I invest in one tech dice per turn for each of the following: UK (41), Japan (41, 42), USA (41, 42). However once a country has two techs die, I stop buying. I think you have a decent enough chance with two, and investing anymore is a waste (because you lose all tech die when anyone hits a 6).
Then once I get a tech, I begin again, investing in one per turn until I have two.
I really like how techs are treated in AA50. It encourages a slow investment that eventually will generate unpredictable benefits. Just like real research!