We used to play a card game with a mat on the table. We had to put chips in the kitty and also in 8 other piles on the mat.
Whoever won the hand got the kitty.
What's the name of this game?
In a similar vein to Gregor, my best guess would be Rummoli.
Players of Rummoli commonly use a plastic mat (though nicer versions exist) that is separated into 8 sections with a kitty pile in the middle.
Play consists of a hand of cards being dealt to each of the 2-8 players, followed by a poker phase then a Rummoli phase. The First player to play all their cards in the Rummoli phase gets to take the kitty.