This children's game is also commonly known as Steal the Old Man's Bundle, Steal the Old Man's Pack or Steal Pile. A very similar game is played by children in Argentina, where it is known as Casita Robada, and in Italy it is known as Rubamazzo.
Stealing Bundles is a fairly simple fishing game, for 2, 3 or 4 players, normally using a standard 52-card pack. To start the game, everyone draws a card and the player drawing the highest card deals first (in case of a tie the tied players draw again).
The dealer shuffles, and then deals the cards out clockwise one at a time: four cards face down to each player and four face up to the centre of the table. The centre cards are laid out separately so that all are visible. The remainder of the pack is kept face down by the dealer and will be used later. The players then pick up their hands of four cards and look at them (but of course are not allowed to look at other players' cards).
The player to the dealer's left starts, the turn to play passes clockwise around the table. At your turn you must play one card from your hand face up to the table. If the card you play matches the rank of any of the face up centre cards, you must take the card you played and any matched cards and place them in a face up pile in front of you, to start your 'bundle'. (Suits are ignored in this game: a King matches a King, an Eight matches an Eight, and so on.) No matter whether you matched a card or not, it is then the next player's turn to play.
Any matched cards that you acquire during the game are always stacked on top of your bundle, with the card you played on top, so that only this top card is visible.
If you play a card that matches the top card of an opponent's bundle, you steal their whole of their bundle and add it to the top of yours, placing the matching card that you played on top.
After everyone has played their four cards, the same dealer takes the remaining undealt cards and deals another four cards face down to each player, one at a time (but no further cards to the layout). Again the players look at their hands, and play continues as before. After all these cards have been played another four cards each are dealt by the same dealer, and this process of dealing and playing continues until all the cards have been dealt and everyone has played their last four cards. At this point, any cards remaining face up in the centre are added to the bundle of the last player who matched a card.
Now the cards in each are counted and whoever has the largest bundle wins.
If you want to play again, the turn to deal now passes to the left. The new dealer shuffles all the cards and another game is played as described above.
The Argentinean game Casita Robata, which was described to me Eduardo de Tello, is essentially the same. The only differences from Stealing Bundles are:
The Italian game Rubamazzo is the same game played counter-clockwise with an Italian 40-card pack.