If the casino has an infinite bankroll, it cannot be bankrupted. You need to be very careful when you assume an invalid proposition or introduce infinity. Look at this from the view of a logician and a mathematician:

Logic

The statement: "If you and the casino have an infinite bankroll, then Martingale works," is true -- but meaningless. You could just as well say: "If you and the casino have an infinite bankroll, then the moon is made of green cheese." That statement is also true. More simply, take the propositional formula: "if 3=4 than 2=1." According to Boolean logic, that statement is true. If x then y is always true if x is false. But, that doesn't mean y is true.

Algebra

a = b
a2 = ab
a2 - b2 = ab-b2
(a-b)(a+b) = b(a-b)
a+b = b
b+b = b
2b = b
2 = 1

We have "proved" that 2=1. But, we made the error of dividing by zero. We introduced infinity into the math. When you do this, you can create an invalid proof.