This afternoon I picked up my New Animal Crossing Happy Home Designer 3DS, five packs of Animal Crossing Amiibo cards, one Happy Home Designer Game *NFC bundle, because I really wanted the box and had a $10 gift card for Target*, Gamestop exclusive Amiibo set R.O.B., Duck Hunt, and Mr. Game & Watch. I was also lucky enough to find one lone Mario Maker cube on a peg at Target!
After purchasing 5 packs of Amiibo cards which total out to 30 cards, I was left with 5 duplicate cards. There are 6 cards to a pack. So you have about a 16% chance of getting a duplicate, according to this rate.
I'm not counting any American/Japanese duplicates as actual duplicates, just ones from the same nationality. Any that are double stacked are duplicated.
While the card packs are a bit larger here, they are also about a dollar more expensive. I guess the packaging is probably the main reason their is a difference in price- the extra cardboard sleeve around the envelope which holds the cards is probably a good way to deter potential theft of these cards. IMO it's kind of cheesy but cute none the less.