In games where you receive more than one piece of card per turn, game creators can use minimums to help control how pieces are dished out.
When a game creator sets a minimum on a card, that many pieces of that card will always be issued to players who take a territory each turn.
If the minimum number of pieces is equal to the number of pieces awarded each turn, then the cards received will be fixed and all players will always receive the same cards. Using this, game creators can take all luck out of the card system.
If the minimum number of pieces is less than the number of pieces awarded each turn, players will get the minimum and the remainder will be randomed as normal. Using this, game creators can reduce the amount that luck effects the game but still leave some luck so that players don't know exactly what their opponents hold.
For example, if the game awards 7 pieces each turn, and the spy card minimum is set to 2 and the reinforcement card minimum is set to 2, then 4 pieces will always be the same and the remaining 3 will be randomed as usual per their weights.
Note: If you set the card income (number of pieces-of-cards received per turn) lower than all of the minimums (minimum number of pieces of a card recieved per turn) from each of the card types added together, the game will show an error message saying that such a scenario is not possible and for you to fix it.