The house advantage on this game is about 0.255%, according to this edge calculator:
http://wizardofodds.com/blackjack/ho...alculator.html
If you assume that you decrease the next day's quota in case you overshoot on the previous day, then you can view this as a
gambler's ruin problem, where you start with $8k and are trying to win $50k. It's reasonable to use a coinflip model with about the same edge and standard deviation.
You lose 0.255% of $20 per hand, or 5.1 cents. The standard deviation is about $23 per hand, so we'll model this as a coinflip for $23, with a win probability set so that you lose 5.1 cents per hand.
The result I get is a probability of success of 0.0000511153, or the odds against you are 19,563:1. Good luck.
By the way, this assumes you don't tip. Tipping is expected if you play for a while. If you start with $10,000, and bet $20/hand until you go bust or reach $10,200, you play an average of about 4875 hands (and you average $9751 when you finish). Usually, you win in only about a hundred hands, but when you lose, it usually takes tens of thousands of hands.