### What are the odds that two of the exact same arena decks have been made since hearthstone was released?

This question is extremely difficult to answer. Even simplifications of it are quite difficult to make a start on. I'll go for the low hanging fruit and quickly outline a worst case scenario before I stop procrastinating from real work.

I make it to be approximately 84400235855343332521292561592004522314004935 possible legal arena decks for any given class. (284Choose26 Cards for the usual picks multiplied by 129Choose4 cards for the milestone picks).

So if Blizzard decides to tell us when the 84400235855343332521292561592004522314004936th arena run of any particular class has been drafted, it has to be a repeat of one of the previous decks.

If everyone on the planet started playing hearthstone and all played the same class and picked the leftmost card every time and retired to make sure to get in 100 drafts an hour, we can be sure in a little over 1.37 * 1028 years that we've drafted at least one repeat deck. That's approximately a billion billion times the current lifespan of the universe.

Having said that, I suspect the odds are actually much more in our favour than the worst because of the way drafting works. The way people draft in general is very different, but assuming we have a complete accurate tier list like the one Trump did a while back, we can probably simplify this to two approachable questions.

If everyone starts using Trump's list to draft and sticks to it 100% while making their choices, what are the choices of drafting a repeat?

The thing I'd be more interested in seeing if someone's got the knowhow and time to tackle it is :

If you ran a computer simulation of a drafting program which drafts according to a tier list and logs each list, but if it's close to drafting a repeat from it's list of done drafts it deviates and picks possibly the 2nd or 3rd best card from the list. How much quicker would we arrive at a repeat then?

It's very possible that all these numbers are astronomical and we can never hope to draft a repeat even with the cleverest of strategies, just putting out some food for thought while procrastinating.