Blue plastic capsules used in the December 1, 1969 U.S. military draft lottery remain on display at the Selective Service System National Headquarters. This picture is from the first page of their 2009 annual report. At right is the original grid of draft numbers assigned that night for induction in 1970, also from the SSS site. Roughly 850,000 men were affected that night. (See if you can find the adjacent date pair with the largest difference.)
This 2010 academic paper describes the results of a multi-decade study (through 1997) of men from the high school class of 1965, anchored in interviews done with them prior to the 1969 lottery. This blew my mind when I found it while researching Covered With Snow. In essence, regardless of what an eligible man's political views were before that night, the number he received that night permanently skewed his political views.