The famouse game "Beggar my Neighbour"
For the rules of the game, one can refer to the wikipedia page https://en.wikipedia.org/wiki/Beggar-my-neighbour.
In this version, I'm using the Italian 40 cards deck, and the penalty cards are the aces, the twos and the threes.
The number of cards required to pay the penalty is indeed equals to the value of the penalty card.