Definitely, I will use martingale strategy because I know, in the end I will win!
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
Am glad you asked cuz I also wanted to ask if he would still be gambling for the major purpose of making profit or to have fun alone and enjoy the lucky winning they will get. When someone already have infinite money, the majore aim of gambling is no longer based on winning alone, if initially it was based on the purpose of making profit alone, you will quickly abandon it once you got that infinite money but if it was not, that means you enjoy gambling for fun too and you will always gamble regardless of your wealth.