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You are almost right, but not quite. In my experience the longer you wait the "luckier" the boards become. Eventually if you play starting boosters the game may let you pass. On a legendary level it may only ever let you pass if you play a booster such as a lollipop hammer or UFO. It's about boosters though, these can be boosters you got in game or had left over from before. Spending money does NOT cause your levels to be made easier by itself.