I remember the draft lottery vividly.   I was 21 and a senior at UCLA.  I had a history of activism dating to co-founding at least one BSU and starting my writing career at 18, having delivered many culturally-relevant essays and poetry for a variety of publications.  I was a jazz and blues disc jockey, music critic and budding show business event producer. I also performed my poetry in some of those shows.  My peer group was in the vanguard of black cultural nationalism in one of the most relevant scenes in the US.

1969 was a watershed year for the protest movement, a crazy, memorable time to be involved in something really relevant to the future of this country.  General Lewis Hershey and the national war machine symbolized all that we thought was a cancer in the national digestive system.  
The lottery was proposed as a compromise strategy to all of the guys who were getting hosed because they were burning their draft cards and engaging in so many other forms of protest. I was doing a lot of draft counseling in the Los Angeles area and personally knew many of the figures who later became heroic in our era.
That said, I went into the preparation for the lottery with no game plan to speak of.  I was definitely NOT going to jail for anybody.  Canada was out, though I had some partners who flew the coop and did quite well there.  So I went into the lottery dice roll, like so many cats, with mixed emotions.  At 21 in 1969, of course I felt as bullet-proof as the next guy.  
The national lottery telecast was shown at UCLA in one of the dorms adjacent to the main campus.  It was in a large room that seated a whole gang of people.  The anxiety was palpable.  Few people were really comfortable being there.
My birthday is January 7th.  I sat in my seat and did not know what to expect when January 6th was awarded something like 63rd position.  
I have never been lucky—even today—at games of chance.  But when my birth date came up lottery number 306, I knew  that was the best luck of the draw in my entire life.
I went on to graduate from college, and ultimately complete my Ph. D. by the age of 27.  I would never have done that if I had been drafted and forced to serve.