Assuming you opened 23 gold chests (which seems high), you calculated 0.25^23 = 1.42*10^-14 however as jaelis pointed out it's .25*(1-0.25)^22 = 0.00044. That's still pretty low but not impossible in a game with half a million players. Still, my gut tells me the 23 chests you opened weren't all gold.
Nope, they were all gold but my math was faulty as jaelis pointed out.
4 chests to win 1st grand prize of the Rock
6 chests to win the 2nd grand prize of the SoK
6 chests to win the 3rd grand prize of the WW
6 chests to win the 4th grand prize of the Pond
1 chest to win the Entrance and be 20 flowers towards the 5th grand prize of the Entrance.
That's 23 total.
If I'd been paying attention, and not continuing out of morbid curiosity to see how long it would take, I wouldn't have opened the 23rd chest since I would have gotten the Entrance eventually anyway. Oh well... Should be able to fill you guys in on what the 6th grand prize is.