First, the term ’pit boss’ is dated. The proper term for a supervisor assigned to several tables is a floorman. The person who oversees an entire pit is a pit manager. The person who oversees all the table games is the shift manager. Nobody in this chain of command may you give money to. The "suits" are supposed to look after the casino’s interests so a cash tip may seem like a bribe. However you may give money to the poker room supervisors. The reason for the poker room exception is the casino does not risk its own money in the poker room, therefore management is indifferent to who wins.