You have the right idea, but Excel can map out all of the bet ranges for you, and you can eliminate all scenarios where you lose, then just look at your survival numbers, then see the pattern.
(hide) Play a game in real time with an online opponent! For this to be possible, you and your opponent have to select the action "Move and stay here" as default and then reload the page with the F5 key! (TeamBundy) (show all tips)