It is unknown...

He has said multiple hundreds of dollars in the past, though. I think he said he spending something like $100 a month (?) on magic cards and now he's using some of that budget on Hearthstone.

However, Hearthstone isn't purely pay-to-win. If you do just the quests and arena then you can build up a sizeable gold stockpile. I only spent $3 on the game (to get the 'free' legendary), and currently have over 2000 gold and 4 legendaries. I've opened a bit more than 100 packages, so my rate is about 1 legendary every $25