That's the only time it's worth it for third.

1) The third draw is 50 gems, not 10 as stated.
2) It's not a shell game, it's a random chance lottery. There is no "right" card. There's a chance you can get a card or not based on its rarity. Purples much much easier than gold. If you have 2 golds and 3 others and you draw 3 times, you have a 95+% chance of drawing the three other cards.
3) If there are 3 cards you specifically want, you'll draw the least rare as third draw, but may well be worth it.

As it looks like cards are cached in place client-side, they probably dismiss it as a "cheat prevention" means. You'll notice that sometimes it'll reveal cards if you refresh, and sometimes it won't. On gut instinct, I'd say they reveal them if you didn't "actually" guess the card and don't if they had to re-hide it.

It is what it is.