This graph shows the answer for house edges 1%, even, -1% (1% player advantage), -2%
For a given number of betting units on the horizontal axis, find the number on the vertical axis for the curve of interest. this number tells the probability that your net gain will be less than the number of betting units you chose.
Interesting to note that for a 2% player advantage (which is high even for the most aggressive card counters), you still have about a 40% chance of going home a loser after 200 hands.
Note: this graph was computed using a unit variance. The variance for blackjack if you bet the same amount on every hand is slightly higher, and if you vary your bets it can be quite a bit higher. For a higher variance, you chances of big wins and big losses increase.