The chance of getting a unique hero in the tavern IS NOT 1 out of 5.
It only appears that way because of the 5 card setup, but the odds are not set up that way.


Each hero has a rarity value associated to it, and each time you shuffle, that is the chance of getting the hero.
For example, Bloodstorm could have a 0.5% chance rarity value.
So if you refresh and see him as one of the choices, clicking on shuffle will give you a 1/200 chance of picking him.