$900/6mo down to $550 (cough Florida). Same coverage.
I called up, asked to cancel, gave the reason of finding a better rate, and the CSR “found new discounts” and dropped my rate significantly (ok, maybe not 50% but 40%). She never asked for the competitor’s rate.
Data point: Insured with GEICO for 3-4 years or so, slight discounts over time but never anything significant.
My advice is if you find even a slightly better rate elsewhere, try for a retention offer; worst case scenario you switch. I also advise not being male, young, single, and/or a renter.