Hearthpwn

Much hangs by the detail of exactly how the Shadow Visions treats duplicates, but let's give some principles.  Perversely, it is often easier to work out the chances of not getting the spell that you want, then your chance of getting the spell that you do want is 100% minus the chance of net getting it.  So if I have 8 spells and want just one of them, the chance of not getting it first draw is 7/8.  Assuming that the 7/8 chance came up, there are now 7 cards left, 6 of which I don't want, so the odds of not getting it with the second draw are 6/7.  If I was 'unlucky' twice, the chances are 5/6.  So my chance of not getting the card I want are (7/8)*(6/7)*(5/6) which comes to 210/336.  So my chance of not getting the card I want is 62.5% , making my chance of getting it 37.5%.  

Curse my typing. Should be (27*26*25)/(30*29*28). My bad. 

Sorry, but your maths proves only that one can be really good at Hearthstone but not understand the math of probability. Your chances of not getting one of three key cards are 27/30, then 26/29 then 25/28. For all three to happen is(27*26*25)/(30*29*2) which is 17550/24630 which is 0.71 or 71%. So our chances of getting at least one of our key 3 is 29%. Of course if we swap those three cards we repeat the trial then our chance of 'failure' is again 71%, and the chance of two successive 71% events happening is (for cash) about 50%. So roughly half of the time we won't have a key card. Our odds are better on coin though.