In a minute to win it game cards are placed between cups to stack them. The contestant then pulls the card out and hopes they will end with a set of stacked cups. Why does this work?

There is no friction between the card and the cup

Inertia will keep the top cup from moving very far .gravity will pull one cup on top of the other.

The opening of the cup is so much bigger than the bottom even though the cup moves they will both be stacked together.

Both cups I moved the same amount by the friction between them and the card