Thanks to
misterman08 for the following comment/solution:

"i noticed on my game and again is probably different from everyone elses that if i picked before he said 1 he would choose paper if i picked between when he said 1 and 2 it was rock and after he said 2 it was scissors" Posted by misterman08 on 18 Jul 13 01:57:54
So, I just started up the "400 Days" DLC and chose Wyatt's picture (he has glasses, mustache, beard, long hair) from the collage of stories to choose from, and about 8:25 into it they play the game. Then I did what misterman08 described.
