The game goes like this:

* pick a Heads/tails pattern of length 3, e.g. "HTT"

* I also pick a pattern, ..maybe "HHT"

* We start flipping coins and the one who's pattern shows up first wins.

I have a strategy that will give me a higher win probability, and it goes in a circle. If you decide to pick my winning pattern then I switch to a better one next time and still have a higher probability to win, and we can endless keep doing that.

Brainteaser:

* What is the lowest probability of me winning assuming I try to maximize it?

* Can you explain how you computed it using simple math concepts? I'm going to trick my son into trying to solve this by winning and not giving the answer directly, only offering math lessons so that he learns to figure it out himself. Maybe some of you have a very elegant, dead simple solution/insight/approach?