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.
I can bet my d**ck that if one has infinite money, that is money that is ever long and can never be exhausted, such person will completely lost interest in gambling after a short while because even the thrill that comes with gambling will be completely gone.
Part of the fun and thrill that comes with gambling has something to do with the fact that our money is limited and can get exhausted if we do not apply caution to our gambling escapedes, fear and excitement is what translates to thrill, when fear of losing money is gone, you are left with only excitement which can only last but for a while, thrill can not be achieved without both fear and excitement coming together, this is why some one with infinite amount of money can only enjoy gambling but for a while before he or she loses interest completely.