Helmuth - Ferguson Head Up Match Theory Question

[Karmic]

Sorry to reply to my own post but I thought about this a bit more on the drive home. You are right if the problem is meant to be structured in a way that you know your opponent so well and are so evenly matched that you have determined the perfect optimal strategy against him and applying that strategy gives you a 50% chance of winning. In that case the games are independant, except for the dependance of a game existing because you lost the last one, and there is no reason to vary your play because you cannot improve your chances of winning.

Also removing all other factors of it being in your advantage to end non terminal games quickly if you would like to play the first 4 as a one hand coin flip and revert back to strategic thinking on the last game, which incidentally is the same scenario if the question is structured that way.

Is this a poker question or a logic puzzle?