Target-Hitting Stake Choice 6

You start with wealth 5. In each of at most 3 rounds, you may bet any integer stake between 0 and your current wealth on an even-money coin that wins with probability 3/5. If you win, your wealth increases by the stake; if you lose, it decreases by the stake. What first-round stake maximizes the probability of finishing with wealth at least 9 after 3 rounds, and what is that maximal probability?