I was pretty much boycotting baseball at the time, post-strike. And only one player participated in both games.
The first person to e-mail me - at firstname.lastname@example.org - with the name of that one player will receive these two DVDs.
UPDATE, 2:51 p.m.: We have a winner! Chris Poulos was the first to properly identify Darryl Strawberry as the one player who participated in both this game and this game. He played a considerably larger role in '86 than he did in '95.
Chris sent a nice e-mail, reading, "I was actually at that Yanks/Mariners game, Donnie Baseball's last home game as a Yankee. After you mail the DVDs, please go watch 'The Godfather.'"