If you don't trade, the expected density of your mine will be G/M, which is just the density of gold in the mountain (by volume). You should trade mines whenever Rg/R < G/M, or in other words, whenever the density of the revealed mine is less than that of the entire mountain; in that case, the expected density of the new mine will exceed the (G/M) expected density of the old one by (R/(M-V-R))(G/M - Rg/R).