Red-and-Black Bold Play from Three-Quarters

In red-and-black you bet on an even-money outcome that comes up with probability $p=0.4$, scaling all amounts so the goal is $\$1$. You currently hold $\$0.75$ and use bold play: stake $\min(\text{current},\ 1-\text{current})$ each round, trying to reach $\$1$ before reaching $\$0$. What is the probability bold play reaches the goal?