Just providing some probabilities:

The chances that you don't collide Mint and Fool's Gold on turn 3 or 4, assuming you buy nothing turn 3, are

5/7*2/7*2*2/5 which is around 16.3%.

So that'll happen once every 6 or 7 times.

If you factor in the fact that if you get turn 3 FG you can guarantee to buy another FG, you can decrease the chance of a non-collision turn 4 because of the reshuffle, but I was too lazy to factor that in. If I did, it might go down to once every 7 or 8 times, but I don't know.

Also, this is just the chance for T3/T4.