Taken from
this thread from last year (and updated info for 2013):
2013 (Kickoff Date: 1/5/13) = 1st Game Hint (12/21/12)
2012 (Kickoff Date: 1/7/12) = 1st Game Hint (12/02/11)
2011 (Kickoff Date: 1/8/11) = 1st Game Hint (12/21/10), 2nd Game Hint (1/4/11)
2010 (Kickoff Date: 1/9/10) = 1st Game Hint (12/24/09), 2nd Game Hint (1/6/10)
2009 (Kickoff Date: 1/10/09 ) = 1st Game Hint (12/4/08.), 2nd Game Hint (12/11/08),
2008 (Kickoff Date: 1/12/08) = 1st Game Hint (12/15/07), 2nd Game Hint (12/21/07), 3rd Game Hint (1/02/08)
2007 (Kickoff Date: 1/13/07) = 1st Game Hint (12/21/06)
2006 (Kickoff Date: 1/7/06) = 1st Game Hint (12/23/05)
2005 (Kickoff Date: 1/8/05) = 1st Game Hint (12/30/04)
2004 (Kickoff Date: 1/10/04) = 1st Game Hint (1/6/04)
I actually totally forgot that I even did this research last year...thanks for reminding me!
And I'll add on:
8. The only year that there were 3 game hints was 2008.
9. Out of the past 10 years, there was only more than one game hint for 4 of them (interestingly, these were 4 consecutive years).
My guess for this year's game hint (yes, I think there'll only be one): Friday, December 20th (since December 21st is a Saturday).