Timid Versus Bold to Quadruple

Starting with $\$1$ you want to reach $\$4$ on an even-money game you win with probability $p=0.4$, quitting when you reach $\$4$ or go broke. Compute the probability of reaching $\$4$ under (A) timid play, betting $\$1$ each round, and (B) bold play, staking $\min(\text{current},\ 4-\text{current})$. Which strategy gives the higher chance of reaching the goal?