It's easier to understand this concept if you look at fair coin toss simulation. It can look like this:
- is players loses, + is players profit.
Now, I've drawn 2 lines. When players loses are equal to his bankroll the game stops, which is seen here as the red line. The house can also go broke, if players profit is higher than their bankroll (yellow line).
So, the likehood of losing all bankroll is determined by the size of bankroll. If you have 1000 BTC and play in casino with 10 BTC bankroll, you have 99% to "beat casino" and take their 10 BTC.
You can also look at any casino and check their profits, they are always much bigger than house edges, because their bankroll is bigger than sum of players bankroll.