I already mentioned in my Optimize play time article that Jewel Hunt is an excellent reward / time invested activity. You can get a lot of fate stones here, which can give you a decent BR increase. This is one of the few activities in Wartune where you should spend balens - just do it wisely!
First of all, you have to understand how Jewel Hunt work. Of course, you understand the game, but you have to know how the rewards work.
If you complete 3 in a row, you get 10 points and a "common" treasure. it is either a refinement lock, a level 1 gem, or a few soul crystals (amount depends on your Jewel Hunt level). The average value is 1 balen, not the best deal (for complete list of item values,
see this article). If, with one movement, you get two or more triples, you get a common treasure for each.
If you complete 4 in a row, you get 20 points and an "uncommon" treasure. This can be a mount training whip, 2 refinement locks, fate stones and soul scrystals. At level 13, I get 2 fate stones or 6 SC, at lvl 17, 4 fate stones and 7 SC. So the value of this depends heavily on your Jewel Hunt level, can be 6-11 balens or even more if your JH level is 20+.
So please note that getting 20 poins with 4 is not the same as getting 2x10 points with 2x 3 in a row. Same points, but much better treasure.
If you complete 5, you get 50 points and a "rare" treasure: a lvl 2 gem, 2 mount training whip, fate stones (double the uncommon number) and soul crystals (16 at lvl 13, 19 at lvl 17, guess the amount for lower and higher levels). This is also the best treasure you can get. If you complete 6 or more, you just get a combined treasure of the above.
So what's the best strat for maximum gain?
1.) Always check if you can complete 5, there are 3 possibilites (and their rotated versions):
2.) If you can't finish 5, look if you can make one in 2 moves. Doing a move which gets you no point at all then completing a 5 is always better than doing 2 x 3, or even, a 3 and a 4.
3.) Check if there is a 4 you can finish.
4.) Check if there is a movement which finish 2 or more 3's at once.
5.) If you can do nothing just a single 3, look what the table is going to look like after you do it. Try to choose one which gets you into the best situation.
When to use the get help option?
Get help can remove any number of stones from 1 to all. It can get you 20 points or 500, so it's a pretty random thing. When to use it?
1.) Use it when you are stuck (no moves left) or you have a pretty bad table (only one 3 and then you don't se how to go on).
2.) If you used all moves, use get help anyway BEFORE you consider adding more moves for balens.
Chest values
The first chest worth about 70 balens without the Jewel Hunt shards. You can change the shards for a temporal mount (you want to buy it only once, to increase the maximum number of whips you can spend) or a "sylph resource pack" which contains either sepulcrum, mahra, sylph xp scroll or gold. Be warned: this is the usual wartune scam. From 15 packs, I got one sepulcrum, no mahra, the rest is sylph xp scoll and gold, so the shards are nar worthless.
Nonetheless, this chest is free, you will always get it from 20 moves and get help.
The second chest worth almost 200 balens. So even if you need to add attempts once for balens, you should do it. If you follow the above steps and have good practice, you prolly never need to add attempts more than once to reach the second chest.
The third chest is tricky. It worth approx. 300 balens, but you need at least 30-40 extra moves to reach it. At level 17 Jewel Hunt, I earn an average of 5 balens per move. So if I can get to the third chest in 30 moves, it worth it. For 30 moves to be enough, you need at least 950 points. So if you have jewel hunt 15+, at least 950 points after you claimed the 2nd chest, and are willing to spend 450 balens, only then go for the third chest.
Fourth chest. Don't even think about it.