If you are scrappy, $20k can get you extremely far at a cost that is "basically" zero (1.5% stake that only converts upon a liquidity event of $100M+ or IPO).
Remember, PG "...started Viaweb with $10k..."[0] in 1995 and "Julian got 10% of Viaweb" for that investment. Viaweb sold to Yahoo! for $49M[1]. The whole reason why YC exists is because PG got a $10k investment!
Back in 2005, pre YC, PG started the Summer Founders Program and invested $20k in each group. "Another of our hypotheses was that you can start a startup on less money than most people think. Other investors were surprised to hear the most we gave any group was $20,000. But we knew it was possible to start on that little because we started Viaweb on $10,000."[2]
The first version of Viaweb.[3]
I keep finding examples of the seeds of YC and they get me really excited. You can see a photo from 2005 from the SFP and YC's roots here[4]
[0] http://old.ycombinator.com/start.html
[1] https://en.wikipedia.org/wiki/Viaweb
[2] http://paulgraham.com/sfp.html
[3] http://web.archive.org/web/19961120231442/http://www.viaweb....