> Here's how those two do against each other in a 1,000 game match:
> 
> 	JEGPaperPlayer vs. JEGQueuePlayer
>         JEGPaperPlayer: 334
>         JEGQueuePlayer: 666
>         JEGQueuePlayer Wins

I would suggest that you need at least 55% to win. (45%-55% is draw)
Otherwise, a strategy simply selecting a random choice will always have a
50% chance of winning - The results of a single run will be highly
unpredictable and change from time to time.