If you are focused on winning with an infinite bankroll then what's the point lol? Remember you have an infinite amount of money, it' means that no matter how much you gamble with it would be inexhaustible, then is there any need in gambling to make profit? At such point you should just gamble for the thrill, you can make use of the martingale strategy a hundred times but this isn't going to affect you in any way
Your question is quite profound and also implies a very serious meaning because, in fact, if someone has so much money that there's no limit, they will never worry about losing through gambling and can take the opportunity to have fun without expecting anything in return. Because most people who have too much hope in gambling are people whose money is still very limited, so they will always worry and always think twice before using it for any kind of gambling.