Table stakes is a gambling term that refers to the rule that states a player may not add or remove any chips from play during an active hand.
This means a player cannot reach in his pocket and simply add an additional amount of cash to the table. It also means they cannot decide to remove a portion of their chips for safekeeping unless they decide to leave the game and take all of their chips with them.
The rule is used to limit the amount of money a player can lose, as well as money other players might have to bet during one hand. It is also used to even out the playing field and make sure players with vastly larger bankrolls cannot bully other players and pressure them into playing with stakes they are uncomfortable with.
However, between hands, players are free to add more chips or re-buy, as long as the game’s rules allow it or if the amount doesn’t exceed the maximum buy-in.