A good strategy is buying GBTC whenever premium is less than 15% and selling whenever it goes over 85% premium. Rinse and repeat.
That sounds wise. Premium ended today at 43%, so we still have some more premium compression to go before I'd consider buying/covering. I do think that the range going forward might be lower than the 15-85% you suggest, because very few U.S. investors had previously known that they could trade the zero-premium European alternatives, and more and more will know over time.
Windows of less than 15% has been very short lived in the past 15 months. You have to be fearless and be committed when it drops. I know that sooner or later the premium will evaporate, probably over night. As a result I am less and less willing to go big on GBTC. If only I could just see the future.