[JadeNB]

At a quick glance, everyone in this thread seems to be assuming 'random' gives you Coke or Pepsi with equal probability ….

[goodcanadian]

Regardless of the probability distribution of the random button, it does not change the optimal strategy. By pressing the Pepsi button, you are either going to get Coke (you "win") or Pepsi (so you know the button is random and you "win" by pressing random on the next go which you now know is Coke).

[JadeNB]

> Regardless of the probability distribution of the random button, it does not change the optimal strategy.

I agree, and didn't mean to suggest otherwise. I was just referring to the specific probability computations being made.