If you open all chests, the board reshuffles automatically without the need to use reshuffle for 45 keys.(...) you're guaranteed to get a daily prize every 400 (or 445 if you're forced to reshuffle after opening the 16 things) keys.
I know, because I keep finding what I aim for in one of the last three chests way too often - then I open the last one or two chests instead of hitting reshuffle. Just today: I aimed for the daily prize and for the 2x2 Temple of the Flame. Of course the Temple was the third last chest and Snowman was the second to last.
PS: It’s not meant as a complaint. There was just one day I was reasonably lucky with the daily prices, but it was the right day. 10 Goblin Gift Shops.