As a free-to-play player, there are two main things you can do with your gems to conserve it; make it last longer:
- Speed up chests that are nearly completed, not those that have just started.
Alternatively, don't use them at all. You should be trying to save it for when cards begin to climb in costs (1,000 Gold at Level 8 to 9) and then [see below]:
Or, to get the most out of it:
- Spend your gems only on gold.
Alternatively, wait until you have 500 Gems and buy the 10,000 Gold pack, and don't buy cards from the store. It is a known fact that you get more cards than gold.
- Never spend your gems on purchasing chests from the store. It's not worth it.
That is, unless you're trying to get guaranteed Epics or Legendary cards, which you shouldn't be doing until most of your cards are maxed as the cards and gold values don't add up, even without the gem prices scaling with your Arena number.
One exception to this are the occasional Epic Chest (using gold) and Legendary Chest (500 gems), which are much more profitable than other chests available for gems, or cards for gold.
As you can see here, the gold contens of a chest very much depends on the arena you currently participate in. You say it is Arena 3 (Barbarian Bowl), so that's what I am assuming throughout the reset of the answer. Higher arena means more gold, so faster gold-getting!
A silver chest will give you (averaged) 38 gold, and a gold chest 127 gold. I disregard the giant and magic chest, see that as a bonus if it pops up :). There are 180 silver and 54 gold chests throughout the whole cycle (source), so roughly 3 silver chests per 1 golden chest. If you open them in order (that is, SSSG), you'll be netted (38*3 + 127) = 241 gold in 17 hours (3*3 + 8).
However, there are also free chests and the crown chests, that add to this amount. You'll get roughly 4 free chests in this time period, and 2/3 of a crown chest. I'm not sure how much this is, feel free to comment this if you are on arena 3 and open a free/crown chest, I'll add it in. This depends on your playstyle: if you play only a few games per day, not enough to win the crown chests, it takes longer. If you play just once a day, you can only open 2 free chests, instead of the theoretical maximum of 6.
Furthermore, you can donate cards in your clan and get money (and experience) in return. How much you donate is completely up to you. As told here, it is a maximum of 4200 gold per week. You'll get 5 gold for a common donations and a staggering 50 gold for a rare donation.
In conclusion, it differs quite much per player. If I can get the gold per crown/free chest, I will calculate the approximated time when you play at maximum efficiency.
Best Answer
You can't, because legendary chests are only available in level 10. Besides, the newest update has made it impossible to demote from arenas. For example, when your trophies are 500, and the arena trophy requirements are 500, then when you lose, your won't get any loss on trophies.