Originally posted on 03/08/2011:

Assuming you play basic strategy with the same doubling/splitting rules as the SBR casino for the same stake each game, the probability of you being ahead is as follows.

After 10 hands - 48.4%
After 100 hands - 42.1%
After 1,000 hands - 36.3%
After 10,000 hands - 15.6%
After 100,000 hands - 0.1%
After 1,000,000 hands - 0.0000001%

This assumes a fair 'RNG', of course.