Tarot game - card draw simulation

I tried to simulate card draw for the specific game of Tarot. I have worked with standard lib random generator in the correct range until now but I realized that the probability of drawing 3 good hands among the 5 hands drawn was incredibly low and lower than I experienced. I think it is due to the fact that card are not properly shuffled between two round but just separated into two packs and the packs inverted. From my point of view, it keeps the cards relatively in the same ordering as when they are played. So I wonder if there was model of random drawing that can include this effect ?

If you have some suggestions or references to share ?

Thanks